Generalized Hamilton-Jacobi-Isaacs formulation-based neural network H∞ control for constrained input nonlinear systems

Authors:
Yuzhu Huang;Derong Liu;Qinglai Wei
Affiliations:
State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China
Venue:
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
Year:
2012

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Abstract

In this paper, the nearly H∞ optimal control solution for discrete-time (DT) constrained input nonlinear systems is considered. First, to deal with the input constraints, a quasi-norm performance index function is introduced. Second, the corresponding constrained Hamilton-Jacobi-Isaacs (HJI) equation is formulated, and then the quasi L2-gain analysis of the nonlinear system is employed. Third, an iterative algorithm based on the game theoretic interpretation of the generalized HJI (GHJI) equation by using neural networks (NNs) is presented. Moreover, the convergence of the algorithm to the optimal saddle point solution is proved, and the stability is also proved. Finally, a simulation example is given to illustrate the performance of the proposed method.