This article develops a novel data-driven safe Q-learning method to design the safe optimal controller which can guarantee constrained states of nonlinear systems always stay in the safe region while providing an opti...This article develops a novel data-driven safe Q-learning method to design the safe optimal controller which can guarantee constrained states of nonlinear systems always stay in the safe region while providing an optimal performance.First,we design an augmented utility function consisting of an adjustable positive definite control obstacle function and a quadratic form of the next state to ensure the safety and optimality.Second,by exploiting a pre-designed admissible policy for initialization,an off-policy stabilizing value iteration Q-learning(SVIQL)algorithm is presented to seek the safe optimal policy by using offline data within the safe region rather than the mathematical model.Third,the monotonicity,safety,and optimality of the SVIQL algorithm are theoretically proven.To obtain the initial admissible policy for SVIQL,an offline VIQL algorithm with zero initialization is constructed and a new admissibility criterion is established for immature iterative policies.Moreover,the critic and action networks with precise approximation ability are established to promote the operation of VIQL and SVIQL algorithms.Finally,three simulation experiments are conducted to demonstrate the virtue and superiority of the developed safe Q-learning method.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
This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [...This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.展开更多
The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approxi...The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.展开更多
The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalize...The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.展开更多
A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which i...A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.展开更多
Necessary conditions for optimality are proved for smooth infinite horizon optimal control problems with unilateral state constraints (pathwise constraints) and with terminal conditions on the states at the infinite h...Necessary conditions for optimality are proved for smooth infinite horizon optimal control problems with unilateral state constraints (pathwise constraints) and with terminal conditions on the states at the infinite horizon. The aim of the paper is to obtain strong necessary conditions including transversality conditions at infinity, which in many cases lead to a set of candidates for optimality containing only a few elements, similar to what is the case in finite horizon problems. However, strong growth conditions are needed for the results to hold.展开更多
In the era of intelligent revolution,pneumatic artificial muscle(PAM)actuators have gained significance in robotics,particularly for tasks demanding high safety and flexibility.Despite their inherent flexibility,PAMs ...In the era of intelligent revolution,pneumatic artificial muscle(PAM)actuators have gained significance in robotics,particularly for tasks demanding high safety and flexibility.Despite their inherent flexibility,PAMs encounter challenges in practical applications because of their complex material properties,including hysteresis,nonlinearity,and low response frequencies,which hinder precise modeling and motion control,limiting their widespread adoption.This study focuses on fuzzy logic dynamic surface control(DSC)for PAMs,addressing full-state constraints and unknown disturbances.We propose an improved neural DSC method,combining enhanced DSC techniques with fuzzy logic system approximation and parameter minimization for PAM systems.The introduction of a novel barrier Lyapunov function during system design effectively resolves full-state constraint issues.A key feature of this control approach is its single online estimation parameter update while maintaining stability characteristics akin to the conventional backstepping method.Importantly,it ensures constraint adherence even in the presence of disturbances.Lyapunov stability analysis confirms signal boundedness within the closed-loop system.Experimental results validate the algorithm’s effectiveness in enhancing control precision and response speed.展开更多
In this paper,the authors propose an adaptive Barrier-Lyapunov-Functions(BLFs)based control scheme for nonlinear pure-feedback systems with full state constraints.Due to the coexist of the non-affine structure and ful...In this paper,the authors propose an adaptive Barrier-Lyapunov-Functions(BLFs)based control scheme for nonlinear pure-feedback systems with full state constraints.Due to the coexist of the non-affine structure and full state constraints,it is very difficult to construct a desired controller for the considered system.According to the mean value theorem,the authors transform the pure-feedback system into a system with strict-feedback structure,so that the well-known backstepping method can be applied.Then,in the backstepping design process,the BLFs are employed to avoid the violation of the state constraints,and neural networks(NNs)are directly used to online approximate the unknown packaged nonlinear terms.The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero.Meanwhile,it is shown that the constraint requirement on the system will not be violated during the operation.Finally,two simulation examples are provided to show the effectiveness of the proposed control scheme.展开更多
This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforce...This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforcement learning(IRL)control algorithm with an actor–critic structure is first proposed.The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated.Thus,optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item.Meanwhile,neural networks are used to approximate the gradient value functions.According to the Lyapunov stability theorem,the boundedness of all signals of the closed-loop system is proved,and the proposed control scheme ensures that the system states are within predefined compact sets.Finally,the effectiveness of the proposed control approach is validated by simulations.展开更多
In this paper,we study the linear quadratic(LQ)optimal control of time-varying difference system with terminal state constraints.The main contribution is to provide the Q-learning algorithm for the optimal controller ...In this paper,we study the linear quadratic(LQ)optimal control of time-varying difference system with terminal state constraints.The main contribution is to provide the Q-learning algorithm for the optimal controller under the case that the time-varying system matrices and input matrices are both unknown,which consists of learning the solution of the Riccati equation and calculating the specific Lagrange multiplier from the data-driven matrix equation.Different from the existing Q-learning algorithms that mainly focus on unconstrained optimal control problems,the novelty of the proposed algorithm can be applied to handle situations with terminal state constraints.The effectiveness of the proposed Q-learning algorithm is demonstrated through a numerical example.展开更多
This paper investigates the issue of event-triggered adaptive finite-time state-constrained control for multi-input multi-output uncertain nonlinear systems.To prevent asymmetric time-varying state constraints from be...This paper investigates the issue of event-triggered adaptive finite-time state-constrained control for multi-input multi-output uncertain nonlinear systems.To prevent asymmetric time-varying state constraints from being violated,a tan-type nonlinear mapping is established to transform the considered system into an equivalent“non-constrained”system.By employing a smooth switch function in the virtual control signals,the singularity in the traditional finite-time dynamic surface control can be avoided.Fuzzy logic systems are used to compensate for the unknown functions.A suitable event-triggering rule is introduced to determine when to transmit the control laws.Through Lyapunov analysis,the closed-loop system is proved to be semi-globally practical finite-time stable,and the state constraints are never violated.Simulations are provided to evaluate the effectiveness of the proposed approach.展开更多
This paper focuses on the leader-following consensus control problem for nonlinear multiagent systems subject to deferred asymmetric time-varying state constraints.A distributed eventtriggered adaptive neural control ...This paper focuses on the leader-following consensus control problem for nonlinear multiagent systems subject to deferred asymmetric time-varying state constraints.A distributed eventtriggered adaptive neural control approach is advanced.By virtue of a distributed sliding-mode estimator,the leader-following consensus control problem is converted into multiple simplified tracking control problems.Afterwards,a shifting function is utilized to transform the error variables such that the initial tracking condition can be totally unknown and the state constraints can be imposed at a specified time instant.Meanwhile,the deferred asymmetric time-varying full state constraints are addressed by a class of asymmetric barrier Lyapunov function.In order to reduce the burden of communication,a relative threshold event-triggered mechanism is incorporated into controller and Zeno behavior is excluded.Based on Lyapunov stability theorem,all closed-loop signals are proved to be semi-globally uniformly ultimately bounded.Finally,a practical simulation example is given to verify the presented control scheme.展开更多
This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state con...This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland＇s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.展开更多
This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by Levy process, while the forward state is constrained in a convex set at the ter...This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by Levy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland＇s variational principle. Finally, the result is applied to the utility optimization problem in a financial market.展开更多
The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（ga...The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.展开更多
In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible ...In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.展开更多
The unmanned dual-arm aerial manipulator system is composed of a multirotor unmanned aerial vehicle(UAV)and two manipulators.Compared to a single manipulator,dual-arm always provides greater°exibility and versati...The unmanned dual-arm aerial manipulator system is composed of a multirotor unmanned aerial vehicle(UAV)and two manipulators.Compared to a single manipulator,dual-arm always provides greater°exibility and versatility in both goods delivery and complex task execution.However,the practical application of the system is limited due to nonlinearities and complex dynamic coupling behavior between the multirotor and the manipulator,as well as the one between the inner and outer loop of the multirotor.In this paper,a holistic model of the dual-arm aerial manipulator system is¯rst derived with complete model information.Subsequently,an adaptive sliding-mode disturbance observer(ASMDO)is proposed to handle external disturbances and unmeasurable disturbances caught by unmeasurable angular velocity and acceleration of the manipulators.Moreover,for safety concerns and transient performance requirements,the state constraints should be guaranteed.To this end,an auxiliary term composed of constrained variable signals is introduced.Then,the performance of the designed method is proven by rigorous analysis.Finally,the proposed method is validated through two sets of simulation tests.展开更多
This paper is devoted to the state-constrained optimal control of systems governed by an evolutionary variational inequality coupled with a semilinear parabolic equation via the constraint of obstacle . Existence and ...This paper is devoted to the state-constrained optimal control of systems governed by an evolutionary variational inequality coupled with a semilinear parabolic equation via the constraint of obstacle . Existence and optimality conditions (in the form of Pontryagin principle) for optimal controls are established.展开更多
基金supported in part by the National Science and Technology Major Project(2021ZD0112302)the National Natural Science Foundation of China(62222301,61890930-5,62021003)。
文摘This article develops a novel data-driven safe Q-learning method to design the safe optimal controller which can guarantee constrained states of nonlinear systems always stay in the safe region while providing an optimal performance.First,we design an augmented utility function consisting of an adjustable positive definite control obstacle function and a quadratic form of the next state to ensure the safety and optimality.Second,by exploiting a pre-designed admissible policy for initialization,an off-policy stabilizing value iteration Q-learning(SVIQL)algorithm is presented to seek the safe optimal policy by using offline data within the safe region rather than the mathematical model.Third,the monotonicity,safety,and optimality of the SVIQL algorithm are theoretically proven.To obtain the initial admissible policy for SVIQL,an offline VIQL algorithm with zero initialization is constructed and a new admissibility criterion is established for immature iterative policies.Moreover,the critic and action networks with precise approximation ability are established to promote the operation of VIQL and SVIQL algorithms.Finally,three simulation experiments are conducted to demonstrate the virtue and superiority of the developed safe Q-learning method.
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This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.
文摘The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.
文摘The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.
文摘A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.
文摘Necessary conditions for optimality are proved for smooth infinite horizon optimal control problems with unilateral state constraints (pathwise constraints) and with terminal conditions on the states at the infinite horizon. The aim of the paper is to obtain strong necessary conditions including transversality conditions at infinity, which in many cases lead to a set of candidates for optimality containing only a few elements, similar to what is the case in finite horizon problems. However, strong growth conditions are needed for the results to hold.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFF0708903)in part by the Ningbo Key Technology Research and Development Program of China(Grant No.2023Z018)+1 种基金in part by the National Natural Science Foundation of China(Grant No.52275043)in part by the Zhejiang Lab Open Research Project of China(Grant No.121001-AB2212).
文摘In the era of intelligent revolution,pneumatic artificial muscle(PAM)actuators have gained significance in robotics,particularly for tasks demanding high safety and flexibility.Despite their inherent flexibility,PAMs encounter challenges in practical applications because of their complex material properties,including hysteresis,nonlinearity,and low response frequencies,which hinder precise modeling and motion control,limiting their widespread adoption.This study focuses on fuzzy logic dynamic surface control(DSC)for PAMs,addressing full-state constraints and unknown disturbances.We propose an improved neural DSC method,combining enhanced DSC techniques with fuzzy logic system approximation and parameter minimization for PAM systems.The introduction of a novel barrier Lyapunov function during system design effectively resolves full-state constraint issues.A key feature of this control approach is its single online estimation parameter update while maintaining stability characteristics akin to the conventional backstepping method.Importantly,it ensures constraint adherence even in the presence of disturbances.Lyapunov stability analysis confirms signal boundedness within the closed-loop system.Experimental results validate the algorithm’s effectiveness in enhancing control precision and response speed.
基金supported in part by the National Natural Science Foundation of China under Grant No.62303278in part by the Taishan Scholar Project of Shandong Province of China under Grant No.tsqn201909078。
文摘In this paper,the authors propose an adaptive Barrier-Lyapunov-Functions(BLFs)based control scheme for nonlinear pure-feedback systems with full state constraints.Due to the coexist of the non-affine structure and full state constraints,it is very difficult to construct a desired controller for the considered system.According to the mean value theorem,the authors transform the pure-feedback system into a system with strict-feedback structure,so that the well-known backstepping method can be applied.Then,in the backstepping design process,the BLFs are employed to avoid the violation of the state constraints,and neural networks(NNs)are directly used to online approximate the unknown packaged nonlinear terms.The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero.Meanwhile,it is shown that the constraint requirement on the system will not be violated during the operation.Finally,two simulation examples are provided to show the effectiveness of the proposed control scheme.
基金Project supported by the National Natural Science Foundation of China(Nos.62203392 and 62373329)the Natural Science Foundation of Zhejiang Province,China(No.LY23F030009)the Baima Lake Laboratory Joint Funds of the Zhejiang Provincial Natural Science Foundation of China(No.LBMHD24F030002)。
文摘This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforcement learning(IRL)control algorithm with an actor–critic structure is first proposed.The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated.Thus,optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item.Meanwhile,neural networks are used to approximate the gradient value functions.According to the Lyapunov stability theorem,the boundedness of all signals of the closed-loop system is proved,and the proposed control scheme ensures that the system states are within predefined compact sets.Finally,the effectiveness of the proposed control approach is validated by simulations.
基金supported by the Natural Science Foundation of Shandong Province(Nos.ZR2021ZD14,ZR2021JQ24,and ZR2024QF198).
文摘In this paper,we study the linear quadratic(LQ)optimal control of time-varying difference system with terminal state constraints.The main contribution is to provide the Q-learning algorithm for the optimal controller under the case that the time-varying system matrices and input matrices are both unknown,which consists of learning the solution of the Riccati equation and calculating the specific Lagrange multiplier from the data-driven matrix equation.Different from the existing Q-learning algorithms that mainly focus on unconstrained optimal control problems,the novelty of the proposed algorithm can be applied to handle situations with terminal state constraints.The effectiveness of the proposed Q-learning algorithm is demonstrated through a numerical example.
基金Project supported by the National Natural Science Foundation of China(Nos.61973204 and 61703275)。
文摘This paper investigates the issue of event-triggered adaptive finite-time state-constrained control for multi-input multi-output uncertain nonlinear systems.To prevent asymmetric time-varying state constraints from being violated,a tan-type nonlinear mapping is established to transform the considered system into an equivalent“non-constrained”system.By employing a smooth switch function in the virtual control signals,the singularity in the traditional finite-time dynamic surface control can be avoided.Fuzzy logic systems are used to compensate for the unknown functions.A suitable event-triggering rule is introduced to determine when to transmit the control laws.Through Lyapunov analysis,the closed-loop system is proved to be semi-globally practical finite-time stable,and the state constraints are never violated.Simulations are provided to evaluate the effectiveness of the proposed approach.
基金partially supported by the China Postdoctoral Science Foundation under Grant Nos.2019M662813,2020M682614 and 2020T130124the Guangdong Basic and Applied Basic Research Foundation under Grant No.2020A1515110974+2 种基金the Local Innovative and Research Teams Project of Guangdong Special Support Program under Grant No.2019BT02X353the Innovative Research Team Program of Guangdong Province Science Foundation under Grant No.2018B030312006the Science and Technology Program of Guangzhou under Grant No.201904020006。
文摘This paper focuses on the leader-following consensus control problem for nonlinear multiagent systems subject to deferred asymmetric time-varying state constraints.A distributed eventtriggered adaptive neural control approach is advanced.By virtue of a distributed sliding-mode estimator,the leader-following consensus control problem is converted into multiple simplified tracking control problems.Afterwards,a shifting function is utilized to transform the error variables such that the initial tracking condition can be totally unknown and the state constraints can be imposed at a specified time instant.Meanwhile,the deferred asymmetric time-varying full state constraints are addressed by a class of asymmetric barrier Lyapunov function.In order to reduce the burden of communication,a relative threshold event-triggered mechanism is incorporated into controller and Zeno behavior is excluded.Based on Lyapunov stability theorem,all closed-loop signals are proved to be semi-globally uniformly ultimately bounded.Finally,a practical simulation example is given to verify the presented control scheme.
基金supported by the National Natural Science Foundation of China under Grant No.11171076Science and Technology Commission,Shanghai Municipality under Grant No.14XD1400400
文摘This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland＇s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.
基金supported by the National Science Fundation of China under Grant No.11271007the National Social Science Fund Project of China under Grant No.17BGL058Humanity and Social Science Research Foundation of Ministry of Education of China under Grant No.15YJA790051
文摘This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by Levy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland＇s variational principle. Finally, the result is applied to the utility optimization problem in a financial market.
基金supported by the National Natural Science Foundation of China(6132106261503100)the China Postdoctoral Science Foundation(2014M550189)
文摘The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.
基金supported by National Natural Science Foundation of China(Grant No.11401091)Postdoctoral Scientific Research Project of Jilin Province(Grant No.RB201357)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.14QNJJ002)China Postdoctoral Science Foundation(Grant No.2014M551152)the China Scholarship Council
文摘In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.
基金supported in part by the National Natural Science Foundation of China under Grant 62273187,and Grant 62233011in part by the Young Elite Scientists Sponsorship Program by Tianjin under Grant TJSQNTJ-2020-21in part by the Haihe Lab of ITAI under Grant 22HHXCJC00003.
文摘The unmanned dual-arm aerial manipulator system is composed of a multirotor unmanned aerial vehicle(UAV)and two manipulators.Compared to a single manipulator,dual-arm always provides greater°exibility and versatility in both goods delivery and complex task execution.However,the practical application of the system is limited due to nonlinearities and complex dynamic coupling behavior between the multirotor and the manipulator,as well as the one between the inner and outer loop of the multirotor.In this paper,a holistic model of the dual-arm aerial manipulator system is¯rst derived with complete model information.Subsequently,an adaptive sliding-mode disturbance observer(ASMDO)is proposed to handle external disturbances and unmeasurable disturbances caught by unmeasurable angular velocity and acceleration of the manipulators.Moreover,for safety concerns and transient performance requirements,the state constraints should be guaranteed.To this end,an auxiliary term composed of constrained variable signals is introduced.Then,the performance of the designed method is proven by rigorous analysis.Finally,the proposed method is validated through two sets of simulation tests.
文摘This paper is devoted to the state-constrained optimal control of systems governed by an evolutionary variational inequality coupled with a semilinear parabolic equation via the constraint of obstacle . Existence and optimality conditions (in the form of Pontryagin principle) for optimal controls are established.
