An Iterative Relaxation Approach to the Solution of the Hamilton-Jacobi-Bellman-Isaacs Equation in Nonlinear Optimal Control

被引：18
作者：
Aliyu, M. D. S. [1 ]
机构：
[1] King Faisal Univ, Dept Elect Engn, Al Hasa 31982, Saudi Arabia
来源：
IEEE-CAA JOURNAL OF AUTOMATICA SINICA | 2018年 / 5卷 / 01期
关键词：
Affine nonlinear system; bounded continuous function; convergence; Hamilton-Jacobi-Bellman-Isaacs equation; Lyapunov equation; relaxation method; Riccati equation; ALGEBRAIC RICCATI; STATE-FEEDBACK; ALGORITHM;
D O I：
10.1109/JAS.2017.7510682
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation (HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.
引用
收藏
页码：360 / 366
页数：7
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