Successive approximation solution of the HJI equation

Author

Wise, Kevin A. ; Sedwick, Jack L.

Author_Institution

McDonnell Douglas Aerosp.-East, St. Louis, MO, USA

Volume

2

fYear

1994

Firstpage

1387

Abstract

A successive approximation solution approach is used to solve the Hamilton-Jacobi-Isaacs partial differential Riccati equation that arises in nonlinear H_∞ optimal control problems. The method of characteristics is used to form integral expressions used to solve the partial differential Riccati equation. Successive approximations are then used to approximate the solution to these integral expressions. Two examples in which the optimal control is known are presented. These examples outline the approximate solution approach and provide insight into what degree of approximation is needed

Keywords

H^∞ control; Riccati equations; approximation theory; nonlinear control systems; nonlinear differential equations; state feedback; HJI equation; Hamilton-Jacobi-Isaacs partial differential Riccati equation; integral expressions; method of characteristics; nonlinear H_∞ optimal control; successive approximation; Attenuation; Differential algebraic equations; Differential equations; Integral equations; Nonlinear equations; Nonlinear systems; Optimal control; Riccati equations; Stability; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on

Conference_Location

Lake Buena Vista, FL

Print_ISBN

0-7803-1968-0

Type

conf

DOI

10.1109/CDC.1994.411255

Filename

411255