A formulation by Minimization of Differential Entropy for Optimal Control System

Masayuki GOTOH  Shigeichi HIRASAWA  Nobuhiko TAWARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.4   pp.569-577
Publication Date: 1996/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
control theory,  differential entropy,  optimal regulator control,  minimum entropy control,  

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This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2} + N{v(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.