期刊
AUTOMATICA
卷 45, 期 4, 页码 881-888出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2008.11.006
关键词
HJBI; Iterative; Exponentially stable
In this paper, an iterative algorithm to solve Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations for a broad class of nonlinear control systems is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton-Jacobi-Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local convergence of the algorithm and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the effectiveness of the proposed algorithm. A game theoretical interpretation of the algorithm is given. (C) 2009 Elsevier Ltd. All rights reserved.
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