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adaptive dynamic programming-based stabilization of nonlinear systems with unknown actuator saturation

NONLINEAR dynamicS 2018年第4期93卷 2089-2103页

作者： Zhao, Bo Jia, Lihao Xia, Hongbing Li, Yuanchun Chinese Acad Sci State Key Lab Management & Control Complex Syst Inst Automat Beijing 100190 Peoples R China Chinese Acad Sci Res Ctr Brain Inspired Intelligence Inst Automat Beijing 100190 Peoples R China Changchun Univ Technol Dept Control Sci & Engn Changchun 130012 Jilin Peoples R China

This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming algorithm. The control strategy is composed of an online nominal optimal control and a neural network (NN)-based feed-forward saturation compensator. For nominal systems without actuator saturation, a critic NN is established to deal with the Hamilton-Jacobi-Bellman equation. Thus, the online approximate nominal optimal control policy can be obtained without action NN. Then, the unknown actuator saturation, which is considered as saturation nonlinearity by simple transformation, is compensated by employing a NN-based feed-forward control loop. The stability of the closed-loop nonlinear system is analyzed to be ultimately uniformly bounded via Lyapunov's direct method. Finally, the effectiveness of the presented control method is demonstrated by two simulation examples.

关键词： adaptive dynamic programming Unknown actuator saturation Continuous-time nonlinear systems Stabilizing control Neural networks

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adaptive dynamic programming for model-free tracking of trajectories with time-varying parameters

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INTERNATIONAL JOURNAL OF adaptive CONTROL AND SIGNAL PROCESSING 2020年第7期34卷 839-856页

作者： Koepf, Florian Ramsteiner, Simon Puccetti, Luca Flad, Michael Hohmann, Soeren Karlsruhe Inst Technol Inst Control Syst Kaiserstr 12 D-76131 Karlsruhe Germany BMW Grp Munich Germany

Recently proposed adaptive dynamic programming (ADP) tracking controllers assume that the reference trajectory follows time-invariant exo-system dynamics-an assumption that does not hold for many applications. In order to overcome this limitation, we propose a new Q-function that explicitly incorporates a parametrized approximation of the reference trajectory. This allows learning to track a general class of trajectories by means of ADP. Once our Q-function has been learned, the associated controller handles time-varying reference trajectories without the need for further training and independent of exo-system dynamics. After proposing this general model-free off-policy tracking method, we provide an analysis of the important special case of linear quadratic tracking. An example demonstrates that our new method successfully learns the optimal tracking controller and outperforms existing approaches in terms of tracking error and cost.

关键词： adaptive control adaptive dynamic programming intelligent control learning systems

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adaptive dynamic programming and distributionally robust optimal control of linear stochastic system using the Wasserstein metric

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INTERNATIONAL JOURNAL OF adaptive CONTROL AND SIGNAL PROCESSING 2024年第8期38卷 2810-2832页

作者： Liang, Qingpeng Hu, Jiangping Shi, Kaibo Wu, Yanzhi Xiang, Linying Southwest Jiaotong Univ Sch Informat Sci & Technol Sichuan Peoples R China Univ Elect Sci & Technol China Sch Automat Engn Sichuan Peoples R China Tiangong Univ Sch Artificial Intelligence Tianjin Peoples R China Chengdu Univ Sch Informat Sci & Engn Sichuan Peoples R China Southwest Jiaotong Univ Sch Elect Engn 999 Xian Rd Chengdu 611756 Sichuan Peoples R China

In this paper, we consider the optimal control of unknown stochastic dynamical system for both the finite-horizon and infinite-horizon cases. The objective of this paper is to find an optimal controller to minimize the expected value of a function which depends on the random disturbance. Throughout this paper, it is assumed that the mean vector and covariance matrix of the disturbance distribution is unknown. An uncertainty set in the space of mean vector and the covariance matrix is introduced. For the finite-horizon case, we derive a closed-form expression of the unique optimal policy and the opponents policy that generates the worst-case distribution. For the infinite-horizon case, we simplify the Riccati equation obtained in the finite-hozion setting to an algebraic Riccati equation, which can guarantee the existence of the solution of the Riccati equation. It is shown that the resulting optimal policies obtained in these two cases can stabilize the expected value of the system state under the worst-case distribution. Furthermore, the unknown system matrices can also be explicitly computed using the adaptive dynamic programming technique, which can help compute the optimal control policy by solving the algebraic Riccati equation. Finally, a simulation example is presented to demonstrate the effectiveness of our theoretical results.

关键词： adaptive dynamic programming linear stochastic system optimal control random disturbance

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adaptive dynamic programming for security of networked control systems with actuator saturation

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INFORMATION SCIENCES 2018年 460卷 51-64页

作者： Yang, Hongjiu Li, Ying Yuan, Huanhuan Liu, Zhixin Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

In this paper, an optimal control problem is investigated for a networked control system with actuator saturation under denial-of-service attacks. An intrusion detection system is introduced to defend denial-of-service attacks in the networked control system. Game theory is used to describe interaction between denial-of-service attacks and the intrusion detection system. A performance index function is presented to deal with actuator saturation by an iterative adaptive dynamic programming algorithm. Back-propagation neural networks are used to realize the iterative adaptive dynamic programming algorithm. Two numerical simulations are given to demonstrate effectiveness of the proposed method. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Networked control systems Denial-of-Service attacks Actuator saturation adaptive dynamic programming Neural networks

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adaptive dynamic programming Approach on Optimal Control for Affinely Pseudo-Linearized Nonlinear System

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IEEE ACCESS 2019年 7卷 75132-75142页

作者： Zhang, Lin Zhu, Yian Shi, Haobin Hwang, Kao-Shing Northwestern Polytech Univ Sch Comp Sci Xian 710129 Shaanxi Peoples R China Northwestern Polytech Univ Minist Ind & Informat Technol Key Lab Big Data Storage & Management Xian 710072 Shaanxi Peoples R China Natl Sun Yat Sen Univ Dept Elect Engn Kaohsiung 80424 Taiwan

This paper concerns the optimal control problem of a general affinely pseudo-linearized nonlinear system and puts forward the solving scheme based on adaptive dynamic programming and neural network. In detail, a new more general affinely pseudo-linearized nonlinear system model is presented and covers more practical scenarios than existing models in engineering. In consideration of the Bellman optimal principle, the corresponding model particulars are then analyzed and its adaptive dynamic programming solving scheme is derived. That is, the modified policy iteration is used to estimate the value function and optimal control at each sampled state, and then the calculated state-control pairs and state critic values are utilized to train two neural networks (one works as state evaluator and the other works as optimal control generator, respectively). Through the above, the discrete state space is smoothed into a continuous state space, and the notorious dimensional curse problem could be addressed. Moreover, in order to improve the efficiency and precision of the network training, the samples calculating and network training processes are simultaneously carried out in this paper. In the end, a related simulation experiment is applied and the results demonstrate that the proposed method has more effectiveness and validation for the optimal control problem of the newly proposed general system model than the compared methods.

关键词： Optimal control adaptive dynamic programming system identification neural network

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adaptive dynamic programming for nonaffine nonlinear optimal control problem with state constraints

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NEUROCOMPUTING 2022年 484卷 128-141页

作者： Duan, Jingliang Liu, Zhengyu Li, Shengbo Eben Sun, Qi Jia, Zhenzhong Cheng, Bo Tsinghua Univ Sch Vehicle & Mobil State Key Lab Automot Safety & Energy Beijing 100084 Peoples R China Carnegie Mellon Univ Inst Robot Pittsburgh PA 15213 USA

This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy itera-tion (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi-layer neural networks to directly map the system states to control inputs and value function, respectively. CADP linearizes the constrained optimization problem locally into a quadratically constrained linear pro-gramming problem, and then obtains the optimal update of the policy network by solving its dual prob-lem. A trust region constraint is added to prevent excessive policy update, thus ensuring linearization accuracy. We determine the feasibility of the policy optimization problem by calculating the minimum trust region boundary and update the policy using two recovery rules when infeasible. The vehicle con-trol problem in the path-tracking task is used to demonstrate the effectiveness of this proposed method.(c) 2021 Elsevier B.V. All rights reserved.

关键词： adaptive dynamic programming Optimal control State constraint Reinforcement learning

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adaptive dynamic programming for Stochastic Systems With State and Control Dependent Noise

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第12期61卷 4170-4175页

作者： Bian, Tao Jiang, Yu Jiang, Zhong-Ping NYU Tandon Sch Engn Dept Elect & Comp Engn Control & Networks Lab Brooklyn NY 11201 USA MathWorks Inc Natick MA 01760 USA

In this technical note, the adaptive optimal control problem is investigated for a class of continuous-time stochastic systems subject to multiplicative noise. A novel non-model-based optimal control design methodology is employed to iteratively update the control policy on-line by using directly the data of the system state and input. Both adaptive dynamic programming (ADP) and robust ADP algorithms are developed, along with rigorous stability and convergence analysis. The effectiveness of the obtained methods is illustrated by an example arising from biological sensorimotor control.

关键词： adaptive dynamic programming adaptive optimal control stochastic systems

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adaptive dynamic programming-based adaptive Optimal Tracking Control of a Class of Strict-feedback Nonlinear System

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2023年第4期21卷 1349-1360页

作者： Zhao, Jin-Gang Weifang Univ Inst Intelligent Percept & Control Complex Syst Sch Mach & Automat Weifang 261061 Shandong Peoples R China

This paper proposes a novel scheme to investigate the adaptive optimal tracking control problem of a class of strict-feedback nonlinear system via adaptive dynamic programming (ADP). First of all, by employing backstepping technique, a tracking error system is established. Then, the solution to adaptive optimal tracking control problem of strict-feedback nonlinear system is shown to be obtainable by solving the optimal regulation problem of established tracking error system. The solution of optimal regulation problem can be found by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. In order to solve the HJB equation, a neural network (NN)-based online ADP algorithm is provided. To relax traditional Persistence of Excitation (PE) conditions, the historical and instantaneous state data are used to deign the NN weights tuning law simultaneously. In the provided ADP algorithm, the optimal control input is calculated in a forward-in-time manner without requiring any value or policy iterations. Based on the Lyapunov theory, we demonstrate that uniform ultimate boundedness (UUB) of all the signals in the closed-loop system are guaranteed. Application to the adaptive optimal tracking control of a nonholonomic mobile robot system demonstrates the efficacy of the provided ADP scheme. The designed ADP scheme achieves good tracking performance under different reference signals.

关键词： adaptive dynamic programming nonholonomic mobile robot nonlinear systems strict-feedback tracking control

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adaptive dynamic programming-based design of integrated neural network structure for cooperative control of multiple MIMO nonlinear systems

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NEUROCOMPUTING 2017年 237卷 12-24页

作者： Nguyen Tan Luy Ind Univ Hochiminh City Ho Chi Minh Vietnam

Solving cooperative problems for multi-agent systems, in which the agent's artificial behaviors are similar to naturally biological behaviors of agents in practice, is a major challenge. The problems become more complex if the controlled agents are multi-input and multi-output (MIMO) nonlinear systems lacking knowledge of internal system dynamics and affected by external disturbances. In this paper, firstly, based on adaptive dynamic programming, three neural networks (NNs) (actor/disturber/critic) of control schemes for two-player games are integrated into the structure with only one NN, known as integrated NN (INN), with the aim of reducing computational complexity and waste of resources. Secondly, an INN weight update law and an online control algorithm, which updates parameters in one iterative step, are designed to find H-infinity optimal cooperative control solutions. With the aid of Lyapunov theory, we prove that the INN weight approximation errors and the cooperative tracking errors are uniformly ultimately bounded (UUB), and the system parameters converge to the approximately optimal values. Finally, two simulation studies, one of Which is compared to three-NN structures in existing literature, are carried out to show the effectiveness of the proposed INN structure. (C) 2016 Elsevier B.V. All rights reserved.

关键词： adaptive dynamic programming Neural network Actor-critic Cooperative multi-agent Graph theory

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adaptive dynamic programming-based optimal control of unknown nonaffine nonlinear discrete-time systems with proof of convergence

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NEUROCOMPUTING 2012年 91卷 48-55页

作者： Zhang, Xin Zhang, Huaguang Sun, Qiuye Luo, Yanhong Northeastern Univ Sch Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China

In this paper, a novel neuro-optimal control scheme is proposed for unknown nonaffine nonlinear discrete-time systems by using adaptive dynamic programming (ADP) method. A neuro identifier is established by employing recurrent neural networks (RNNs) model to reconstruct the unknown system dynamics. The convergence of the identification error is proved by using the Lyapunov theory. Then based on the established RNN model, the ADP method is utilized to design the approximate optimal controller. Two neural networks (NNs) are used to implement the iterative algorithm. The convergence of the action NN error and weight estimation errors is demonstrated while considering the NN approximation errors. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme. (C) 2012 Published by Elsevier B.V.

关键词： Optimal control adaptive dynamic programming Recurrent neural network System identification

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