A transformation approach for solving the Hamilton-Jacobi-Bellman equation in H2 deterministic and stochastic optimal control of affine nonlinear systems

被引：19
|
作者：
Aliyu, MDS [1 ]
机构：
[1] Louisiana State Univ, Dept Elect & Comp Engn, Baton Rouge, LA 70803 USA
来源：
AUTOMATICA | 2003年 / 39卷 / 07期
关键词：
nonlinear systems; Hamilton-Jacobi-Bellman equation; Lyapunov equation; viscosity solution; stochastic control;
D O I：
10.1016/S0005-1098(03)00080-3
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 present a transformation approach for solving the Hamilton-Jacobi-Bellman equations (HJBEs) arising in H-2 or quadratic-cost control of nonlinear deterministic and stochastic systems. We show that the HJBE can be solved analogously to a scalar quadratic equation, and we give a parameterization of solutions to the HJBE characterizing the solution of the optimal control problem. The procedure is also generalized to include nonsmooth or viscosity solutions of the (S)HJBE. (C) 2003 Elsevier Science Ltd. All rights reserved.
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页码：1243 / 1249
页数：7
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