Overview
ABSTRACT
This tutorial presents an introduction to the analysis and design of systems with finite/fixed-time convergence. The main attention is paid to finite-time and fixed-time convergent dynamics. Two large groups of approaches to the analysis/synthesis of this type of convergence are described: based on Lyapunov functions and the theory of homogeneous systems. Some popular control and estimation algorithms, which have accelerated convergence rates, are reviewed. The discretization problems of finite/fixed time convergent systems are discussed. All given results are illustrated by simple examples (scalar or planar).
Read this article from a comprehensive knowledge base, updated and supplemented with articles reviewed by scientific committees.
Read the articleAUTHORS
-
Denis EFIMOV : Chercheur - Affiliation Inria, Univ. Lille, CNRS, UMR 9189 – CRIStAL, F-59000 Lille, France
-
Andrey POLYAKOV : Chercheur - Affiliation Inria, Univ. Lille, CNRS, UMR 9189 – CRIStAL, F-59000 Lille, France
INTRODUCTION
Lhe theory of control is used to design the regulators for dynamical systems, to estimate the internal state variables or parameters of the plants, to monitor and detect the faults, in many domains of engineering, technical or natural sciences. Important quality requirements, which are associated with these designs, deal with the time of convergence of the estimation or control errors to zero, and their robustness with respect to unmodeled disturbances and measurement noises, or delays in actuation or sensing. To this end, the concepts of convergence in a finite or in a fixed time show their importance, since imposing these acceleration constraints on the closed-loop dynamics also implies remarkable robustness features of these systems. This tutorial provides the basic motivations, definitions of properties finite-time and fixed-time convergent systems, with corresponding design of controls and state observers. A special attention is paid to discrete-time implementation of this kind of algorithms, which is particularly challenging. The exposition is accompanied by illustrative simple examples.
Exclusive to subscribers. 97% yet to be discovered!
Already subscribed? Log in!
KEYWORDS
Automatic control | State estimation | Finite-time stability | Fixed-time stability | Homogeneous systems
Fixed-time and finite-time control and estimation
Introduction and motivation
Bibliographical sources
Exclusive to subscribers. 97% yet to be discovered!
Already subscribed? Log in!
Article included in this offer
"Control and systems engineering"
(
145 articles
)
Updated and enriched with articles validated by our scientific committees
A set of exclusive tools to complement the resources
