Set invariance in control
type: Item
instance of: scholarly article
title: Set invariance in control
zbMATH Open document ID: 0935.93005
DOI: 10.1016/S0005-1098(99)00113-2
author: Franco Blanchini
published in: Automatica
publication date: 2000-05-09T00:00:00Z
review text: This is an overview paper on the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems, which contains the following sections. (1) Introduction. (2) Basic definitions of (robustly) positively invariant sets, (robustly) controlled invariant sets for systems and some other related concepts. (3) Basic results including some classical positive invariance conditions and the relation between positively invariant sets and Lyapunov functions. In particular, it is shown how a convex and compact invariant set containing the origin in its interior can ``shape'' a Lyapunov function. (4) Special families of positively invariant sets, which presents the main properties of the two most currently used families of candidate invariant sets: ellipsoids and polytopes. Invariant sets of some other types are also roughly reviewed. (5) Construction of invariant sets and control synthesis, in which some basic construction techniques are reviewed and the structure of the controllers that can be associated to controlled-invariant sets are investigated. (6) Applications of set invariance, which was classified into six subsections: Invariant set as a theoretical tool; invariance and control problems with time-domain constraints; invariance and robustness; disturbance rejection; performance analysis via invariant sets and the receding horizon control. (7) Concluding remarks with some current research directions. There are 176 publications as references, most of them are very recently published.
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93B50
zbMATH DE Number: 1355381
zbMATH Keywords: positively invariant sets
zbMATH Keywords: synthesis
zbMATH Keywords: controlled invariant set
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: time-domain constraints
zbMATH Keywords: robustness
zbMATH Keywords: disturbance rejection
zbMATH Keywords: performance analysis
zbMATH Keywords: receding horizon control
Wikidata QID: Q56851766
reviewed by: Wenming Bian
MaRDI profile type: Publication
full work available at URL: s0005-1098(99)00113-2
OpenAlex ID: W2171505650
description: scientific article; zbMATH DE number 1355381