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
This paper introduces an optimized backstepping control method for Flexible Airbreathing Hypersonic Vehicles(FAHVs).The approach incorporates nonlinear disturbance observation and reinforcement learning to address com...This paper introduces an optimized backstepping control method for Flexible Airbreathing Hypersonic Vehicles(FAHVs).The approach incorporates nonlinear disturbance observation and reinforcement learning to address complex control challenges.The Minimal Learning Parameter(MLP)technique is applied to manage unknown nonlinear dynamics,significantly reducing the computational load usually associated with Neural Network(NN)weight updates.To improve the control system robustness,an MLP-based nonlinear disturbance observer is designed,which estimates lumped disturbances,including flexibility effects,model uncertainties,and external disruptions within the FAHVs.In parallel,the control strategy integrates reinforcement learning using an MLP-based actor-critic framework within the backstepping design to achieve both optimality and robustness.The actor performs control actions,while the critic assesses the optimal performance index function.To minimize this index function,an adaptive gradient descent method constructs both the actor and critic.Lyapunov analysis is employed to demonstrate that all signals in the closed-loop system are semiglobally uniformly ultimately bounded.Simulation results confirm that the proposed control strategy delivers high control performance,marked by improved accuracy and reduced energy consumption.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are o...Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.展开更多
Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in a...Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in an algebra,then the solution(and also the control gain in many cases)is also in the same algebra.The main result is verified by a numerical simulation.展开更多
The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical pe...The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.展开更多
The dense integration of residential distributed photovoltaic(PV)systems into three-phase,four-wire low-voltage(LV)distribution networks results in reverse power flow and three-phase imbalance,leading to voltage viola...The dense integration of residential distributed photovoltaic(PV)systems into three-phase,four-wire low-voltage(LV)distribution networks results in reverse power flow and three-phase imbalance,leading to voltage violations that hinder the growth of rural distributed PV systems.Traditional voltage droop-based control methods regulate PV power output solely based on local voltage measurements at the point of PV connection.Due to a lack of global coordination and optimization,their efficiency is often subpar.This paper presents a centralized coordinated active/reactive power control strategy for PV inverters in rural LV distribution feeders with high PV penetration.The strategy optimizes residential PV inverter reactive and active power control to enhance voltage quality.It uses sensitivity coefficients derived from the inverse Jacobian matrix to assign adjustment weights to individual PV units and iteratively optimize their power outputs.The control sequence prioritizes reactive power increases;if the coefficients are below average or the inverters reach capacity,active power is curtailed until voltage issues are resolved.A simulation based on a real 37-node rural distribution network shows that the proposed method significantly reduces PV curtailment.Typical daily results indicate a curtailment rate of 1.47%,which is significantly lower than the 15.4%observed with the voltage droop-based control method.The total daily PV power output(measured every 15 min)increases from 5.55 to 6.41 MW,improving PV hosting capacity.展开更多
Realizing optimal control performance for continuum robots(CRs) poses huge challenges on traditional modelbased optimal control approaches due to their high degrees of freedom,complex nonlinear dynamics and soft conti...Realizing optimal control performance for continuum robots(CRs) poses huge challenges on traditional modelbased optimal control approaches due to their high degrees of freedom,complex nonlinear dynamics and soft continuum morphologies which are difficult to explicitly model.This paper proposes a model-free adaptive optimal control algorithm(ADAPT)for CRs.In our strategy,we consider CRs as a class of nonlinear continuous-time dynamical systems in the state space,wherein the position of the end-effector is considered as the state and the input torque is mapped as the control input.Then,the optimized Hamilton-Jacobi-Bellman(HJB) equation is derived by optimal control principles,and subsequently solved by the proposed ADAPT algorithm without requiring knowledge of the original system dynamics.Under some mild assumptions,the global stability and convergence of the closed-loop control approach are guaranteed.Several simulation experiments are conducted on a magnetic CR(MCR) to demonstrate the practicality and effectiveness of the ADAPT algorithm.展开更多
Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over p...Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over predictive control input sequences,deriving multiple optimal predictive control input sequences from its solution.展开更多
In this paper,an adaptive neural-network(NN)output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics,input saturation and state constraints.Neu...In this paper,an adaptive neural-network(NN)output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics,input saturation and state constraints.Neural networks are used to approximate unknown internal dynamics and an adaptive NN state observer is developed to estimate immeasurable states.Under the framework of the backstepping design,by employing the actor-critic architecture and constructing the tan-type Barrier Lyapunov function(BLF),the virtual and actual optimal controllers are developed.In order to accomplish optimal control effectively,a simplified reinforcement learning(RL)algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function,instead of employing existing optimal control methods.In addition,to ensure that all the signals in the closed-loop system are bounded and the output can follow the reference signal within a bounded error,all state variables are confined within their compact sets all times.Finally,a simulation example is given to illustrate the effectiveness of the proposed control strategy.展开更多
In early 2018,the Boliden Garpenberg operation implemented an optimized control strategy as an addition to the existing ventilation on demand system.The purpose of the strategy is to further minimize energy use for ma...In early 2018,the Boliden Garpenberg operation implemented an optimized control strategy as an addition to the existing ventilation on demand system.The purpose of the strategy is to further minimize energy use for main and booster fans,whilst also fulfilling airflow setpoints without violating constraints such as min/max differential pressure over fans and interaction of air between areas in mines.Using air flow measurements and a dynamical model of the ventilation system,a mine-wide coordination control of fans can be carried out.The numerical model is data driven and derived from historical operational data or step changes experiments.This makes both initial deployment and lifetime model maintenance,as the mine evolves,a comparably easy operation.The control has been proven to operate in a stable manner over long periods without having to re-calibrate the model.Results prove a 40%decrease in energy use for the fans involved and a greater controllability of air flow.Moreover,a 15%decrease of the total air flow into the mine will give additional proportional heating savings during winter periods.All in all,the multivariable controller shows a correlation between production in the mine and the ventilation system performance superior to all of its predecessors.展开更多
Continued increases in the emission of greenhouse gases by passenger ve<span style="font-family:Verdana;">hicles ha</span><span style="font-family:Verdana;">ve</span><spa...Continued increases in the emission of greenhouse gases by passenger ve<span style="font-family:Verdana;">hicles ha</span><span style="font-family:Verdana;">ve</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> accelerated the production of hybrid electric vehicles. With this increase in production, there has been a parallel demand for continuously improving strategies of hybrid electric vehicle control. The goal of an ideal control strategy is to maximize fuel economy while minimizing emissions. Methods exist by which the globally optimal control strategy may be found. However, these methods are not applicable in real-world driving applications since these methods require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the upcoming drive cycle. Real-time control strategies use the global optimal as a benchmark against which performance can be evaluated. The goal of this work is to use a previously defined strategy that has been shown to closely approximate the global optimal and implement a radial basis function (RBF) artificial neural network (ANN) that dynamically adapts the strategy based on past driving conditions. The strate</span><span style="font-family:Verdana;">gy used is the Equivalent Consumption Minimization Strategy (ECMS),</span><span style="font-family:Verdana;"> which uses an equivalence factor to define the control strategy and the power train </span><span style="font-family:Verdana;">component torque split. An equivalence factor that is optimal for a single</span><span style="font-family:Verdana;"> drive cycle can be found offline</span></span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">with </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the drive cycle. The RBF-ANN is used to dynamically update the equivalence factor by examining a past time window of driving characteristics. A total of 30 sets of training data (drive cycles) are used to train the RBF-ANN. For the majority of drive cycles examined, the RBF-ANN implementation is shown to produce fuel economy values that are within ±2.5% of the fuel economy obtained with the optimal equivalence factor. The advantage of the RBF-ANN is that it does not require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> drive cycle knowledge and is able to be implemented in real-time while meeting or exceeding the performance of the optimal ECMS. Recommendations are made on how the RBF-ANN could be improved to produce better results across a greater array of driving conditions.</span></span>展开更多
Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical mode...Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical model for heat transferring process in the CDQ unit, a mathematical model for heat transferring process in the boiler and a combustion model for circulating gas in the CDQ-Boiler system. The model was verified by field data, then a series of simulations under several typical operating conditions of CDQ-Boiler were carried on, and in turn, the online relation formulas between the productivity and the optimal circulating gas, and the one between the productivity and the optimal second air, were achieved respectively. These relation equations have been success- fully used in a CDQ-Boiler computer control system in the Baosteel, to realize online optimized guide and control, and meanwhile high efficiency in the CDQ-Boiler system has been achieved.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
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv...Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the 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
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
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 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
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
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co-supported by the National Natural Science Foundation of China(Nos.62303380,62176214,62101590,62003268)。
文摘This paper introduces an optimized backstepping control method for Flexible Airbreathing Hypersonic Vehicles(FAHVs).The approach incorporates nonlinear disturbance observation and reinforcement learning to address complex control challenges.The Minimal Learning Parameter(MLP)technique is applied to manage unknown nonlinear dynamics,significantly reducing the computational load usually associated with Neural Network(NN)weight updates.To improve the control system robustness,an MLP-based nonlinear disturbance observer is designed,which estimates lumped disturbances,including flexibility effects,model uncertainties,and external disruptions within the FAHVs.In parallel,the control strategy integrates reinforcement learning using an MLP-based actor-critic framework within the backstepping design to achieve both optimality and robustness.The actor performs control actions,while the critic assesses the optimal performance index function.To minimize this index function,an adaptive gradient descent method constructs both the actor and critic.Lyapunov analysis is employed to demonstrate that all signals in the closed-loop system are semiglobally uniformly ultimately bounded.Simulation results confirm that the proposed control strategy delivers high control performance,marked by improved accuracy and reduced energy consumption.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金supported in part by the National Science and Technology Council under Grant NSTC 114-2221-E-027-104.
文摘Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.
文摘Dear Editor,In this letter,we focus on the algebraic relationship between the coefficient matrices and the solution of the stochastic algebraic Riccati equation.It is revealed that,if the coefficient matrices are in an algebra,then the solution(and also the control gain in many cases)is also in the same algebra.The main result is verified by a numerical simulation.
基金supported by the National Nature Science Foundation of China under Grant No.11902332。
文摘The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.
基金supported by the Provincial Industrial Science and Technology Project of State Grid Jiangsu Electric Power Co.,Ltd.of China,grant number JC2024118.
文摘The dense integration of residential distributed photovoltaic(PV)systems into three-phase,four-wire low-voltage(LV)distribution networks results in reverse power flow and three-phase imbalance,leading to voltage violations that hinder the growth of rural distributed PV systems.Traditional voltage droop-based control methods regulate PV power output solely based on local voltage measurements at the point of PV connection.Due to a lack of global coordination and optimization,their efficiency is often subpar.This paper presents a centralized coordinated active/reactive power control strategy for PV inverters in rural LV distribution feeders with high PV penetration.The strategy optimizes residential PV inverter reactive and active power control to enhance voltage quality.It uses sensitivity coefficients derived from the inverse Jacobian matrix to assign adjustment weights to individual PV units and iteratively optimize their power outputs.The control sequence prioritizes reactive power increases;if the coefficients are below average or the inverters reach capacity,active power is curtailed until voltage issues are resolved.A simulation based on a real 37-node rural distribution network shows that the proposed method significantly reduces PV curtailment.Typical daily results indicate a curtailment rate of 1.47%,which is significantly lower than the 15.4%observed with the voltage droop-based control method.The total daily PV power output(measured every 15 min)increases from 5.55 to 6.41 MW,improving PV hosting capacity.
基金supported in part by the Innovation and Technology Commission of Hong Kong,China(ITS/136/20,ITS/234/21,MHP/096/22,ITS/235/22)Multi-Scale Medical Robotics Center,InnoHK,China(8312051)+1 种基金Research Grants Council(RGC) of Hong Kong,China(CUHK 14217822,CUHK14207823,AoE/E-407/24-N)The Chinese University of Hong Kong(CUHK) Direct Grant。
文摘Realizing optimal control performance for continuum robots(CRs) poses huge challenges on traditional modelbased optimal control approaches due to their high degrees of freedom,complex nonlinear dynamics and soft continuum morphologies which are difficult to explicitly model.This paper proposes a model-free adaptive optimal control algorithm(ADAPT)for CRs.In our strategy,we consider CRs as a class of nonlinear continuous-time dynamical systems in the state space,wherein the position of the end-effector is considered as the state and the input torque is mapped as the control input.Then,the optimized Hamilton-Jacobi-Bellman(HJB) equation is derived by optimal control principles,and subsequently solved by the proposed ADAPT algorithm without requiring knowledge of the original system dynamics.Under some mild assumptions,the global stability and convergence of the closed-loop control approach are guaranteed.Several simulation experiments are conducted on a magnetic CR(MCR) to demonstrate the practicality and effectiveness of the ADAPT algorithm.
基金supported by the National Natural Science Foundation of China(62433014,62373287,62573324,62333005,62273255)in part by the International Exchange Program for Graduate Students of Tongji University(4360143306)+3 种基金in part by the Fundamental Research Funds for Central Universities(22120230311)supported by DeutscheForschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy(EXC 2075390740016,468094890)support by the Stuttgart Center for Simulation Science(SimTech)the International Max Planck Research School for Intelligent Systems(IMPRS-IS)for supporting Y.Xie。
文摘Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over predictive control input sequences,deriving multiple optimal predictive control input sequences from its solution.
基金This work was supported by National Natural Science Foundation of China(61822307,61773188).
文摘In this paper,an adaptive neural-network(NN)output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics,input saturation and state constraints.Neural networks are used to approximate unknown internal dynamics and an adaptive NN state observer is developed to estimate immeasurable states.Under the framework of the backstepping design,by employing the actor-critic architecture and constructing the tan-type Barrier Lyapunov function(BLF),the virtual and actual optimal controllers are developed.In order to accomplish optimal control effectively,a simplified reinforcement learning(RL)algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function,instead of employing existing optimal control methods.In addition,to ensure that all the signals in the closed-loop system are bounded and the output can follow the reference signal within a bounded error,all state variables are confined within their compact sets all times.Finally,a simulation example is given to illustrate the effectiveness of the proposed control strategy.
文摘In early 2018,the Boliden Garpenberg operation implemented an optimized control strategy as an addition to the existing ventilation on demand system.The purpose of the strategy is to further minimize energy use for main and booster fans,whilst also fulfilling airflow setpoints without violating constraints such as min/max differential pressure over fans and interaction of air between areas in mines.Using air flow measurements and a dynamical model of the ventilation system,a mine-wide coordination control of fans can be carried out.The numerical model is data driven and derived from historical operational data or step changes experiments.This makes both initial deployment and lifetime model maintenance,as the mine evolves,a comparably easy operation.The control has been proven to operate in a stable manner over long periods without having to re-calibrate the model.Results prove a 40%decrease in energy use for the fans involved and a greater controllability of air flow.Moreover,a 15%decrease of the total air flow into the mine will give additional proportional heating savings during winter periods.All in all,the multivariable controller shows a correlation between production in the mine and the ventilation system performance superior to all of its predecessors.
文摘Continued increases in the emission of greenhouse gases by passenger ve<span style="font-family:Verdana;">hicles ha</span><span style="font-family:Verdana;">ve</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> accelerated the production of hybrid electric vehicles. With this increase in production, there has been a parallel demand for continuously improving strategies of hybrid electric vehicle control. The goal of an ideal control strategy is to maximize fuel economy while minimizing emissions. Methods exist by which the globally optimal control strategy may be found. However, these methods are not applicable in real-world driving applications since these methods require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the upcoming drive cycle. Real-time control strategies use the global optimal as a benchmark against which performance can be evaluated. The goal of this work is to use a previously defined strategy that has been shown to closely approximate the global optimal and implement a radial basis function (RBF) artificial neural network (ANN) that dynamically adapts the strategy based on past driving conditions. The strate</span><span style="font-family:Verdana;">gy used is the Equivalent Consumption Minimization Strategy (ECMS),</span><span style="font-family:Verdana;"> which uses an equivalence factor to define the control strategy and the power train </span><span style="font-family:Verdana;">component torque split. An equivalence factor that is optimal for a single</span><span style="font-family:Verdana;"> drive cycle can be found offline</span></span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">with </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> knowledge of the drive cycle. The RBF-ANN is used to dynamically update the equivalence factor by examining a past time window of driving characteristics. A total of 30 sets of training data (drive cycles) are used to train the RBF-ANN. For the majority of drive cycles examined, the RBF-ANN implementation is shown to produce fuel economy values that are within ±2.5% of the fuel economy obtained with the optimal equivalence factor. The advantage of the RBF-ANN is that it does not require </span><i><span style="font-family:Verdana;">a</span></i> <i><span style="font-family:Verdana;">priori</span></i><span style="font-family:Verdana;"> drive cycle knowledge and is able to be implemented in real-time while meeting or exceeding the performance of the optimal ECMS. Recommendations are made on how the RBF-ANN could be improved to produce better results across a greater array of driving conditions.</span></span>
文摘Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical model for heat transferring process in the CDQ unit, a mathematical model for heat transferring process in the boiler and a combustion model for circulating gas in the CDQ-Boiler system. The model was verified by field data, then a series of simulations under several typical operating conditions of CDQ-Boiler were carried on, and in turn, the online relation formulas between the productivity and the optimal circulating gas, and the one between the productivity and the optimal second air, were achieved respectively. These relation equations have been success- fully used in a CDQ-Boiler computer control system in the Baosteel, to realize online optimized guide and control, and meanwhile high efficiency in the CDQ-Boiler system has been achieved.
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.
基金supported in part by the National Natural Science Foundation of China(62173255,62188101)Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)
文摘Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the 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.
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 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.
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.
