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Online optimal control of nonlinear discrete-time systems using approximate dynamic programming

控制理论与应用（英文版） 2011年第3期9卷 361-369页

作者： Travis DIERKS sarangapani jagannathan DRS Sustainment Systems Inc.201 Evans Lane Department of Electrical and Computer Engineering Missouri University of Science and Technology

In this paper,the optimal control of a class of general affine nonlinear discrete-time(DT) systems is undertaken by solving the Hamilton Jacobi-Bellman(HJB) equation online and forward in *** proposed approach,referred normally as adaptive or approximate dynamic programming(ADP),uses online approximators(OLAs) to solve the infinite horizon optimal regulation and tracking control problems for affine nonlinear DT systems in the presence of unknown internal *** the regulation and tracking controllers are designed using OLAs to obtain the optimal feedback control signal and its associated cost ***,the tracking controller design entails a feedforward portion that is derived and approximated using an additional OLA for steady state *** update laws for tuning the unknown parameters of the OLAs online are *** techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signals approach the optimal control inputs with small bounded *** the absence of OLA reconstruction errors,an optimal control is *** results verify that all OLA parameter estimates remain bounded,and the proposed OLA-based optimal control scheme tunes itself to reduce the cost HJB equation.

关键词： Online nonlinear optimal control Hamilton Jacobi-Bellman Online approximators Discrete-time systems

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Near Optimal Output Feedback Control of Nonlinear Discrete-time Systems Based on Reinforcement Neural Network Learning

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IEEE/CAA Journal of Automatica Sinica 2014年第4期1卷 372-384页

作者： Qiming Zhao Hao Xu sarangapani jagannathan the DENSO International America Inc. with the College of Science and Engineering Texas A&M University the Department of Electrical&Computer Engineering Missouri University of Science and Technology

In this paper, the output feedback based finitehorizon near optimal regulation of nonlinear affine discretetime systems with unknown system dynamics is considered by using neural networks(NNs) to approximate Hamilton-JacobiBellman(HJB) equation solution. First, a NN-based Luenberger observer is proposed to reconstruct both the system states and the control coefficient matrix. Next, reinforcement learning methodology with actor-critic structure is utilized to approximate the time-varying solution, referred to as the value function, of the HJB equation by using a NN. To properly satisfy the terminal constraint, a new error term is defined and incorporated in the NN update law so that the terminal constraint error is also minimized over time. The NN with constant weights and timedependent activation function is employed to approximate the time-varying value function which is subsequently utilized to generate the finite-horizon near optimal control policy due to NN reconstruction errors. The proposed scheme functions in a forward-in-time manner without offline training phase. Lyapunov analysis is used to investigate the stability of the overall closedloop system. Simulation results are given to show the effectiveness and feasibility of the proposed method.

关键词： Artificial neural networks Observers Optimal control Learning (artificial intelligence) Approximation methods Feedback Nonlinear dynamical systems

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