Brief paper: An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games

Authors:
Huaguang Zhang;Qinglai Wei;Derong Liu
Affiliations:
School of Information Science and Engineering, Northeastern University, Shenyang 110004, PR China;Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China;Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

In this paper, a new iterative adaptive dynamic programming (ADP) method is proposed to solve a class of continuous-time nonlinear two-person zero-sum differential games. The idea is to use the ADP technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero-sum differential games. If the saddle point does not exist, the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum. Stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved. Two simulation examples are given to illustrate the performance of the proposed method.