TOWARDS FULLY PROBABILISTIC CONTROL DESIGN

Control design for stochastic systems is traditionally based on optimi zation of the expected value of a suitably chosen loss function. Despi te the theoretical attractiveness of such a design methodology, its ap plicability is very limited owing to its computational overhead. Thus it is worthwhile to seek an alternative formulation resulting in a mor e tractable design. In this paper, an alternative is presented that le ads to a simpler form of design equations. The proposed controller min imizes the Kullback-Leibler distance between the actual probabilistic descriptions of the closed-loop behaviour and the desired one. Its exp licit 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 Gauss ian systems, and the desired result is obtained: The optimal controlle r is determined by a discrete-time Riccati equation. Copyright (C) 199 6 Elsevier Science Ltd.