Conservation Laws and Lumped System Dynamics
Physical systems modeling, aimed at network modeling of complex multi-physics systems, has especially flourished in the fifties and sixties of the 20-th century, see e.g. [11, 12] and references provided therein. With the reinforcement of the ’systems’ legacy in Systems & Control, the growing recognition that ’control’ is not confined to developing algorithms for processing the measurements of the system into control signals (but instead is concerned with the design of the total controlled system), and facing the complexity of modern technological and natural systems, systematic methods for physical systems modeling of large-scale lumpedand distributed-parameter systems capturing their basic physical characteristics are needed more than ever.
KeywordsBoundary Current Boundary Vertex Oriented Graph Open Graph Dirac Structure
Unable to display preview. Download preview PDF.
- Bamberg, P., Sternberg, S.: A course in mathematics for students physics: 2. Cambridge University Press (1999)Google Scholar
- Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. John Wiley and Sons (2002)Google Scholar
- Bollobas, B.: Modern Graph Theory. Graduate Texts in Mathematics, vol. 184, Springer, New York (1998)Google Scholar
- Bosgra, O.H.: Lecture Notes ‘Mathematical Modelling of Dynamical Engineering Systems’. Delft University of Technology.Google Scholar
- Kondo, K., Iri, M.: On the theory of trees, cotrees, multi-trees and multi-cotrees. RAAG Memoirs 2, Div. A-VII, 220–261 (1958)Google Scholar
- Mizoo, Y., Iri, M., Kondo, K.: On the torsion and linkage characteristics and the duality of electric, magnetic and dielectric networks. RAAG Memoirs 2, Div. A-VIII, 261-295 (1958)Google Scholar
- van der Schaft, A.J.: L 2-Gain and Passivity Techniques in Nonlinear Control. Lect. Notes in Control and Information Sciences, vol. 218, Springer-Verlag, Berlin, (1996), p. 168, 2nd revised and enlarged edition, Springer-Verlag, Laondon (2000) (Springer Communications and Control Engineering series), p. xvi+249.Google Scholar
- vand der Schaft, A.J., Maschke, B.M.: The Hamiltonian formulation of energy conserving physical systems with external ports. Archiv für Elekrtonik und Übertragungstechnik 49, 362–371 (1995)Google Scholar
- van der Schaft, A.J., Maschke, B.M.: Conservation laws and open systems on higher-dimensional networks. In: Proc. 47th IEEE Conf. on Decision and Control, Cancum, Mexico, December 9- 11, 799–804 (2008)Google Scholar