Modeling and Analysis of Modal Switching in Networked Transport Systems

• Published in: Applied mathematics & optimization Vol. 59; no. 2; pp. 275 - 292
• Main Authors: Hante, Falk M., Leugering, Günter, Seidman, Thomas I.
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01-04-2009; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Control; Control systems; CONTROL THEORY; Differential equations; Dynamical systems; Dynamics; FEEDBACK; GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Graphs; Mathematical and Computational Physics; MATHEMATICAL METHODS AND COMPUTING; Mathematical Methods in Physics; Mathematical models; MATHEMATICAL SOLUTIONS; Mathematics; Mathematics and Statistics; Network operating systems; Numerical and Computational Physics; Optimization; Ordinary differential equations; PARTIAL DIFFERENTIAL EQUATIONS; SENSORS; SIMULATION; Studies; Switching; Systems analysis; Systems Theory; Theoretical; Transport; TRANSPORT THEORY; Transport equation; Networked system; Automated switching; Optimal control; Hybrid system
• ISSN: 0095-4616; 1432-0606
• DOI: 10.1007/s00245-008-9057-6

We consider networked transport systems defined on directed graphs: the dynamics on the edges correspond to solutions of transport equations with space dimension one. In addition to the graph setting, a major consideration is the introduction and propagation of discontinuities in the solutions when the system may discontinuously switch modes, naturally or as a hybrid control. This kind of switching has been extensively studied for ordinary differential equations, but not much so far for systems governed by partial differential equations. In particular, we give well-posedness results for switching as a control, both in finite horizon open loop operation and as feedback based on sensor measurements in the system.