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H∞ optimal control of unknown linear systems by adaptive dynamic programming with applications to time-delay systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2021年第12期31卷 5602-5617页

作者： Jiang, Huai-Yuan Zhou, Bin Liu, Guo-Ping Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China Wuhan Univ Dept Artificial Intelligence & Automat Wuhan Peoples R China

In this paper, a new value iteration (VI) based method is proposed to solve the H-infinity control problem of continuous-time linear systems. The problem is transformed into solving a nonlinear differential equation, and the local stability of its solution is proved. Then a VI based iteration scheme for getting the approximation of the H-infinity optimal controller is proposed. Compared with the existing results, the proposed scheme does not need any special initial matrix or extra condition to solve the problem and provides a relatively small disturbance attenuation bound. The related result is also applied to the quadratic guaranteed cost control of linear time-delay systems. Simulation examples verify the effectiveness of the proposed schemes.

关键词： adaptive dynamic programming linear H-infinity control model free control time-delay systems zero-sum differential games

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Data-driven adaptive dynamic programming for continuous-time fully cooperative games with partially constrained inputs

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NEUROCOMPUTING 2017年 238卷 377-386页

作者： Zhang, Qichao Zhao, Dongbin Zhu, Yuanheng Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

In this paper, the fully cooperative game with partially constrained inputs in the continuous-time Markov decision process environment is investigated using a novel data-driven adaptive dynamic programming method. First, the model-based policy iteration algorithm with one iteration loop is proposed, where the knowledge of system dynamics is required. Then, it is proved that the iteration sequences of value functions and control policies can converge to the optimal ones. In order to relax the exact knowledge of the system dynamics, a model-free iterative equation is derived based on the model-based algorithm and the integral reinforcement learning. Furthermore, a data-driven adaptive dynamic programming is developed to solve the model-free equation using generated system data. From the theoretical analysis, we prove that this model-free iterative equation is equivalent to the model-based iterative equations, which means that the data-driven algorithm can approach the optimal value function and control policies. For the implementation purpose, three neural networks are constructed to approximate the solution of the model-free iteration equation using the off-policy learning scheme after the available system data is collected in the online measurement phase. Finally, two examples are provided to demonstrate the effectiveness of the proposed scheme. (C) 2017 Published by Elsevier B.V.

关键词： adaptive dynamic programming Optimal control Neural network Fully cooperative games Data-driven Constrained input

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Pareto optimal control of the mean-field stochastic systems by adaptive dynamic programming algorithm

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ISA TRANSACTIONS 2020年 102卷 81-90页

作者： Ge, Yingying Liu, Xikui Li, Yan Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao 266590 Peoples R China Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China

The Pareto game for the model-free continuous-time stochastic system is studied through approximate/adaptive dynamic programming (ADP) in this paper. Firstly, the model-based online iterative algorithm is proposed, and it is proved that the control iterative sequence converges to the Pareto efficient solution, but the algorithm requires complete system parameters. Then, we derive the modelfree iterative equation and develop the ADP algorithm to calculate the equation by collecting updated states and input information online. From the derivation of the ADP algorithm, the model-free iterative equation and the model-based iterative equation have the same solution, which means that the ADP algorithm can approximate the Pareto optimal solution. Next, the convergence analysis shows that the Pareto optimal strategy is uniquely determined by the ADP algorithm. Finally, two simulation examples confirm the feasibility of the ADP algorithm. (C) 2020 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Pareto game adaptive dynamic programming Mean-field system Optimal control

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Event-triggered adaptive dynamic programming for multi-player zero-sum games with unknown dynamics

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SOFT COMPUTING 2021年第3期25卷 2237-2251页

作者： Zhang, Yongwei Zhao, Bo Liu, Derong Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Beijing Normal Univ Sch Syst Sci Beijing 100875 Peoples R China

In this paper, a novel event-triggered optimal control approach is developed to solve zero-sum game problems for continuous-time multi-player nonlinear systems with unknown dynamics. To begin with, a model neural network (NN) is employed to reconstruct the unknown multi-player nonlinear system by measured input and output data. Then, a critic NN is used to solve the event-triggered Hamilton-Jacobi-Isaacs (HJI) equation for multi-player zero-sum game. Meanwhile, the optimal control law and the worst disturbance law are approximated with the help of critic NN only, respectively. Compared with time-triggered method, the developed control law and the disturbance law are updated only when the triggering condition is violated;thus, the computational and communication burden are reduced. The Lyapunov stability analysis shows that the closed-loop system can be guaranteed to be stable. Finally, two simulation examples are provided to validate the effectiveness of the proposed method.

关键词： adaptive dynamic programming Event-triggered control Neural network Multi-player zero-sum game

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Model-Free H Control Design for Unknown Continuous-Time Linear System Using adaptive dynamic programming

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ASIAN JOURNAL OF CONTROL 2016年第2期18卷 609-618页

作者： Qin, Chunbin Zhang, Huaguang Luo, Yanhong Henan Univ Sch Comp & Informat Engn Kaifeng Henan Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang Liaoning Peoples R China

In this paper, a new online model-free adaptive dynamic programming algorithm is developed to solve the H control problem of the continuous-time linear system with completely unknown system dynamics. Solving the game algebraic Riccati equation, commonly used in H state feedback control design, is often referred to as a two-player differential game where one player tries to minimize the predefined performance index while the other tries to maximize it. Using data generated in real time along the system trajectories, this new method can solve online the game algebraic Riccati equation without requiring the full knowledge of system dynamics. A rigorous proof of convergence of the proposed algorithm is given. Finally, simulation studies on two examples demonstrate the effectiveness of the proposed method.

关键词： H control differential game continuous-time linear system unknown dynamics adaptive dynamic programming

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Optimal torque control of permanent magnet synchronous motors using adaptive dynamic programming

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IET POWER ELECTRONICS 2020年第12期13卷 2442-2449页

作者： Khiabani, Ataollah Gogani Heydari, Ali Southern Methodist Univ Dept Mech Engn 6425 Boaz Lane Dallas TX 75205 USA

In this study, a new approach based on adaptive dynamic programming (ADP) is proposed to control permanent magnet synchronous motors (PMSMs). The objective of this study is to control the torque and consequently the speed of a PMSM when an unknown load torque is applied to it. The proposed controller achieves a fast transient response, low ripples and small steady-state error. The control algorithm uses two neural networks, called critic and actor. The former is utilised to evaluate the cost and the latter is used to generate control signals. The training is done once offline and the calculated optimal weights of actor network are used in online control to achieve fast and accurate torque control of PMSMs. This algorithm is compared with field oriented control (FOC) and direct torque control based on space vector modulation. Simulations and experimental results show that the proposed algorithm provides desirable results under both accurate and uncertain modelled dynamics. Although the performance of FOC method is comparable with ADP under nominal conditions, the torque and speed response of ADP is better than FOC under realistic scenarios, that is, when parameter uncertainties exist.

关键词： angular velocity control transient response torque control synchronous motor drives dynamic programming synchronous motors machine vector control permanent magnet motors actor network online control direct torque control uncertain modelled dynamics ADP optimal torque control permanent magnet synchronous motors adaptive dynamic programming unknown load torque fast transient response steady-state error control algorithm control signals optimal weights PMSM

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Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming

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SOFT COMPUTING 2017年第15期21卷 4465-4480页

作者： Kumar, Rajesh Srivastava, Smriti Gupta, J. R. P. Netaji Subhas Inst Technol Div Instrumentat & Control Engn Sect 3 New Delhi 110078 India

This paper presents a novel control and identification scheme based on adaptive dynamic programming for nonlinear dynamical systems. The aim of control in this paper is to make output of the plant to follow the desired reference trajectory. The dynamics of plants are assumed to be unknown, and to tackle the problem of unknown plant's dynamics, parameter variations and disturbance signal effects, a separate neural network-based identification model is set up which will work in parallel to the plant and the control scheme. Weights update equations of all neural networks present in the proposed scheme are derived using both gradient descent (GD) and Lyapunov stability (LS) criterion methods. Stability proof of LS-based algorithm is also given. Weight update equations derived using LS criterion ensure the global stability of the system, whereas those obtained through GD principle do not. Further, adaptive learning rate is employed in weight update equation instead of constant one in order to have fast learning of weight vectors. Also, L-Sand GD-based weight update equations are also tested against parameter variation and disturbance signal. Three nonlinear dynamical systems (of different complexity) including the forced rigid pendulum trajectory control are used in this paper on which the proposed scheme is applied. The results obtained with LS method are found more accurate than those obtained with the GD-based method.

关键词： adaptive dynamic programming Nonlinear dynamical systems Lyapunov stability Identification and adaptive control Gradient descent principle

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Distributed optimal coordination control for nonlinear multi-agent systems using event-triggered adaptive dynamic programming method

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ISA TRANSACTIONS 2019年 91卷 184-195页

作者： Zhao, Wei Zhang, Huaipin Southeast Univ Sch Math Nanjing 210096 Jiangsu Peoples R China Nanjing Univ Posts & Telecommun Inst Adv Technol Nanjing 210023 Jiangsu Peoples R China

This paper is concerned with the design of distributed optimal coordination control for nonlinear multi agent systems (NMASs) based on event-triggered adaptive dynamic programming (ETADP) method. The method is firstly introduced to design the distributed coordination controllers for NMASs, which not only avoids the transmission of redundant data compared with traditional time-triggered adaptive dynamic programming (TTADP) strategy and minimizes the performance function of each agent. The event-triggered conditions are proposed based on Lyapunov functional method, which is deduced by guaranteeing the stability of NMASs. Then a new adaptive policy iteration algorithm is presented to obtain the online solutions of the Hamiton-Jocabi-Bellman (HJB) equations. In order to implement the proposed ETADP method, the fuzzy hyperbolic model based critic neural networks (NN) are utilized to approximate the value functions and help calculate the control policies. In critic NNs, the NN weight estimations are updated at the event-triggered instants leading to aperiodic weight tuning laws so that computation cost is reduced. It is proved that the weight estimation errors and the local neighborhood coordination errors is uniformly ultimately bounded (UUB). Finally, two simulation examples are provided to show the effectiveness of the proposed ETADP method. (C) 2019 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Multi-agent systems Event-triggered sampling Distributed optimal coordination control adaptive dynamic programming

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Dual iterative adaptive dynamic programming for a class of discrete-time nonlinear systems with time-delays

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NEURAL COMPUTING & APPLICATIONS 2013年第7-8期23卷 1851-1863页

作者： Wei, Qinglai Wang, Ding Zhang, Dehua Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China

In this paper, a new dual iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for a class of nonlinear systems with time-delays in state and control variables. The idea is to use the dynamic programming theory to solve the expressions of the optimal performance index function and control. Then, the dual iterative ADP algorithm is introduced to obtain the optimal solutions iteratively, where in each iteration, the performance index function and the system states are both updated. Convergence analysis is presented to prove the performance index function to reach the optimum by the proposed method. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the dual iterative ADP algorithm. Simulation examples are given to demonstrate the validity of the proposed optimal control scheme.

关键词： adaptive dynamic programming Approximate dynamic programming adaptive critic designs Optimal control Time-delay Nonlinear systems

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Event-triggered decentralized optimal fault tolerant control for mismatched interconnected nonlinear systems through adaptive dynamic programming

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OPTIMAL CONTROL APPLICATIONS & METHODS 2021年第5期42卷 1365-1384页

作者： Luo, Fangchao Zhao, Bo Liu, Derong Guangdong Univ Technol Sch Automat Guangzhou Peoples R China Beijing Normal Univ Sch Syst Sci 19 Xinjiekouwai St Beijing 100875 Peoples R China

In this paper, we propose an event-triggered decentralized optimal fault tolerant control (ETDOFTC) scheme based on adaptive dynamic programming for mismatched interconnected nonlinear systems with actuator failures. For fault-free dynamic models, the decentralized control problem is addressed by developing a set of decentralized optimal control strategies for isolated subsystems with modified value functions, which are approximated by critic neural networks. Meanwhile, the neural network-based decentralized observer is established to approximate actuator failures and mismatched unknown interconnections. The weights of the neural networks are aperiodically updated at the designed triggering instants. Then, the proposed ETDOFTC scheme is obtained by combining the event-triggered decentralized optimal control strategies with the adaptive fault compensators. Furthermore, it is proved that all the signals of the closed-loop system are uniformly ultimately bounded via the Lyapunov stability analysis. Finally, simulation results of two examples are presented to confirm the effectiveness of the proposed ETDOFTC scheme.

关键词： adaptive dynamic programming decentralized control event‐ triggered control fault tolerant control mismatched interconnected nonlinear systems neural networks reinforcement learning

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