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

TL;DR

This paper investigates optimal guaranteed control strategies for systems with disturbances constrained by $L_p$-compact sets, establishing conditions for optimality and methods for constructing effective strategies.

Contribution

It introduces a condition on the system and methods for constructing optimal strategies under $L_p$-compact disturbance constraints, ensuring non-improvability of guaranteed results.

Findings

Optimal guaranteed results coincide with quasi-strategies.

Additional conditions improve control algorithm effectiveness.

Constructive methods for optimal strategies are provided.

Abstract

The paper deals with the problem of optimization of a guaranteed (worst case) result for a control system described by an ordinary differential equation. 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 side that forms the control actions. The controlling side uses positional full-memory strategies and does not observe the disturbance. When the constraints family consists of $L_p$-compact sets the optimal guaranteed result is non-improvable in the sense that it coincides with that obtained in the class of quasi-strategies -- nonanticipatory transformations of disturbances into controls. In this paper for the effectiveness of implemented control algorithm an additional condition on the system and appropriate ways of constructing an optimal strategy are specified.