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Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach

Chinese Physics B 2015年第3期24卷 87-94页

作者：魏庆来刘德荣徐延才 The State Key Laboratory of Management and Control for Complex Systems Institute of AutomationChinese Academy of Sciences

A policy iteration algorithm of adaptive dynamic programming（ADP） is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then,the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks,the developed optimal tracking control scheme for chaotic systems is verified by a simulation.

关键词： adaptive critic designs adaptive dynamic programming approximate dynamic programming neuro-dynamic programming

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Event-Triggered Decentralized Tracking Control of Modular Reconfigurable Robots Through adaptive dynamic programming

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2020年第4期67卷 3054-3064页

作者： Zhao, Bo Liu, Derong Beijing Normal Univ Sch Syst Sci Beijing 100875 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China

This paper develops an event-triggered decentralized tracking control (DTC) approach for modular reconfigurable robots (MRRs) by using adaptive dynamic programming. By establishing a decentralized neural network (NN) observer, which uses local input-output data and desired states of coupling subsystems, the local dynamics of MRR subsystem can be obtained. In order to obtain the DTC, the tracking error subsystem is augmented by the exosystem with the desired trajectory. Based on the event-triggered mechanism and a modified local cost function, the DTC is derived by solving the local Hamilton-Jacobi-Bellman equation via a local critic NN with asymptotically stable structure. The stability of the entire closed-loop MRR system is analyzed by Lyapunovs direct method. The simulation of a two-degree of freedom MRR system ensures that the developed event-triggered DTC scheme is effective.

关键词： Decentralized control Couplings Optimal control Robots dynamic programming Artificial neural networks Trajectory adaptive dynamic programming decentralized tracking control event-triggered mechanism modular reconfigurable robots optimal control reinforcement learning

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Optimal containment control for multi-agent systems using fast adaptive dynamic programming

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ASIAN JOURNAL OF CONTROL 2024年第0期

作者： Cao, Ao Wang, Fuyong Liu, Zhongxin Chen, Zengqiang Nankai Univ Coll Artificial Intelligence Tianjin 300350 Peoples R China

In this paper, an innovative adaptive dynamic programming (ADP) algorithm with fast convergence speed is designed for the optimal containment control problem of discrete-time linear multi-agent systems. Precisely, a quadratic input energy cost function, including local containment error information and actuator information in the neighborhood, is designed for each follower. Solving the stationary condition of the cost function, the optimal containment controllers are obtained. Traditional ADP methods use actor-critic neural networks to approximate optimal costs and control strategies, it is time-consuming to solve large-scale multi-agent problems due to the computational complexity of neural networks. In order to seek faster convergence speed of optimal containment control without knowing the model information, the fast ADP algorithm framework is designed, it is proved theoretically that the convergence speed is determined by some configurable parameters, and the whale optimization algorithm is employed to globally optimize the parameters of given spaces to derive the optimal configuration. Finally, numerical simulation results are given to verify the effectiveness of the designed algorithm.

关键词： adaptive dynamic programming faster convergence speed multi-agent system optimal containment control whale optimization algorithm

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Data-based approximate optimal control for nonzero-sum games of multi-player systems using adaptive dynamic programming

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NEUROCOMPUTING 2018年 275卷 192-199页

作者： Jiang, He Zhang, Huaguang Xiao, Geyang Cui, Xiaohong Northeastern Univ Coll Informat Sci & Engn Box 134 Shenyang 110819 Liaoning Peoples R China

This paper investigates the non-zerosum game issue for unknown nonlinear systems with multi-player by using data-based adaptive dynamic programming (ADP) methods. It is known that the traditional ADP approaches require accurate system models to compute the solutions of non-zerosum games. However, for the practical nonlinear systems, system models are difficult to be obtained and thus these methods will be invalid. To overcome this difficulty, we propose two neural-network-based identification schemes. Combined with the identification results, we design a data-based actor-critic algorithm to learn and approximate the optimal solutions in real time. Subsequently, in order to reduce the computation burden of dual network algorithm, we develop a single network one. To test the feasibility and validity of our schemes, we provide two simulation examples including a linear one and a nonlinear one. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Reinforcement learning adaptive dynamic programming Data-based Neural networks

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Distributed adaptive dynamic programming for data-driven optimal control

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SYSTEMS & CONTROL LETTERS 2018年 120卷 36-43页

作者： Tang, Wentao Daoutidis, Prodromos Univ Minnesota Dept Chem Engn & Mat Sci 421 Washington Ave SE Minneapolis MN 55455 USA

adaptive dynamic programming (ADP), as an important optimal control technique, can be exploited in the setting of data-driven control based on an approximate regression-based solution of the Hamilton-Jacobi-Bellman (HJB) equations. Distributed optimization algorithms, which are extensively studied in statistics and machine learning, have not yet been applied to the solution of data-driven ADP problems. In this work, we identify the data-driven ADP problem as a consensus optimization problem for nonlinear affine systems, and apply the alternating direction method of multipliers (ADMM) and its accelerated variants for its solution. For the input-constrained optimal control problem, we define a combined optimal primal-dual function to develop a data-based version of the input-constrained HJB equation. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Data-driven control Process control adaptive dynamic programming Distributed optimization

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Bounded robust control design for uncertain nonlinear systems using single-network adaptive dynamic programming

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NEUROCOMPUTING 2017年 266卷 128-140页

作者： Huang, Yuzhu Wang, Ding Liu, Derong Natl Res Ctr Gas Turbine & IGCC Technol Syst Control Res Sect Beijing 100084 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China

This paper is an effort towards developing an optimal learning algorithm to design the bounded robust controller for uncertain nonlinear systems with control constraints using single-network adaptive dynamic programming (ADP). First, the bounded robust control problem is transformed into an optimal control problem of the nominal system by a modified cost function with nonquadratic utility, which is used not only to account for all possible uncertainties, but also to deal with the control constraints. Then based on single-network ADP, an optimal learning algorithm is proposed for the nominal system by a single critic network to approximate the solution of Hamilton-Jacobi-Bellman (HJB) equation. An additional adjusting term is employed to stabilize the system and relax the requirement for an initial stabilizing control. Besides, uniform ultimate boundedness of the closed-loop system is guaranteed by Lyapunov's direct method during the learning process. Moreover, the equivalence of the approximate optimal solution of optimal control problem and the solution of bounded robust control problem is also shown. Finally, four simulation examples are provided to demonstrate the effectiveness of the proposed approach. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Neural networks Optimal control adaptive dynamic programming Bounded robust control Uncertain nonlinear systems

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Data-driven adaptive dynamic programming schemes for non-zero-sum games of unknown discrete-time nonlinear systems

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NEUROCOMPUTING 2018年 275卷 649-658页

作者： Jiang, He Zhang, Huaguang Zhang, Kun Cui, Xiaohong Northeastern Univ Coll Informat Sci & Engn Box 134 Shenyang 110819 Liaoning Peoples R China

This paper integrates game theory, optimal control theory and reinforcement learning to deal with the discrete-time (DT) multi-player non-zero-sum game issue. As is known, the solutions to non-zero-sum game problems are the outcomes of coupled Riccati equations or coupled Hamilton-Jacobi ones, which are generally difficult to solve analytically and require the knowledge of accurate system mathematical models. However, for most practical industrial systems, the system dynamics cannot be obtained accurately or even unavailable, and the conventional model-based methods will be invalid. To overcome this deficiency, we develop data-based adaptive dynamic programming (ADP) algorithms for completely unknown multi-player systems. Firstly, the Nash equilibrium and stationarity conditions are used to formulate the DT multi-player non-zero-sum game, and then policy iteration algorithm is applied to approximate optimal solutions successively. Secondly, a novel online ADP algorithm combined with a neural-network-based identification scheme is designed and only requires the system data instead of the real system models. Subsequently, a data-driven action-dependent heuristic dynamic programming approach is presented and circumvents the estimation errors caused by the identification learning procedure. Finally, two simulation examples are provided to illustrate the feasibility of our schemes. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Reinforcement learning adaptive dynamic programming Data-driven Non-zero-sum games Neural networks

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Nonlinear Control of Ship-Mounted Rotary Crane Based on adaptive dynamic programming

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IEEE ACCESS 2024年 12卷 104869-104877页

作者： Xi, Huan Wu, Qiangying Ouyang, Huimin Nanjing Tech Univ Coll Elect Engn & Control Sci Nanjing 211816 Peoples R China

As a crucial component in marine transportation, the precision of ship-mounted rotary cranes directly impacts the efficiency and safety of lifting operations. However, the inability to directly control the swing angle of the load through the drive mechanism renders ship-mounted rotary cranes inherently complex, featuring underactuated and coupled characteristics. In this study, we propose an optimal feedback controller leveraging adaptive dynamic programming (ADP), which integrates sliding mode control with optimal control strategies. Specifically, we devise a judicious cost function and solve the Hamilton-Jacobi-Bellman (HJB) equation using the adaptive dynamic programming approach. Subsequently, the optimal feedback controller is derived through iterative batch neural network training facilitated by the adaptive update algorithm. Moreover, we establish the stability of the proposed controller through rigorous Lyapunov techniques and LaSalle's invariance principle. Experimental validation confirms the efficacy of our approach, highlighting its practical utility in real-world scenarios.

关键词： Cranes Mathematical models Optimal control Vehicle dynamics Uncertainty Safety Perturbation methods Motion control Vibration control Underactuated systems adaptive dynamic programming motion control vibration control

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Value iteration and adaptive dynamic programming for data-driven adaptive optimal control design

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AUTOMATICA 2016年 71卷 348-360页

作者： Bian, Tao Jiang, Zhong-Ping NYU Tandon Sch Engn Dept Elect & Comp Engn Control & Networks LabMetrotech Ctr 5 Brooklyn NY 11201 USA

This paper presents a novel non-model-based, data-driven adaptive optimal controller design for linear continuous-time systems with completely unknown dynamics. Inspired by the stochastic approximation theory, a continuous-time version of the traditional value iteration (VI) algorithm is presented with rigorous convergence analysis. This VI method is crucial for developing new adaptive dynamic programming methods to solve the adaptive optimal control problem and the stochastic robust optimal control problem for linear continuous-time systems. Fundamentally different from existing results, the a priori knowledge of an initial admissible control policy is no longer required. The efficacy of the proposed methodology is illustrated by two examples and a brief comparative study between VI and earlier policy iteration methods. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Value iteration adaptive dynamic programming Optimal control adaptive control Stochastic approximation

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Path tracking control of an autonomous vehicle with model-free adaptive dynamic programming and RBF neural network disturbance compensation

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2022年第5期236卷 825-841页

作者： Wang, Hongbo Hu, Chenglei Zhou, Juntao Feng, Lizhao Ye, Bin Lu, Yongjie Hefei Univ Technol Sch Automot & Transportat Engn Hefei Peoples R China Anhui Intelligent Vehicle Engn Lab Hefei Peoples R China Shijiazhuang Tiedao Univ State Key Lab Mech Behav & Syst Safety Traff Engn Room 719Jiaotong Bldg Shijiazhuang 050043 Hebei Peoples R China

The performance of the model-based controller is always affected by the uncertainty and nonlinearity of the model parameters in the vehicle path tracking process. To address this issue, a novel path tracking controller based on model-free adaptive dynamic programming (ADP) is proposed for autonomous vehicles in this paper. To be specific, the proposed controller obtains information from the online state and front-wheel angle input data which are repeatedly used to calculate the controller gain iteratively. So, this controller features not requiring accurate knowledge of vehicle model parameters for controller development. Meanwhile, the path tracking performance of the autonomous vehicle will be inevitably disturbed by unknown nonlinear external disturbance. To approximate this disturbance, the learning characteristics of Radial Basis Function Neural Network (RBFNN) are applied to generate compensation for the front-wheel angle. Afterward, the weight updating law of RBFNN is derived by Lyapunov function to ensure the stability and convergence of the whole system. Finally, Hardware in the loop (HIL) test results demonstrate that the proposed ADP-RBF controller can improve the comprehensive performance of the vehicle path tracking control system and achieve the balance between path tracking accuracy and minimum sideslip angle.

关键词： Autonomous vehicle path tracking model-free adaptive dynamic programming disturbance compensation

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