An optimal control approach for hybrid systems

European Journal of Control

Volumn 9, Issue 5, 2003, Pages 449-458

  Riedinger, P ^a   Iung, C ^a   Kratz, F ^a  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

Author keywords

Dynamic programming; Hybrid automata; Hybrid systems; Maximum principle; Optimal control

Indexed keywords

ALGORITHMS; DYNAMIC PROGRAMMING; HAMILTONIANS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

BELLMAN PRINCIPLE; CLASSICAL CASE; HAMILTONIAN SYSTEMS; HYBRID SYSTEMS;

OPTIMAL CONTROL SYSTEMS;

EID: 33845380556     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.9.449-458     Document Type: Article

References (27)

1. Bogoliubov NN, Mitropolsky YA. Asymptotic methods in the theory of nonlinear oscillations. Gordon and Breach, NY, 1961
2. Sanders JA, Verhulst F. Averaging Methods in Non-linear Dynamical Systems, Springer, NY, 1985
3. Levis A, Marcus S, Perkins W, Kokotovic P, Athans M, Brockett R, Willsky A. Challenge to control, a collective view. IEEE Trans Autom Control 1987; 32(12): 274-285
4. Grossman RL, Nerode A, Ravn AP, Rischel H. Hybrid systems. vol 736 of LNCS, Springer, 1993
5. Antsaklis P, Kohn W, Nerode A, Sastry S. Hybrid systems II. vol 999 of LNCS. Springer, 1995
6. Alur R, Henzinger T, Sontag E. Hybrid systems III - verification and control, vol 1066 of LNCS, Springer, 1996
7. Antsaklis P, Kohn W, Nerode A, Sastry S. Hybrid systems IV. vol 1273 of LNCS. Springer, 1997
8. Antsaklis P, Kohn W, Lemmon M, Nerode A, Sastry S. Hybrid systems V. LNCS. Springer, 1998
9. Special Issue on Hybrid Control Systems. IEEE Trans Autom Control 1998; 43(4):
10. A Special Issue on Hybrid Systems. Automatica 1999; 35(3):
11. Antsaklis PJ, Nerode A. Hybrid control systems: an introductory discussion to the special issue. IEEE Trans Autom Control 1998; 43(4): 457-460
12. Ye H, Michel AN, Hou L. Stability theory for hybrid dynamical systems. 34th CDC 1995; 2679-2684.
13. Lennartson B, Tittus M, Edgardt B, Pettersson S. Hybrid systems in process control. IEEE Cont Syst 1996; 16(5): 45-56
14. Branicky MS, Borkar VS, Mitter SK. A unified framework for hybrid control: model and optimal control theory. IEEE Trans Autom Control 1998; 43(1): 31-43
15. Riedinger P, Iung C. Optimal control for hybrid systems: an hysteresis example. In: Proceedings of the IEEE system, man and cybernetics, pp I.188-I.193; 1999
16. Ghost MK, Arapostathis A, Marcus SI. Optimal control of hybrid system with pathwise average cost. 31st CDC, 1992; 1061-1066
17. Nguyen M, Gaitsgory V. Asymptotic optimization for a class of nonlinear stochastic hybrid systems on infinite time horizon. ACC'97, 1997
18. Riedinger P, Kratz F, Iung C, Zanne C. Linear quadratic optimization for hybrid systems, In: proceedings of the IEEE conference on decision and control. 1999, pp 3059-3064
19. Riedinger P, Zanne C, Kratz F. Time optimal control of hybrid systems. In: Proceedings of the American control conference, 1999, pp 2466-2470
20. Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF. The mathematical theory of optimal processes. Pergamon, 1964
21. Young L. Optimal control theory. Cambridge University Press, 1980
22. Lewis F. Optimal control. Wiley NY, 1986
23. Bryson AE, Ho YC. Applied optimal control. Gin and Co., 1969
24. Clarke FH. Optimization and nonsmooth analysis. SIAM, 1990
25. Macki J, Strauss A. Introduction to optimal control theory. Springer-Verlag, 1982
26. Lootsma YL, van der Schaft AJ, Camlibel MK. Uniqueness of solutions of linear relay systems. Automatica 1999; 35(3): 467-478
27. Jakubczyk B, Respondek W. Geometry of feedback and optimal control. Marcel DEKKER, 1998