Some Inverse Problems in Optimal Control
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概要
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The inverse problem in optimal control is to find all possible performance indices or loss functions under a given optimal control law. The solutions of this problem are expected to offer general properties of optimal control systems as well as useful informations about the relation between the optimal control theory and the conventional feedback theory.In this paper, the author proposes a new method for solving this problem where the loss functions are previously assumed to have a quadratic form of input variables.He applies this method to the feedback system where a multi-input linear plant is governed by a linear control law. The minimal loss function in this case is expressed not only by a quadratic form with some arbitrariness but also by an arbitrary scalar-valued function which is restricted by a certain constraint depending on the plant characteristic. This arbitrariness results from the fact that there may be some performance indices independent of the manipulating input. From these observations, a new concept "uncontrollability of performance index" is introduced. This concept is considered as one of the fundamental properties of optimal control systems.Furthermore, this paper presents a necessary and sufficient condition in the frequency domain for multivariable stationary feedback systems to be optimal in the sense that the minimal quadratic loss function becomes nonnegative or positive definite. This is an extension of Kalman's result for single-input feedback systems and is related to the concept of parameter sensitivity in the conventional feedback theory.
- 公益社団法人 計測自動制御学会の論文
公益社団法人 計測自動制御学会 | 論文
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