Strongly autonomous interconnections and stabilization of 2D behaviors

Napp, Diego; Rocha, Paula

doi:10.1002/asjc.170

Cited by 6 publications

(4 citation statements)

References 28 publications

(70 reference statements)

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“…Let C c be the controllable part of C. Obviously, B (w,c) ∩ C c ⊂ B (w,c) ∩ C implies π w (B (w,c) ∩ C c ) ⊂ π w (B (w,c) ∩ C) and therefore π w (B (w,c) ∩ C c ) is S-stable as π w (B (w,c) ∩ C) is S-stable. Moreover, the intersection of B (w,c) and C c is regular by [9,Prop. 11].…”

Section: Corollary 15 Let B (Wc) Be a Behavior And S A Stability Conmentioning

confidence: 93%

“…Proof The equivalence of between (1) and (2) has been shown in [9]. Assume now that B (w,c) is S-stabilizable by regular partial interconnection.…”

Section: Corollary 15 Let B (Wc) Be a Behavior And S A Stability Conmentioning

confidence: 95%

“…Hence, a finite dimensional behavior is implementable by regular full interconnection from kerL. According to [9,Theorem 16] we conclude that the controllable part of kerL is rectifiable. But since kerL is controllable (being L an MLA of R), it coincides with its controllable part and then kerL is itself rectifiable, or in other words, L is ZP.…”

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confidence: 92%

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Stabilization of discrete 2D behaviors by regular partial interconnection

Napp

Rocha

2011

Math. Control Signals Syst.

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In this work, we consider linear, shift-invariant and complete twodimensional (2D) discrete systems from a behavioral point of view. In particular, we examine behaviors with two types of variables: the variables that we are interested to control (the to-be-controlled variables) and the variables on which we are allowed to enforce restrictions (the control variables). The main purpose of this contribution is to derive necessary and sufficient conditions for the stabilization of the to-be-controlled variables by 'attaching' a controller to the control variables. This problem turns out to be related to the decomposition of a given behavior into the sum of two sub-behaviors. Moreover, we show that under certain conditions, it is possible to obtain a constructive solution and characterize the structure of the to-be-controlled behavior. Mathematics Subject Classification (2000)93B05 · 93B07 · 93B25 · 93C05 · 93C35 · 93C65 · 93D15

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Section: Corollary 15 Let B (Wc) Be a Behavior And S A Stability Conmentioning

confidence: 93%

“…Proof The equivalence of between (1) and (2) has been shown in [9]. Assume now that B (w,c) is S-stabilizable by regular partial interconnection.…”

Section: Corollary 15 Let B (Wc) Be a Behavior And S A Stability Conmentioning

confidence: 95%

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Stabilization of discrete 2D behaviors by regular partial interconnection

Napp

Rocha

2011

Math. Control Signals Syst.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

A Generalized Tracking and Disturbance Rejection Problem for Multidimensional Behaviors

Scheicher

Blumthaler

Bisiacco

et al. 2015

SIAM J. Control Optim.

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In this paper we study a generalized tracking and disturbance rejection problem for multidimensional behaviours. Given a multidimensional plant, our first goal is to design a compensator to be connected to the plant through regular partial interconnection, in such a way that the overall controlled system is autonomous and stable, when no exogenous signal acts on the system. On the other hand, when exogenous signals affect the controlled system evolution, we want to impose that a suitable linear combination of the overall system trajectories is "negligibile" in a sense we will clarify within the paper. This problem setup formalizes a number of classical control problems, first of all tracking of some (reference) signal together with rejection of another (disturbance) signal. The adopted approach is extremely general and it is based on the idea of describing all behaviour trajectories as the sum of a "transient signal" and a "steady state" component, a decomposition that relies on Gabriel's localization theory. Necessary and sufficient conditions for the problem solvability are provided, and the compensators that satisfy the control goal are characterized in terms of an internal model condition. Furthermore, a parametrization of all such compensators is provided.

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Implementation of Behavioral Systems

Napp

Rocha

2015

Mathematical Control Theory II

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In this paper, we study control by interconnection of a given linear differential system (the plant behavior) with a suitable controller. The problem formulations and their solutions are completely representation free, and specified only in terms of the system dynamics. A controller is a system that constrains the plant behavior through a certain set of variables. In this context, there are two main situations to be considered: either all the system variables are available for control, i.e., are control variables (full control) or only some of the variables are control variables (partial control). For systems evolving over a time domain (1D) the problems of implementability by partial (regular) interconnection are well-understood. In this paper we study why similar results are not valid in the multidimensional (nD) case. Finally, we study two important classes of controllers, namely, canonical controllers and regular controllers.

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Strongly autonomous interconnections and stabilization of 2D behaviors

Cited by 6 publications

References 28 publications

Stabilization of discrete 2D behaviors by regular partial interconnection

Stabilization of discrete 2D behaviors by regular partial interconnection

A Generalized Tracking and Disturbance Rejection Problem for Multidimensional Behaviors

Implementation of Behavioral Systems

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