Given the recent trend in systems theory and in applications towards a synthesis of time and frequencydomain methods, there is a need for an introductory text which treats both state space and frequencydomain aspects in an integrated fashion. Foundations and trends r in systemsand control vol. This chapter presents the formulation of distributed parameter systems in terms of porthamiltonian system. Pdf stability and stabilization of infinitedimensional. Robust output regulation of porthamiltonian systems has been considered by the authors in 10, 11 where rst and evenorder porthamiltonian systems were considered, respectively. It is shown that the zero dynamics for any port hamiltonian system. Pdf in this paper, we consider nonlinear pdes in a porthamiltonian setting based on an underlying jetbundle structure. Based on the dual product, the following linear operator is well defined. Energybased control of nonlinear infinitedimensional.
This chapter presents the formulation of distributed parameter systems in terms of port hamiltonian system. Linear porthamiltonian systems on infinitedimensional spaces. His current research interests include stability, controllability, and control of infinite dimensional systems, in particular for port hamiltonian systems. Since 2011, he also has a oneday per week position in the dynamic and control group, department of mechanical engineering, eindhoven university of technology. This book is the first textbook on infinitedimensional porthamiltonian systems. This combined approach leads to easily verifiable conditions for wellposedness and stability. In the first part it is shown, for different examples of physical systems defined on one dimensional spatial domains, how the dirac structure and the port hamiltonian formulation arise from the description of distributed parameter systems as systems of conservation laws. Infinitedimensional linear systems theory mathematics. We developed a riemannian optimal model reduction method for linear stable porthamiltonian systems. Indeed, it opens up the way to formulate control problems in a way that is different. From a mathematical point of view we will show that the mathematical formalism of port hamiltonian systems provides various useful techniques, ranging from casimir functions, lyapunov function generation, shaping of the dirac structure by composition, and the possibility to combine finitedimensional and infinite dimensional systems.
Pdf energybased control of nonlinear infinitedimensional. Infinite dimensional port hamiltonian representation of reaction. Wellposedness and stability for interconnection structures of port. In the next session we discuss a special class of state space models. On exact controllability of infinitedimensional linear. Ppt infinitedimensional linear port hamiltonian systems. Infinitedimensional porthamiltonian systems springerlink. Her current research interests include the area of infinitedimensional systems and operator theory, particularly wellposed linear systems and porthamiltonian systems. Infinitedimensional linear port hamiltonian systems a state space approach christian harkort and joachim deutscher cdps 2011, wuppertal 20. This class is general enough to include models of beams and waves as well as. In the first part it is shown, for different examples of physical systems defined on onedimensional spatial domains, how the dirac structure and the porthamiltonian formulation arise from the description of distributed parameter systems as systems of. An abstract functional analytical approach is combined with the physical approach to hamiltonian systems. We discuss in this chapter a number of approaches to exploit the model structure of porthamiltonian systems for control purposes. Control of finitedimensional porthamiltonian systems.
Outside robust regulation, stability, stabilization and dynamic boundary control of porthamiltonian systems have been considered, e. Robust regulation of infinitedimensional porthamiltonian. Introduction to infinitedimensional systems theory a. Pdf infinite dimensional linear control systems download. Stabilisation of infinitedimensional porthamiltonian systems via. Infinite dimensional porthamiltonian systems, networks of. Also part of the linear operators and linear systems book sub series lols, volume 223. Curtain and of linear porthamiltonian systems on infinitedimensional spaces with b. Pdf stability and stabilization of infinitedimensional linear port. This book provides a selfcontained introduction to the theory of infinitedimensional systems theory and its applications to porthamiltonian systems. He is the coauthor of many papers and of the text books an introduction to linear infinitedimensional system theory, springer verlag, 1995, with r. Infinitedimensional linear porthamiltonian systems on a 1d spatial domain with full boundary control and without internal damping are studied. Stability and stabilization of linear porthamiltonian systems on infinitedimensional spaces are investigated.
Klappentext zu linear porthamiltonian systems on infinitedimensional spaces this book provides a selfcontained introduction to the theory of infinitedimensional systems theory and its applications to porthamiltonian systems. Actually, the formulation of physical control systems as porthamiltonian systems may lead in some cases to a rethinking of standard control paradigms. The textbook starts with elementary known results, then progresses smoothly to. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current. Since 2010, she has been with the university of wuppertal, germany, where she is a full professor in analysis. Linear porthamiltonian systems on infinitedimensional. The model reduction problem was formulated as an optimization problem on the product manifold of the set of skew symmetric matrices, the manifold of the symmetric positive definite matrices, and euclidean space. Port hamiltonian formulation of infinite dimensional systems i. Pdf stability and stabilization of linear porthamiltonian systems on infinite dimensional spaces are investigated. We developed a riemannian optimal model reduction method for linear stable port hamiltonian systems. Stabilization of infinite dimensional porthamiltonian. Request pdf linear porthamiltonian systems on infinitedimensional spaces 1 introduction. Nov 19, 2017 port hamiltonian systems with inv ertible feedthrough as another port hamiltonian system on the same state space is given. Download infinite dimensional systems is now an established area of research.
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