Controllability and optimization for differential linear repetitive processes

Abstract

Differential linear repetitive processes are a class of continuous-discrete 2D systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. In this paper we develop an operator theory approach for the study of basic systems theoretic structural and control properties of these processes. In particular, we first develop a characterization of the range space of an operator generated by dynamics of the processes under consideration and use it to characterize a controllability property. Also we extend this operator setting to produce new results for a (again physically relevant) linear-quadratic optimization problem for these processes and the resulting optimal feedback control law.

Optimisation problem for some class of hybrid differential-difference systems with delay

“…We denote by U T ⋅ ( ) the set of the all T-admissible control functions for the system (1) -(3) corresponding to the set  in (7). By analogy with [9; 10] it can be shown that  is the convex set.…”

“…Moreover, it is already known that [6] links between some types of linear repetitive processes and delay systems, which can, where appropriate, be used to great effect in the control related analysis of these processes. This paper is based on the work [7] and gives some new results on optimisation theory for delayed differential-difference linear processes. There are only a few research works in the literature devoted to optimisation theory (see, for example [8], and references therein).…”