汎関数展開に基づく非線形系の準最適制御

概要

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This paper is concerned with representing the response of non-linear differential systems by functional expansions, and we consider a suboptimal control problem by using this expansions. The use of functional expansions to represent the response of dynamic systems is a well-established concept. Since then functional expansions have played an important role in the modeling of nonlinear systems, both when the underlying system eqations are known and when the system is characterized only by the availability of input-output data. The dynamic system is described by a systems of nonlinear differential equations and the objective is to obtain a local approximation of the system output by a functional expansion operating on the input. Usually, although not always, the exparnsion is a trancated power series. A perturbation methord have been applied to optimal control problem in some class of nonlinear systems. We propose a new perturbation methord which use functional expansions, and apply this method to nonlinear systems which is described by the Kolmogorov-Gabor's nonlinear differential equation. This equation is very universal, and include Duffing's equation, Van der, Pol's Rayleigh's, etc. ... Examples are given to illustrate the method.
山口大学の論文