Stability analysis and controller synthesis for hybrid dynamical systems

W.P.M.H. Heemels, B. Schutter, de, J. Lunze, M. Lazar

Research output: Contribution to journalArticleAcademicpeer-review

39 Citations (Scopus)
2 Downloads (Pure)

Abstract

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.
Original languageEnglish
Pages (from-to)4937-4960
Number of pages23
JournalPhilosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences
Volume368
Issue number1930
DOIs
Publication statusPublished - 2010

Fingerprint

Hybrid Dynamical Systems
dynamical systems
Stability Analysis
controllers
Dynamical systems
Synthesis
Hybrid systems
Controller
Controllers
logic
mathematical models
synthesis
Mathematical models
Hybrid Systems
difference equations
decision making
System theory
Difference equations
Mathematical Model
Logic

Cite this

@article{ac0e5fdbd8a740728f2da54a87d16173,
title = "Stability analysis and controller synthesis for hybrid dynamical systems",
abstract = "Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.",
author = "W.P.M.H. Heemels and {Schutter, de}, B. and J. Lunze and M. Lazar",
year = "2010",
doi = "10.1098/rsta.2010.0187",
language = "English",
volume = "368",
pages = "4937--4960",
journal = "Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences",
issn = "1364-503X",
publisher = "Royal Society of London",
number = "1930",

}

Stability analysis and controller synthesis for hybrid dynamical systems. / Heemels, W.P.M.H.; Schutter, de, B.; Lunze, J.; Lazar, M.

In: Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 368, No. 1930, 2010, p. 4937-4960.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Stability analysis and controller synthesis for hybrid dynamical systems

AU - Heemels, W.P.M.H.

AU - Schutter, de, B.

AU - Lunze, J.

AU - Lazar, M.

PY - 2010

Y1 - 2010

N2 - Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

AB - Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

U2 - 10.1098/rsta.2010.0187

DO - 10.1098/rsta.2010.0187

M3 - Article

C2 - 20921005

VL - 368

SP - 4937

EP - 4960

JO - Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences

SN - 1364-503X

IS - 1930

ER -