Towards fully probabilistic control design

Miroslav Kárný

doi:10.1016/S0005-1098(96)80009-4

Towards fully probabilistic control design

1996-12-01

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Miroslav Kárný *

DOI：10.1016/S0005-1098(96)80009-4

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Control design for stochastic systems is traditionally based on optimization of the expected value of a suitably chosen loss function. Despite the theoretical attractiveness of such a design methodology, its applicability is very limited owing to its computational overhead. Thus it is worthwhile to seek an alternative formulation resulting in a more tractable design. In this paper, an alternative is presented that leads to a simpler form of design equations. The proposed controller minimizes the Kullback-Leibler distance between the actual probabilistic descriptions of the closed-loop behaviour and the desired one. Its explicit randomized form depends on the solution of a functional equation with a simpler structure than that of the general dynamic programming equations. A basic paradigm is proposed, and the resulting algorithm is discussed. For illustration purposes, it is applied to linear Gaussian systems, and the desired result is obtained: The optimal controller is determined by a discrete-time Riccati equation. Copyright (C) 1996 Elsevier Science Ltd.

Keyword:

stochastic control design

Kullback-Leibler distance measure

probability density function

dynamic programming

Towards fully probabilistic control design

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