Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
An Approximate Realization of Nonlinear H Control Based on Hamilton-Jacobi Equation
Masakatsu KAWATANaomitsu SHIMAZUKazuo INOUE
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1998 Volume 11 Issue 7 Pages 401-410

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Abstract

In this paper, a novel numerical approach of the Hamilton-Jacobi Equation (HJE) in the nonlinear H control problems is proposed. First of all, it is assumed that the solution of the HJE is an extended quadratic form, and a state-dependent Riccati Equation (sRE) is derived. Next, the solution of the sRE is approximated with a polynominal matrix by the least square method, and the approximated solution of the HJE is selected as the extended quadratic form approximately corresponding to this polynominal. Our proposal is applied to an inverted pendulum system, and its validity is shown through simulations as compared with the linear H control and the nonlinearH control based on the conventional methods.

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