A feedback control motivation for generalized solutions to hybrid systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3927 LNCS, Issue , 2006, Pages 522-536

  Sanfelice, Ricardo G ^a   Goebel, Rafal ^a   Teel, Andrew R ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HYBRID CONTROL; HYBRID SYSTEM; MEASUREMENT NOISE;

ACOUSTIC NOISE; ASYMPTOTIC STABILITY; FEEDBACK CONTROL; HYBRID COMPUTERS; ROBUSTNESS (CONTROL SYSTEMS);

CONTROL SYSTEMS;

EID: 33745781690     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11730637_39     Document Type: Conference Paper

References (42)

1. R.C. Arkin. Behavior Based Robotics. The MIT Press, 1998.
2. J.-P. Aubin and A. Cellina. Differential Inclusions. Springer-Verlag, 1984.
3. J.-P. Aubin, J. Lygeros, M. Quincampoix, S. S. Sastry, and N. Seube. Impulse differential inclusions: a viability approach to hybrid systems. IEEE Trans. Aut. Cont., 47(1):2-20, 2002.
4. A. Back, J. Guckenheimer, and M. Myers. A dynamical simulation facility for hybrid systems. In Hybrid Systems volume 36 of Lecture Notes in Computer Science, pages 255-267, 1993.
5. D. D. Bainov and P.S. Simeonov. Systems with Impulse Effect: Stability, Theory, and Applications. Ellis Horwood Limited, 1989.
6. O. Beker, C.V. Hollot, Y. Chait, and H. Han. Fundamental properties of reset control systems. Automatica, 40(6):905-915, 2004.
7. M. Boccadoro, Y. Wardi, M. Egerstedt, and E. Verriest. Optimal control of switching surfaces in hybrid dynamical systems. Discrete Event Dynamic Systems-Theory and Applications, 15(4):433-448, 2005.
8. M. S. Branicky. Studies in hybrid systems: Modeling, analysis, and control. Ph.D. dissertation, Dept. Elec. Eng. and Computer Sci., MIT, 1995.
9. R. W. Brocket. Hybrid models for motion control systems. In Essays in control, pages 29-53, 1993.
10. C. Cai, A.R. Teel, and R. Goebel. Converse Lyapunov theorems and robust asymptotic stability for hybrid systems. In Proc. 24th American Control Conference, pages 12-17, 2005.
11. F. Ceragioli. Some remarks on stabilization by means of discontinuous feedbacks. Systems Control Lett., 45(4):271-281, 2002.
12. V. Chellaboina, S.P. Bhat, and W.H. Haddad. An invariance principle for nonlinear hybrid and impulsive dynamical systems. Nonlin. Anal., 53:527-550, 2003.
13. F.H. Clarke, Y.S. Ledyaev, E.D. Sontag, and A.I. Subbotin. Asymptotic controllability implies feedback stabilization. IEEE Trans. Aut. Cont., 42(10):1394-1407, 1997.
14. J. C. Clegg. A nonlinear integrator for servomechanisms. Transactions A.I.E.E., 77 (Part II):41-42, 1958.
15. P. Collins. A trajectory-space approach to hybrid systems. In Proc. 16th MTNS, 2004.
16. J-M. Coron and L. Rosier. A relation between continuous time-varying and discontinuous feedback stabilization. Journal of Math. Sys., Est., and Control, 4(1): 67-84, 1994.
17. M. Egerstedt. Behavior based robotics using hybrid automata. Hybrid Systems: Computation and Control Lecture Notes in Computer Science, 1790:103-116, 2000.
18. A.F. Filippov. Differential equations with discontinuous right-hand sides (english). Matemat. Sbornik., 51(93):99-128, 1960.
19. R. Goebel, J.P. Hespanha, A.R. Teel, C. Cai, and R.G. Sanfelice. Hybrid systems: Generalized solutions and robust stability. In Proc. 6th IFAC NOLCOS, pages 1-12, 2004.
20. R. Goebel and A.R. Teel. Results on solution sets to hybrid systems with applications to stability theory. In Proc. 24th American Control Conference, pages 557-562, 2005.
21. R. Goebel and A.R. Teel. Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. To appear in Automatica, 2006.
22. O. Hàjek. Discontinuous differential equations I. Journal of Diff. Eqn., 32:149-170, 1979.
23. H. Hermes. Discontinuous vector fields and feedback control. Diff. Eqn. & Dyn. Systems, pages 155-165, 1967.
24. C. M. Kellet and A. R. Teel. Smooth Lyapunov functions and robustness of stability for differential inclusions. Sys. & Cont. Lett., 52:395-405, 2004.
25. N.N. Krasovskii. Game-Theoretic Problems of Capture. Nauka, Moscow, 1970.
26. N.N. Krasovskii and A.I. Subbotin. Game-Theoretical Control Problems. Springer-Verlag, 1988.
27. K.R. Krishnan and I.M. Horowitz. Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed system tolerances. International Journal of Control, 19:689-706, 1974.
28. J. Lygeros, K.H. Johansson, S. S. Sastry, and M. Egerstedt. On the existence of executions of hybrid automata. In Proc. 38th IEEE Conference on Decision and Control, pages 2249-2254, 1999.
29. J. Lygeros, K.H. Johansson, S.N. Simić, J. Zhang, and S. S. Sastry. Dynamical properties of hybrid automata. IEEE Trans. Aut. Cont., 48(1):2-17, 2003.
30. D. Nesic, L. Zaccarian, and A.R. Teel. Stability properties of reset systems. In Proc. 16th IFAC World Congress in Prague, 2005.
31. C. Prieur, R. Goebel, and A. R. Teel. Results on robust stabilization of asymptotically controllable systems by hybrid feedback. In Proc. 44th IEEE Conference on Decision and Control and European Control Conference, pages 2598-2603, 2005.
32. R.T. Rockafellar and R. J-B Wets. Variational Analysis. Springer, 1998.
33. A.V. Roup, D.S. Bernstein, S.G. Nersesov, W.M. Haddad, and V. Chellaboina. Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and poincare maps. International Journal of Control, 76(17): 1685-1698, 2003.
34. R.G. Sanfelice, R. Goebel, and A.R. Teel. Generalized solutions to hybrid dynamical systems. Submitted, 2005.
35. R.G. Sanfelice, R. Goebel, and A.R. Teel. Results on convergence in hybrid systems via detectability and an invariance principle. In Proc. 24th American Control Conference, pages 551-556, 2005.
36. J. Sprinkle, A. D. Ames, A. Pinto, H. Zheng, and S. S. Sastry. On the partitioning of syntax and semantics for hybrid systems tools. In Proc. 44th IEEE Conference on Decision and Control and European Control Conference, 2005.
37. S.Y. Tang and R.A. Cheke. State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences. Journal of Mathematical Biology, 50(3):257-292, 2005.
38. L. Tavernini. Differential automata and their discrete simulators. Nonlin. Anal., 11(6):665-683, 1987.
39. S. E. Tuna, R. G. Sanfelice, M. J. Messina, and A. R. Teel. Hybrid MPC: Open-minded but not easily swayed. In International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 2005.
40. A. van der Schaft and H. Schumacher. An Introduction to Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, Springer, 2000.
41. H. S. Witsenhausen. A class of hybrid-state continuous-time dynamic systems. IEEE Trans. Aut. Cont., 11(2):161-167, 1966.
42. L. Zaccarian, D. Nesic, and A.R. Teel. First order reset elements and the Clegg integrator revisited. In Proc. 24th American Control Conference, pages 563-568, 2005.