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.

[1]  Arjan van der Schaft,et al.  Hamiltonian discretization of boundary control systems , 2004, Autom..

[2]  J. Willems.  The Behavioral Approach to Open and Interconnected Systems , 2007, IEEE Control Systems.

[3]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[4]  R. Ho.  Algebraic Topology , 2022 .

[5]  A. Schaft,et al.  Hamiltonian formulation of distributed-parameter systems with boundary energy flow , 2002 .

[6]  Arjan van der Schaft,et al.  Interconnection of port-Hamiltonian systems and composition of Dirac structures , 2007, Autom..

[7]  Frank Harary,et al.  Graph Theory , 2016 .

[8]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[9]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[10]  A. G. J. MacFarlane,et al.  Dynamical system models , 1970 .

[11]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[12]  Arjan van der Schaft,et al.  Conservation laws and open systems on higher-dimensional networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[13]  A. Dold.  Lectures on Algebraic Topology , 1972 .

[14]  G. Kirchhoff.  Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .

[15]  Gebräuchliche Fertigarzneimittel,et al.  V , 1893, Therapielexikon Neurologie.

[16]  P. Bamberg,et al.  A course in mathematics for students of physics , 1990 .

[17]  Alan J. Davies.  A course in mathematics for students of physics 2 , by Paul Bamberg and Shlomo Sterberg. Pp 443. £60 (hardback). 1990. ISBN 0-521-33245-1 (Cambridge University Press) , 1991 .