On non-improvability of full-memory strategies in problems of optimization of the guaranteed result

Abstract

The paper addresses the problem of optimization of a guaranteed (worst case) result for a control system driven by a controlling side in presence of a dynamical disturbance. The disturbances as functions of time are subject to functional constraints belonging to a given family of constraints. The latter family is known to the controlling side that does not observe the disturbance and uses full-memory strategies to form the control actions. The study is focused on the case where disturbance varies in open-loop disturbances chosen in advance and the case where the disturbances are restricted to a $L_2$--compact set fixed in advance but unknown to the controlling side. In these cases it is shown that the optimal guaranteed result is non-improvable in the sense that it coincides with that obtained in the class of quasi-strategies -- nonantisipatory transformations of disturbances into controls. An $\epsilon$--optimal full-memory strategy is constructed. An illustrative nonlinear example is given.

arXiv commentThis article is the English version of the Russian publication: D.A Serkov. On non-improvability of full--memory strategies in problems of optimization of the guaranteed result. Trudy Inst. Mat. i Mekh. UrO RAN, 20(3), 2014

Cited by in corpus (1)

• Guaranteed control design under $L_p$-compact constraints on the disturbance