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
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
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
In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in...In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.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
Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the...Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.展开更多
A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.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
Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this wor...Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.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
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 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
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
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
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
This study introduces a real-time data-driven battery management scheme designed to address uncertainties in load and generation forecasts,which are integral to an optimal energy storage control system.By expanding on...This study introduces a real-time data-driven battery management scheme designed to address uncertainties in load and generation forecasts,which are integral to an optimal energy storage control system.By expanding on an existing algorithm,this study resolves issues discovered during implementation and addresses previously overlooked concerns,resulting in significant enhancements in both performance and reliability.The refined real-time control scheme is integrated with a day-ahead optimization engine and forecast model,which is utilized for illustrative simulations to highlight its potential efficacy on a real site.Furthermore,a comprehensive comparison with the original formulation was conducted to cover all possible scenarios.This analysis validated the operational effectiveness of the scheme and provided a detailed evaluation of the improvements and expected behavior of the control system.Incorrect or improper adjustments to mitigate forecast uncertainties can result in suboptimal energy management,significant financial losses and penalties,and potential contract violations.The revised algorithm optimizes the operation of the battery system in real time and safeguards its state of health by limiting the charging/discharging cycles and enforcing adherence to contractual agreements.These advancements yield a reliable and efficient real-time correction algorithm for optimal site management,designed as an independent white box that can be integrated with any day-ahead optimization control system.展开更多
Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,s...Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,so it can handle optimal control problems effectively.This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno(T-S)fuzzy systems.Based on learner systems,an expert system is constructed,where the learner system only knows the expert system's optimal control policy.To reconstruct the unknown cost function,we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known.The developed model-based learning algorithm is consists of two learning stages:an inner reinforcement learning loop and an outer inverse optimal control loop.The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy.Then,to eliminate the requirement that the system dynamics must be known,a data-driven integral learning algorithm is presented.It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable.Finally,we apply the proposed fuzzy optimal control to the truck-trailer system,and the computer simulation results verify the effectiveness of the presented approach.展开更多
Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This r...Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.展开更多
This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading d...This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.展开更多
To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target...To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.展开更多
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.
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.
基金supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander,Colombia,project 3704.
文摘In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.
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the financial support from the National Natural Science Foundation of China(12171405 and 11661074)the Program for New Century Excellent Talents in Fujian Province University+2 种基金the financial support from the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)Collaborative Innovation Center of Statistical Data Engineering Technology&ApplicationDigital+Discipline Construction Project(SZJ2022B004)。
文摘Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
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supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302100)the National Natural Science Foundation of China(Grant Nos.12361131576,92265205,and 92476205).
文摘Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.
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 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 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 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 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.
基金supported by the Israeli Ministry of Infrastructure,Energy and Water Resources.
文摘This study introduces a real-time data-driven battery management scheme designed to address uncertainties in load and generation forecasts,which are integral to an optimal energy storage control system.By expanding on an existing algorithm,this study resolves issues discovered during implementation and addresses previously overlooked concerns,resulting in significant enhancements in both performance and reliability.The refined real-time control scheme is integrated with a day-ahead optimization engine and forecast model,which is utilized for illustrative simulations to highlight its potential efficacy on a real site.Furthermore,a comprehensive comparison with the original formulation was conducted to cover all possible scenarios.This analysis validated the operational effectiveness of the scheme and provided a detailed evaluation of the improvements and expected behavior of the control system.Incorrect or improper adjustments to mitigate forecast uncertainties can result in suboptimal energy management,significant financial losses and penalties,and potential contract violations.The revised algorithm optimizes the operation of the battery system in real time and safeguards its state of health by limiting the charging/discharging cycles and enforcing adherence to contractual agreements.These advancements yield a reliable and efficient real-time correction algorithm for optimal site management,designed as an independent white box that can be integrated with any day-ahead optimization control system.
基金The National Natural Science Foundation of China(62173172).
文摘Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,so it can handle optimal control problems effectively.This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno(T-S)fuzzy systems.Based on learner systems,an expert system is constructed,where the learner system only knows the expert system's optimal control policy.To reconstruct the unknown cost function,we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known.The developed model-based learning algorithm is consists of two learning stages:an inner reinforcement learning loop and an outer inverse optimal control loop.The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy.Then,to eliminate the requirement that the system dynamics must be known,a data-driven integral learning algorithm is presented.It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable.Finally,we apply the proposed fuzzy optimal control to the truck-trailer system,and the computer simulation results verify the effectiveness of the presented approach.
文摘Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.
基金Project supported the Natural Science Foundation of Zhejiang Province, China (Grant No. LQN25F030011)the Fundamental Research Project of Hangzhou Dianzi University (Grant No. KYS065624391)+1 种基金the National Natural Science Foundation of China (Grant No. 61573148)the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2019A050520001)。
文摘This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.
基金Defense Industrial Technology Development Program (JCKY2020204B016)National Natural Science Foundation of China (92471206)。
文摘To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.
