Consistent approximations of the Zeno behaviour in affine-type switched dynamic systems
type: Item
instance of: scholarly article
title: Consistent approximations of the Zeno behaviour in affine-type switched dynamic systems
zbMATH Open document ID: 1470.34130
DOI: 10.1155/2016/2091526
author: Vadim Azhmyakov
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes.
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34A38
Mathematics Subject Classification ID: 93C30
zbMATH DE Number: 6929351
describes a project that uses: UMDES
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/2091526
OpenAlex ID: W2411609464
Wikidata QID: Q59121511
cites work: A unified framework for hybrid control: model and optimal control theory
cites work: Introduction to Discrete Event Systems
cites work: Switching in systems and control
cites work: Attractive ellipsoids in robust control
cites work: The Sensitivity of Hybrid Systems Optimal Cost Functions with Respect to Switching Manifold Parameters
cites work: An introduction to hybrid dynamical systems
cites work: Perturbation analysis of communication networks with feedback control using stochastic hybrid models
cites work: On-Line Optimization of Switched-Mode Dynamical Systems
cites work: Hybrid systems tools for compiling controllers for cyber-physical systems
cites work: Supervisory control of hybrid systems within a behavioural framework
cites work: On the Hybrid Optimal Control Problem: Theory and Algorithms
cites work: Stability and Completion of Zeno Equilibria in Lagrangian Hybrid Systems
cites work: On the regularization of Zeno hybrid automata
cites work: Sufficient Conditions for Zeno Behavior in Lagrangian Hybrid Systems
cites work: Lyapunov Theory for Zeno Stability
cites work: Zeno hybrid systems
cites work: Q4038702
cites work: Applications of the strong approximability property to a class of affine switched systems and to relaxed differential equations with affine structure
cites work: Approximability of nonlinear affine control systems
cites work: Theory of chattering control with applications to astronautics, robotics, economics, and engineering
cites work: Theoretical Numerical Analysis
cites work: Variational Analysis in Sobolev andBVSpaces
cites work: Q5667036
cites work: Q3996569
cites work: Nonlinear systems.
cites work: On the set-valued approach to optimal control of sliding mode processes
cites work: Sliding modes in control and optimization. Transl. from the Russian
cites work: Q3511145
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description: scientific article; zbMATH DE number 6929351