Non-uniqueness in reverse time of hybrid system trajectories

Lecture Notes in Computer Science

Volumn 3414, Issue , 2005, Pages 339-353

  Hiskens, Ian A ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; HYBRID COMPUTERS; ORDINARY DIFFERENTIAL EQUATIONS;

HOMOTOPY ALGORITHMS; HYBRID SYSTEM TRAJECTORIES; HYPERSURFACES; LIPSCHITZ CONDITIONS;

TRAJECTORIES;

EID: 24344450871     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-31954-2_22     Document Type: Conference Paper

References (19)

1. Hirsch, M., Smale, S.: Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, Orlando, FL (1974)
2. Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston (2003)
3. van der Schaft, A., Schumacher, J.: Complementarity modeling of hybrid systems. IEEE Transactions on Automatic Control 43 (1998) 483-490
4. Lootsma, Y., van der Schaft, A., Çamlibel, M.: Uniqueness of solutions of linear relay systems. Automatica 35 (1999) 467-478
5. Pogromsky, A., Heemels, W., Nijmeijer, H.: On solution concepts and well-posedness of linear relay systems. Automatica 39 (2003) 2139-2147
6. Heemels, W., Çamlibel, M., Schumacher, J.: On the dynamic analysis of piecewise-linear networks. IEEE Transactions on Circuits and Systems-I 49 (2002) 315-327
7. Imura, J.I., van der Schaft, A.: Characterization of well-posedness of piecewise-linear systems. IEEE Transactions on Automatic Control 45 (2000) 1600-1619
8. Lygeros, J., Johansson, K., Simić, S., Zhang, J., Sastry, S.: Dynamical properties of hybrid automata. IEEE Transactions on Automatic Control 48 (2003) 2-17
9. Errico, R.: What is an adjoint model? Bulletin of the American Meteorological Society 78 (1997) 2577-2591
10. Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24 (2003) 1076-1089
11. Wardi, Y., Egerstedt, M., Boccadoro, M., Verriest, E.: Optimal control of switching surfaces. In: Proceedings of the 43rd Conference on Decision and Control, Paradise Island, Bahamas (2004) 1854-1859
12. Khalil, H.: Nonlinear Systems. 2nd edn. Prentice Hall, Upper Saddle River, NJ (1996)
13. Perko, L.: Differential Equations and Dynamical Systems. Springer-Verlag, New York, NY (1996)
14. Hiskens, I., Pai, M.: Trajectory sensitivity analysis of hybrid systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47 (2000) 204-220
15. Donde, V., Hiskens, I.: Shooting methods for locating grazing phenomena in hybrid systems. International Journal of Bifurcation and Chaos (2004) Submitted.
16. Kailath, T.: Linear Systems. Prentice Hall, Upper Saddle River, NJ (1980)
17. Goodwin, G., Graebe, S., Salgado, M.: Control System Design. Upper Saddle River, New Jersey: Prentice Hall (2001)
18. Garcia, C., Zangwill, W.: Pathways to Solutions, Fixed Points and Equilibria. Prentice Hall, Englewood Cliffs, NJ (1981)
19. Sauer, P., Pai, M.: Power System Dynamics and Stability. Prentice Hall, Upper Saddle River, NJ (1998)