Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming

Authors:
Ding Wang;Derong Liu;Qinglai Wei;Dongbin Zhao;Ning Jin
Affiliations:
State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China;State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China;State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China;State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China;Department of Electrical and Computer Engineering, University of Illinois, Chicago, IL 60607, USA
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

An intelligent-optimal control scheme for unknown nonaffine nonlinear discrete-time systems with discount factor in the cost function is developed in this paper. The iterative adaptive dynamic programming algorithm is introduced to solve the optimal control problem with convergence analysis. Then, the implementation of the iterative algorithm via globalized dual heuristic programming technique is presented by using three neural networks, which will approximate at each iteration the cost function, the control law, and the unknown nonlinear system, respectively. In addition, two simulation examples are provided to verify the effectiveness of the developed optimal control approach.