Tracking and regulation in the behavioral framework

Abstract

Given a plant together with an exosystem generating the disturbances and the reference signals, the problem of asymptotic tracking and regulation is to find a controller such that the plant variable tracks the reference signal regardless of the disturbance acting on the system. If a controller achieves this design objective, we call it a regulator for the plant with respect to the given exosystem. In this paper, we formulate the asymptotic tracking and regulation problem in the behavioral framework, with control by interconnection.

Synthesis and application of a real‐time model‐free behavioral controller with bumpless switching mechanism

“…Theoretically, in [9,Theorem 16], the so-called regularity of interconnection is imposed for the 'design' of the canonical controller. The paper [10] established algorithms for the computation of controllers that regularly implement a given desired behavior, while solutions by designing controllers in the behavioral framework, of the so-called asymptotic tracking and regulation problem, are presented in [11]. Nevertheless, the reported computation procedure in the aforesaid literature requires the knowledge of plant parameters in real time.…”

A Generalized Tracking and Disturbance Rejection Problem for Multidimensional Behaviors

“…Stimulated by two milestone contributions [20,21], dealing with the control of one-dimensional behaviours, a long stream of research on these topics flourished, dealing either with one-dimensional (1D) behaviours (e.g. [1,3,4,12]) or with the wider class of multidimensional (nD) behaviours [5,6,8,13,18].…”

“…The tracking and disturbance rejection problem for 1D behaviours was first addressed in [3], where necessary and sufficient conditions for the problem solvability, under the assumption that the exogenous system generating both the reference signal and the disturbance is autonomous, have been provided. Interestingly enough, the solvability conditions involve the well-known internal model principle, first pointed out in the behavioural context for observers in [19].…”

On real-time smooth interconnection of online synthesized controllers in the behavioral framework

“…Trentelman, Yoe, and Praagman (2007) established algorithms for the computation of controllers that regularly implement a given desired behavior. While solutions, by designing controllers in the behavioral framework, of the so-called asymptotic tracking and regulation problem are presented in Fiaz, Takaba, and Trentelman (2011). Nevertheless, the reported computation procedure in the aforesaid literature requires the knowledge of plant parameters in real-time.…”