Foundations and Trends® in Systems and Control > Vol 1 > Issue 2-3

Port-Hamiltonian Systems Theory: An Introductory Overview

By Arjan van der Schaft, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, The Netherlands, a.j.van.der.schaft@rug.nl | Dimitri Jeltsema, Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands, d.jeltsema@tudelft.nl

 
Suggested Citation
Arjan van der Schaft and Dimitri Jeltsema (2014), "Port-Hamiltonian Systems Theory: An Introductory Overview", Foundations and Trends® in Systems and Control: Vol. 1: No. 2-3, pp 173-378. http://dx.doi.org/10.1561/2600000002

Publication Date: 24 Jun 2014
© 2014 A. van der Schaft and D. Jeltsema
 
Subjects
Systems Theory
 
Keywords
Port-Hamiltonian systems, Network modeling, Multi-physics systems, Geometric dynamics, Passivity-based control
 

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In this article:
1. Introduction 
2. From Modeling to Port-Hamiltonian Systems 
3. Port-Hamiltonian Systems on Manifolds 
4. Input-State-Output Port-Hamiltonian Systems 
5. Representations of Dirac Structures 
6. Interconnection of Port-Hamiltonian Systems 
7. Port-Hamiltonian Systems and Passivity 
8. Conserved Quantities and Algebraic Constraints 
9. Incrementally Port-Hamiltonian Systems 
10. Input-Output Hamiltonian Systems 
11. Pseudo-Gradient Representations 
12. Port-Hamiltonian Systems on Graphs 
13. Switching Port-Hamiltonian Systems 
14. Distributed-Parameter Systems 
15. Control of Port-Hamiltonian Systems 
References 

Abstract

An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief introduction to control of port-Hamiltonian systems.

DOI:10.1561/2600000002

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ISBN: 978-1-60198-786-0
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Table of contents:
1. Introduction
2. From Modeling to Port-Hamiltonian Systems
3. Port-Hamiltonian Systems on Manifolds
4. Input-State-Output Port-Hamiltonian Systems
5. Representations of Dirac Structures
6. Interconnection of Port-Hamiltonian Systems
7. Port-Hamiltonian Systems and Passivity
8. Conserved Quantities and Algebraic Constraints
9. Incrementally Port-Hamiltonian Systems
10. Input-Output Hamiltonian Systems
11. Pseudo-Gradient Representations
12. Port-Hamiltonian Systems on Graphs
13. Switching Port-Hamiltonian Systems
14. Distributed-Parameter Systems
15. Control of Port-Hamiltonian Systems
References

Port-Hamiltonian Systems Theory

Apart from offering a systematic and insightful framework for modeling and analysis of multi-physics systems, port-Hamiltonian systems theory provides a natural starting point for control. Especially in the nonlinear case it is widely recognized that physical properties of the system - such as balance and conservation laws and energy considerations - should be exploited and respected in the design of control laws which are robust and physically interpretable.

Port-Hamiltonian Systems Theory: An Introductory Overview provides a concise and easily accessible description of the foundations underpinning the subject, and goes on to emphasize novel developments in the field that will be of interest to a broad range of researchers. The tutorial style makes it suitable for use in a course and by students.

 
SYS-002