The integration of renewable energy sources into modern power systems necessitates efficient and robust control strategies to address challenges such as power quality,stability,and dynamic environmental variations.Thi...The integration of renewable energy sources into modern power systems necessitates efficient and robust control strategies to address challenges such as power quality,stability,and dynamic environmental variations.This paper presents a novel sparrow search algorithm(SSA)-tuned proportional-integral(PI)controller for grid-connected photovoltaic(PV)systems,designed to optimize dynamic perfor-mance,energy extraction,and power quality.Key contributions include the development of a systematic SSA-based optimization frame-work for real-time PI parameter tuning,ensuring precise voltage and current regulation,improved maximum power point tracking(MPPT)efficiency,and minimized total harmonic distortion(THD).The proposed approach is evaluated against conventional PSO-based and P&O controllers through comprehensive simulations,demonstrating its superior performance across key metrics:a 39.47%faster response time compared to PSO,a 12.06%increase in peak active power relative to P&O,and a 52.38%reduction in THD,ensuring compliance with IEEE grid standards.Moreover,the SSA-tuned PI controller exhibits enhanced adaptability to dynamic irradiancefluc-tuations,rapid response time,and robust grid integration under varying conditions,making it highly suitable for real-time smart grid applications.This work establishes the SSA-tuned PI controller as a reliable and efficient solution for improving PV system performance in grid-connected scenarios,while also setting the foundation for future research into multi-objective optimization,experimental valida-tion,and hybrid renewable energy systems.展开更多
This paper presents an optimized shared control algorithm for human–AI interaction, implemented through a digital twin framework where the physical system and human operator act as the real agent while an AI-driven d...This paper presents an optimized shared control algorithm for human–AI interaction, implemented through a digital twin framework where the physical system and human operator act as the real agent while an AI-driven digital system functions as the virtual agent. In this digital twin architecture, the real agent acquires an optimal control strategy through observed actions, while the AI virtual agent mirrors the real agent to establish a digital replica system and corresponding control policy. Both the real and virtual optimal controllers are approximated using reinforcement learning(RL) techniques. Specifically, critic neural networks(NNs) are employed to learn the virtual and real optimal value functions, while actor NNs are trained to derive their respective optimal controllers. A novel shared mechanism is introduced to integrate both virtual and real value functions into a unified learning framework, yielding an optimal shared controller. This controller adaptively adjusts the confidence ratio between virtual and real agents, enhancing the system's efficiency and flexibility in handling complex control tasks. The stability of the closed-loop system is rigorously analyzed using the Lyapunov method. The effectiveness of the proposed AI–human interactive system is validated through two numerical examples: a representative nonlinear system and an unmanned aerial vehicle(UAV) control system.展开更多
Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precurs...Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.展开更多
The high proportion of uncertain distributed power sources and the access to large-scale random electric vehicle(EV)charging resources further aggravate the voltage fluctuation of the distribution network,and the exis...The high proportion of uncertain distributed power sources and the access to large-scale random electric vehicle(EV)charging resources further aggravate the voltage fluctuation of the distribution network,and the existing research has not deeply explored the EV active-reactive synergistic regulating characteristics,and failed to realize themulti-timescale synergistic control with other regulatingmeans,For this reason,this paper proposes amultilevel linkage coordinated optimization strategy to reduce the voltage deviation of the distribution network.Firstly,a capacitor bank reactive power compensation voltage control model and a distributed photovoltaic(PV)activereactive power regulationmodel are established.Additionally,an external characteristicmodel of EVactive-reactive power regulation is developed considering the four-quadrant operational characteristics of the EVcharger.Amultiobjective optimization model of the distribution network is then constructed considering the time-series coupling constraints of multiple types of voltage regulators.A multi-timescale control strategy is proposed by considering the impact of voltage regulators on active-reactive EV energy consumption and PV energy consumption.Then,a four-stage voltage control optimization strategy is proposed for various types of voltage regulators with multiple time scales.Themulti-objective optimization is solved with the improvedDrosophila algorithmto realize the power fluctuation control of the distribution network and themulti-stage voltage control optimization.Simulation results validate that the proposed voltage control optimization strategy achieves the coordinated control of decentralized voltage control resources in the distribution network.It effectively reduces the voltage deviation of the distribution network while ensuring the energy demand of EV users and enhancing the stability and economic efficiency of the distribution network.展开更多
Uneven power distribution,transient voltage,and frequency deviations are observed in the photovoltaic storage hybrid inverter during the switching between grid-connected and island modes.In response to these issues,th...Uneven power distribution,transient voltage,and frequency deviations are observed in the photovoltaic storage hybrid inverter during the switching between grid-connected and island modes.In response to these issues,this paper proposes a grid-connected/island switching control strategy for photovoltaic storage hybrid inverters based on the modified chimpanzee optimization algorithm.The proposed strategy incorporates coupling compensation and power differentiation elements based on the traditional droop control.Then,it combines the angular frequency and voltage amplitude adjustments provided by the phase-locked loop-free pre-synchronization control strategy.Precise pre-synchronization is achieved by regulating the virtual current to zero and aligning the photovoltaic storage hybrid inverter with the grid voltage.Additionally,two novel operators,learning and emotional behaviors are introduced to enhance the optimization precision of the chimpanzee algorithm.These operators ensure high-precision and high-reliability optimization of the droop control parameters for photovoltaic storage hybrid inverters.A Simulink model was constructed for simulation analysis,which validated the optimized control strategy’s ability to evenly distribute power under load transients.This strategy effectively mitigated transient voltage and current surges during mode transitions.Consequently,seamless and efficient switching between gridconnected and island modes was achieved for the photovoltaic storage hybrid inverter.The enhanced energy utilization efficiency,in turn,offers robust technical support for grid stability.展开更多
We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of ...We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.展开更多
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty...This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.展开更多
The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the u...The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult.Therefore,it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties.In this framework,the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties.The robust control problem is translated into the optimal control problem,where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function.The optimal control method is used to solve the robust control problem.The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties.The simulation and experimental results demonstrate the performance of the designed control scheme.The performance indices such as integral absolute error(IAE),integral square error(ISE),integral time absolute error(ITAE),and integral time square error(ITSE)are compared for both uncertainties to showcase the robustness of the designed control scheme.展开更多
Modern automated generation control(AGC)is increasingly complex,requiring precise frequency control for stability and operational accuracy.Traditional PID controller optimisation methods often struggle to handle nonli...Modern automated generation control(AGC)is increasingly complex,requiring precise frequency control for stability and operational accuracy.Traditional PID controller optimisation methods often struggle to handle nonlinearities and meet robustness requirements across diverse operational scenarios.This paper introduces an enhanced strategy using a multi-objective optimisation framework and a modified non-dominated sorting genetic algorithm Ⅱ(SNSGA).The proposed model optimises the PID controller by minimising key performance metrics:integration time squared error(ITSE),integration time absolute error(ITAE),and rate of change of deviation(J).This approach balances convergence rate,overshoot,and oscillation dynamics effectively.A fuzzy-based method is employed to select the most suitable solution from the Pareto set.The comparative analysis demonstrates that the SNSGA-based approach offers superior tuning capabilities over traditional NSGA-Ⅱ and other advanced control methods.In a two-area thermal power system without reheat,the SNSGA significantly reduces settling times for frequency deviations:2.94s for Δf_(1) and 4.98s for Δf_(2),marking improvements of 31.6%and 13.4%over NSGA-Ⅱ,respectively.展开更多
This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are de...This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.展开更多
This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-d...This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.展开更多
For optimization algorithms,the most important consideration is their global optimization performance.Our research is conducted with the hope that the algorithm can robustly find the optimal solution to the target pro...For optimization algorithms,the most important consideration is their global optimization performance.Our research is conducted with the hope that the algorithm can robustly find the optimal solution to the target problem at a lower computational cost or faster speed.For stochastic optimization algorithms based on population search methods,the search speed and solution quality are always contradictory.Suppose that the random range of the group search is larger;in that case,the probability of the algorithm converging to the global optimal solution is also greater,but the search speed will inevitably slow.The smaller the random range of the group search is,the faster the search speed will be,but the algorithm will easily fall into local optima.Therefore,our method is intended to utilize heuristic strategies to guide the search direction and extract as much effective information as possible from the search process to guide an optimized search.This method is not only conducive to global search,but also avoids excessive randomness,thereby improving search efficiency.To effectively avoid premature convergence problems,the diversity of the group must be monitored and regulated.In fact,in natural bird flocking systems,the distribution density and diversity of groups are often key factors affecting individual behavior.For example,flying birds can adjust their speed in time to avoid collisions based on the crowding level of the group,while foraging birds will judge the possibility of sharing food based on the density of the group and choose to speed up or escape.The aim of this work was to verify that the proposed optimization method is effective.We compared and analyzed the performances of five algorithms,namely,self-organized particle swarm optimization(PSO)-diversity controlled inertia weight(SOPSO-DCIW),self-organized PSO-diversity controlled acceleration coefficient(SOPSO-DCAC),standard PSO(SPSO),the PSO algorithm with a linear decreasing inertia weight(SPSO-LDIW),and the modified PSO algorithm with a time-varying acceleration constant(MPSO-TVAC).展开更多
This paper highlights the utilization of parallel control and adaptive dynamic programming(ADP) for event-triggered robust parallel optimal consensus control(ETRPOC) of uncertain nonlinear continuous-time multiagent s...This paper highlights the utilization of parallel control and adaptive dynamic programming(ADP) for event-triggered robust parallel optimal consensus control(ETRPOC) of uncertain nonlinear continuous-time multiagent systems(MASs).First, the parallel control system, which consists of a virtual control variable and a specific auxiliary variable obtained from the coupled Hamiltonian, allows general systems to be transformed into affine systems. Of interest is the fact that the parallel control technique's introduction provides an unprecedented perspective on eliminating the negative effects of disturbance. Then, an eventtriggered mechanism is adopted to save communication resources while ensuring the system's stability. The coupled HamiltonJacobi(HJ) equation's solution is approximated using a critic neural network(NN), whose weights are updated in response to events. Furthermore, theoretical analysis reveals that the weight estimation error is uniformly ultimately bounded(UUB). Finally,numerical simulations demonstrate the effectiveness of the developed ETRPOC method.展开更多
This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optim...This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.展开更多
The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel ma...The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization compartments.The population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection cases.The proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible region.Additionally,the model is demonstrated to be well-posed with a unique solution.Equilibrium points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are determined.Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number.Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity.Furthermore,an optimal control problem is defined to minimize disease transmission and to control strategy costs.The purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the controls.The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health.This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.展开更多
Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the l...Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.展开更多
Finding the optimal control is of importance to quantum metrology under a noisy environment.In this paper,we tackle the problem of finding the optimal control to enhance the performance of quantum metrology under an a...Finding the optimal control is of importance to quantum metrology under a noisy environment.In this paper,we tackle the problem of finding the optimal control to enhance the performance of quantum metrology under an arbitrary non-Markovian bosonic environment.By introducing an equivalent pseudomode model,the non-Markovian dynamic evolution is reduced to a Lindblad master equation,which helps us to calculate the gradient of quantum Fisher information and perform the gradient ascent algorithm to find the optimal control.Our approach is accurate and circumvents the need for the Born-Markovian approximation.As an example,we consider the frequency estimation of a spin with pure dephasing under two types of non-Markovian environments.By maximizing the quantum Fisher information at a fixed evolution time,we obtain the optimal multi-axis control,which results in a notable enhancement in quantum metrology.The advantage of our method lies in its applicability to the arbitrary non-Markovian bosonic environment.展开更多
This study proposes a system for biometric access control utilising the improved Cultural Chicken Swarm Optimization(CCSO)technique.This approach mitigates the limitations of conventional Chicken Swarm Optimization(CS...This study proposes a system for biometric access control utilising the improved Cultural Chicken Swarm Optimization(CCSO)technique.This approach mitigates the limitations of conventional Chicken Swarm Optimization(CSO),especially in dealing with larger dimensions due to diversity loss during solution space exploration.Our experimentation involved 600 sample images encompassing facial,iris,and fingerprint data,collected from 200 students at Ladoke Akintola University of Technology(LAUTECH),Ogbomoso.The results demonstrate the remarkable effectiveness of CCSO,yielding accuracy rates of 90.42%,91.67%,and 91.25%within 54.77,27.35,and 113.92 s for facial,fingerprint,and iris biometrics,respectively.These outcomes significantly outperform those achieved by the conventional CSO technique,which produced accuracy rates of 82.92%,86.25%,and 84.58%at 92.57,63.96,and 163.94 s for the same biometric modalities.The study’s findings reveal that CCSO,through its integration of Cultural Algorithm(CA)Operators into CSO,not only enhances algorithm performance,exhibiting computational efficiency and superior accuracy,but also carries broader implications beyond biometric systems.This innovation offers practical benefits in terms of security enhancement,operational efficiency,and adaptability across diverse user populations,shaping more effective and resource-efficient access control systems with real-world applicability.展开更多
The high-speed reentry vehicle operates across a broad range of speeds and spatial domains,where optimal aerodynamic shapes for different speeds are contradictory.This makes it challenging for a single-Mach optimizati...The high-speed reentry vehicle operates across a broad range of speeds and spatial domains,where optimal aerodynamic shapes for different speeds are contradictory.This makes it challenging for a single-Mach optimization design to meet aerodynamic performance requirements throughout the vehicle’s flight envelope.Additionally,the strong coupling between aerodynamics and control adds complexity,as fluctuations in aerodynamic parameters due to speed variations complicate control system design.To address these challenges,this study proposes an aerodynamic/control coupling optimization design approach.This method,based on aerodynamic optimization principles,incorporates active control technology,treating aerodynamic layout and control system design as primary components during the conceptual design phase.By integrating the design and evaluation of aerodynamics and control,the approach aims to reduce design iterations and enhance overall flight performance.The comprehensive design of the rotary reentry vehicle,using this optimization strategy,effectively balances performance at supersonic and hypersonic speeds.The results show that the integrated design model meets aerodynamic and control performance requirements over a broader range of Mach numbers,preventing performance degradation due to deviations from the design Mach number,and providing a practical solution for high-speed reentry vehicle design.展开更多
In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and co...In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.展开更多
文摘The integration of renewable energy sources into modern power systems necessitates efficient and robust control strategies to address challenges such as power quality,stability,and dynamic environmental variations.This paper presents a novel sparrow search algorithm(SSA)-tuned proportional-integral(PI)controller for grid-connected photovoltaic(PV)systems,designed to optimize dynamic perfor-mance,energy extraction,and power quality.Key contributions include the development of a systematic SSA-based optimization frame-work for real-time PI parameter tuning,ensuring precise voltage and current regulation,improved maximum power point tracking(MPPT)efficiency,and minimized total harmonic distortion(THD).The proposed approach is evaluated against conventional PSO-based and P&O controllers through comprehensive simulations,demonstrating its superior performance across key metrics:a 39.47%faster response time compared to PSO,a 12.06%increase in peak active power relative to P&O,and a 52.38%reduction in THD,ensuring compliance with IEEE grid standards.Moreover,the SSA-tuned PI controller exhibits enhanced adaptability to dynamic irradiancefluc-tuations,rapid response time,and robust grid integration under varying conditions,making it highly suitable for real-time smart grid applications.This work establishes the SSA-tuned PI controller as a reliable and efficient solution for improving PV system performance in grid-connected scenarios,while also setting the foundation for future research into multi-objective optimization,experimental valida-tion,and hybrid renewable energy systems.
基金supported by China Postdoctoral Science Foundation(Project ID:2024M762602)the National Natural Science Foundation of China under Grant No.62306232Natural Science Basic Research Program of Shaanxi Province under Grant No.2023-JC-QN-0662.
文摘This paper presents an optimized shared control algorithm for human–AI interaction, implemented through a digital twin framework where the physical system and human operator act as the real agent while an AI-driven digital system functions as the virtual agent. In this digital twin architecture, the real agent acquires an optimal control strategy through observed actions, while the AI virtual agent mirrors the real agent to establish a digital replica system and corresponding control policy. Both the real and virtual optimal controllers are approximated using reinforcement learning(RL) techniques. Specifically, critic neural networks(NNs) are employed to learn the virtual and real optimal value functions, while actor NNs are trained to derive their respective optimal controllers. A novel shared mechanism is introduced to integrate both virtual and real value functions into a unified learning framework, yielding an optimal shared controller. This controller adaptively adjusts the confidence ratio between virtual and real agents, enhancing the system's efficiency and flexibility in handling complex control tasks. The stability of the closed-loop system is rigorously analyzed using the Lyapunov method. The effectiveness of the proposed AI–human interactive system is validated through two numerical examples: a representative nonlinear system and an unmanned aerial vehicle(UAV) control system.
基金supported by the National Natural Science Foundation of China(Nos.42005086,91844301,and 41805100)the National Key Research and Development Programof China(No.2022YFC3703500)+2 种基金China Postdoctoral Science Foundation(No.2023M733028)the Key Research and Development Program of Zhejiang Province(Nos.2021C03165 and 2022C03084)the Ecological and Environmental Scientific Research and Achievement Promotion Project of Zhejiang Province(No.2020HT0048).
文摘Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.
基金funded by the State Grid Corporation Science and Technology Project(5108-202218280A-2-391-XG).
文摘The high proportion of uncertain distributed power sources and the access to large-scale random electric vehicle(EV)charging resources further aggravate the voltage fluctuation of the distribution network,and the existing research has not deeply explored the EV active-reactive synergistic regulating characteristics,and failed to realize themulti-timescale synergistic control with other regulatingmeans,For this reason,this paper proposes amultilevel linkage coordinated optimization strategy to reduce the voltage deviation of the distribution network.Firstly,a capacitor bank reactive power compensation voltage control model and a distributed photovoltaic(PV)activereactive power regulationmodel are established.Additionally,an external characteristicmodel of EVactive-reactive power regulation is developed considering the four-quadrant operational characteristics of the EVcharger.Amultiobjective optimization model of the distribution network is then constructed considering the time-series coupling constraints of multiple types of voltage regulators.A multi-timescale control strategy is proposed by considering the impact of voltage regulators on active-reactive EV energy consumption and PV energy consumption.Then,a four-stage voltage control optimization strategy is proposed for various types of voltage regulators with multiple time scales.Themulti-objective optimization is solved with the improvedDrosophila algorithmto realize the power fluctuation control of the distribution network and themulti-stage voltage control optimization.Simulation results validate that the proposed voltage control optimization strategy achieves the coordinated control of decentralized voltage control resources in the distribution network.It effectively reduces the voltage deviation of the distribution network while ensuring the energy demand of EV users and enhancing the stability and economic efficiency of the distribution network.
基金received funding from the Postgraduate Research&Practice Innovation Program of Jiangsu Province(SJCX23_1633)2023 University Student Innovation and Entrepreneurship Training Program(202311463009Z)+1 种基金Changzhou Science and Technology Support Project(CE20235045)Open Project of Jiangsu Key Laboratory of Power Transmission&Distribution Equipment Technology(2021JSSPD12).
文摘Uneven power distribution,transient voltage,and frequency deviations are observed in the photovoltaic storage hybrid inverter during the switching between grid-connected and island modes.In response to these issues,this paper proposes a grid-connected/island switching control strategy for photovoltaic storage hybrid inverters based on the modified chimpanzee optimization algorithm.The proposed strategy incorporates coupling compensation and power differentiation elements based on the traditional droop control.Then,it combines the angular frequency and voltage amplitude adjustments provided by the phase-locked loop-free pre-synchronization control strategy.Precise pre-synchronization is achieved by regulating the virtual current to zero and aligning the photovoltaic storage hybrid inverter with the grid voltage.Additionally,two novel operators,learning and emotional behaviors are introduced to enhance the optimization precision of the chimpanzee algorithm.These operators ensure high-precision and high-reliability optimization of the droop control parameters for photovoltaic storage hybrid inverters.A Simulink model was constructed for simulation analysis,which validated the optimized control strategy’s ability to evenly distribute power under load transients.This strategy effectively mitigated transient voltage and current surges during mode transitions.Consequently,seamless and efficient switching between gridconnected and island modes was achieved for the photovoltaic storage hybrid inverter.The enhanced energy utilization efficiency,in turn,offers robust technical support for grid stability.
基金supported by the National Natural Science Foundation of China(Grant Nos.12441502,12122506,12204230,and 12404554)the National Science and Technology Major Project of the Ministry of Science and Technology of China(2024ZD0300404)+6 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2021B1515020070)Shenzhen Science and Technology Program(Grant No.RCYX20200714114522109)China Postdoctoral Science Foundation(CPSF)(2024M762114)Postdoctoral Fellowship Program of CPSF(GZC20231727)supported by the National Natural Science Foundation of China(Grant Nos.92165206 and 11974330)Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301603)the Fundamental Research Funds for the Central Universities。
文摘We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.
基金co-supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF21-BJ-J-1180)。
文摘This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.
文摘The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult.Therefore,it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties.In this framework,the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties.The robust control problem is translated into the optimal control problem,where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function.The optimal control method is used to solve the robust control problem.The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties.The simulation and experimental results demonstrate the performance of the designed control scheme.The performance indices such as integral absolute error(IAE),integral square error(ISE),integral time absolute error(ITAE),and integral time square error(ITSE)are compared for both uncertainties to showcase the robustness of the designed control scheme.
基金supported in part by the Science and Technology Innovation Program of Hunan Province under Grant 2022RC4028in part by the National Natural Science Foundation of China under Grant 62473204+3 种基金in part by the Chunhui Program Collaborative Scientific Research Project under Grant 202202004in part by the Natural Science Foundation of Nanjing University of Posts and Telecommunications under Grants NY221082,NY222144,and NY223075in part by the Huali Program for Excellent Talents in Nanjing University of Posts and Telecommunicationsin part by the Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant KYCX24_1215.
文摘Modern automated generation control(AGC)is increasingly complex,requiring precise frequency control for stability and operational accuracy.Traditional PID controller optimisation methods often struggle to handle nonlinearities and meet robustness requirements across diverse operational scenarios.This paper introduces an enhanced strategy using a multi-objective optimisation framework and a modified non-dominated sorting genetic algorithm Ⅱ(SNSGA).The proposed model optimises the PID controller by minimising key performance metrics:integration time squared error(ITSE),integration time absolute error(ITAE),and rate of change of deviation(J).This approach balances convergence rate,overshoot,and oscillation dynamics effectively.A fuzzy-based method is employed to select the most suitable solution from the Pareto set.The comparative analysis demonstrates that the SNSGA-based approach offers superior tuning capabilities over traditional NSGA-Ⅱ and other advanced control methods.In a two-area thermal power system without reheat,the SNSGA significantly reduces settling times for frequency deviations:2.94s for Δf_(1) and 4.98s for Δf_(2),marking improvements of 31.6%and 13.4%over NSGA-Ⅱ,respectively.
基金supported in part by the Thai Nguyen University of Technology,Vietnam.
文摘This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.
基金Supported by the National Natural Science Foundation of China(Grant Nos.125610811246108612271147)。
文摘This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.
文摘For optimization algorithms,the most important consideration is their global optimization performance.Our research is conducted with the hope that the algorithm can robustly find the optimal solution to the target problem at a lower computational cost or faster speed.For stochastic optimization algorithms based on population search methods,the search speed and solution quality are always contradictory.Suppose that the random range of the group search is larger;in that case,the probability of the algorithm converging to the global optimal solution is also greater,but the search speed will inevitably slow.The smaller the random range of the group search is,the faster the search speed will be,but the algorithm will easily fall into local optima.Therefore,our method is intended to utilize heuristic strategies to guide the search direction and extract as much effective information as possible from the search process to guide an optimized search.This method is not only conducive to global search,but also avoids excessive randomness,thereby improving search efficiency.To effectively avoid premature convergence problems,the diversity of the group must be monitored and regulated.In fact,in natural bird flocking systems,the distribution density and diversity of groups are often key factors affecting individual behavior.For example,flying birds can adjust their speed in time to avoid collisions based on the crowding level of the group,while foraging birds will judge the possibility of sharing food based on the density of the group and choose to speed up or escape.The aim of this work was to verify that the proposed optimization method is effective.We compared and analyzed the performances of five algorithms,namely,self-organized particle swarm optimization(PSO)-diversity controlled inertia weight(SOPSO-DCIW),self-organized PSO-diversity controlled acceleration coefficient(SOPSO-DCAC),standard PSO(SPSO),the PSO algorithm with a linear decreasing inertia weight(SPSO-LDIW),and the modified PSO algorithm with a time-varying acceleration constant(MPSO-TVAC).
基金supported in part by the National Key Research and Development Program of China(2021YFE0206100)the National Natural Science Foundation of China(62425310,62073321)+2 种基金the National Defense Basic Scientific Research Program(JCKY2019203C029,JCKY2020130C025)the Science and Technology Development FundMacao SAR(FDCT-22-009-MISE,0060/2021/A2,0015/2020/AMJ)
文摘This paper highlights the utilization of parallel control and adaptive dynamic programming(ADP) for event-triggered robust parallel optimal consensus control(ETRPOC) of uncertain nonlinear continuous-time multiagent systems(MASs).First, the parallel control system, which consists of a virtual control variable and a specific auxiliary variable obtained from the coupled Hamiltonian, allows general systems to be transformed into affine systems. Of interest is the fact that the parallel control technique's introduction provides an unprecedented perspective on eliminating the negative effects of disturbance. Then, an eventtriggered mechanism is adopted to save communication resources while ensuring the system's stability. The coupled HamiltonJacobi(HJ) equation's solution is approximated using a critic neural network(NN), whose weights are updated in response to events. Furthermore, theoretical analysis reveals that the weight estimation error is uniformly ultimately bounded(UUB). Finally,numerical simulations demonstrate the effectiveness of the developed ETRPOC method.
基金supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF-21-BJ-J-1180).
文摘This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.
基金supported by NASA Oklahoma Established Program to Stimulate Competitive Research(EPSCoR)Infrastructure Development,“Machine Learning Ocean World Biosignature Detection from Mass Spec”(PI:BrettMcKinney),Grant No.80NSSC24M0109Tandy School of Computer Science,University of Tulsa.
文摘The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization compartments.The population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection cases.The proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible region.Additionally,the model is demonstrated to be well-posed with a unique solution.Equilibrium points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are determined.Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number.Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity.Furthermore,an optimal control problem is defined to minimize disease transmission and to control strategy costs.The purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the controls.The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health.This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.
基金funded by Taif University,Saudi Arabia,Project No.(TU-DSPP-2024-52).
文摘Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.
基金supported by the National Natural Science Foundation of China(Grant No.12274019)the NSAF Joint Fund(Grant No.U2230402)。
文摘Finding the optimal control is of importance to quantum metrology under a noisy environment.In this paper,we tackle the problem of finding the optimal control to enhance the performance of quantum metrology under an arbitrary non-Markovian bosonic environment.By introducing an equivalent pseudomode model,the non-Markovian dynamic evolution is reduced to a Lindblad master equation,which helps us to calculate the gradient of quantum Fisher information and perform the gradient ascent algorithm to find the optimal control.Our approach is accurate and circumvents the need for the Born-Markovian approximation.As an example,we consider the frequency estimation of a spin with pure dephasing under two types of non-Markovian environments.By maximizing the quantum Fisher information at a fixed evolution time,we obtain the optimal multi-axis control,which results in a notable enhancement in quantum metrology.The advantage of our method lies in its applicability to the arbitrary non-Markovian bosonic environment.
基金supported by Ladoke Akintola University of Technology,Ogbomoso,Nigeria and the University of Zululand,South Africa.
文摘This study proposes a system for biometric access control utilising the improved Cultural Chicken Swarm Optimization(CCSO)technique.This approach mitigates the limitations of conventional Chicken Swarm Optimization(CSO),especially in dealing with larger dimensions due to diversity loss during solution space exploration.Our experimentation involved 600 sample images encompassing facial,iris,and fingerprint data,collected from 200 students at Ladoke Akintola University of Technology(LAUTECH),Ogbomoso.The results demonstrate the remarkable effectiveness of CCSO,yielding accuracy rates of 90.42%,91.67%,and 91.25%within 54.77,27.35,and 113.92 s for facial,fingerprint,and iris biometrics,respectively.These outcomes significantly outperform those achieved by the conventional CSO technique,which produced accuracy rates of 82.92%,86.25%,and 84.58%at 92.57,63.96,and 163.94 s for the same biometric modalities.The study’s findings reveal that CCSO,through its integration of Cultural Algorithm(CA)Operators into CSO,not only enhances algorithm performance,exhibiting computational efficiency and superior accuracy,but also carries broader implications beyond biometric systems.This innovation offers practical benefits in terms of security enhancement,operational efficiency,and adaptability across diverse user populations,shaping more effective and resource-efficient access control systems with real-world applicability.
基金supported by the National Natural Science Foundation of China(Grant Nos.52192633,92371201,11872293,and 92152301)the Natural Science Foundation of Shaanxi Province(Grant No.2022JC-03).
文摘The high-speed reentry vehicle operates across a broad range of speeds and spatial domains,where optimal aerodynamic shapes for different speeds are contradictory.This makes it challenging for a single-Mach optimization design to meet aerodynamic performance requirements throughout the vehicle’s flight envelope.Additionally,the strong coupling between aerodynamics and control adds complexity,as fluctuations in aerodynamic parameters due to speed variations complicate control system design.To address these challenges,this study proposes an aerodynamic/control coupling optimization design approach.This method,based on aerodynamic optimization principles,incorporates active control technology,treating aerodynamic layout and control system design as primary components during the conceptual design phase.By integrating the design and evaluation of aerodynamics and control,the approach aims to reduce design iterations and enhance overall flight performance.The comprehensive design of the rotary reentry vehicle,using this optimization strategy,effectively balances performance at supersonic and hypersonic speeds.The results show that the integrated design model meets aerodynamic and control performance requirements over a broader range of Mach numbers,preventing performance degradation due to deviations from the design Mach number,and providing a practical solution for high-speed reentry vehicle design.
基金supported by the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation.
