Hybrid necessary principle

SIAM Journal on Control and Optimization

Volumn 43, Issue 5, 2005, Pages 1867-1887

  Garavello, Mauro ^a   Piccoli, Benedetto ^a  

^a FONDAZIONE POLICLINICO UNIVERSITARIO A GEMELLI IRCCS   (Italy)

Author keywords

Necessary conditions; Optimal control; Switching strategy

Indexed keywords

COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; PROBLEM SOLVING; SET THEORY;

HYBRID NECESSARY PRINCIPLE (HNP); OPTIMAL HYBRID TRAJECTORY; SWITCHING STRATEGIES;

OPTIMAL CONTROL SYSTEMS;

EID: 27644475559     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012903416219     Document Type: Article

References (29)

1. A. A. AGRACHEV, R. V. GAMKRELIDZE, AND A. V. SARYCHEV, Local invariants of smooth control systems, Acta Appl. Math., 14 (1989), pp. 191-237.
2. A. A. AGRACHEV, G. STEFANI, AND P. ZEZZA, An invariant second variation in optimal control, Internat. J. Control, 71 (1998), pp. 689-715.
3. P. J. ANTSAKLIS AND A. NERODE, EDS., Special issue on hybrid systems, IEEE Trans. Automat. Control, 43 (1998).
4. R. M. BIANCHINI, Good needle-like variations, in Differential Geometry and Control (Boulder, CO, 1997), Proc. Sympos. Pure Math. 64, AMS, Providence, RI, 1999, pp. 91-101.
5. U. BOSCAIN AND B. PICCOLI, Optimal Syntheses for Control Systems on 2-D Manifolds, Math. Appl. 43, Springer-Verlag, Berlin, 2004.
6. M. S. BRANICKY, V. S. BORKAR, AND S. K. MITTER, A unified framework for hybrid control: Model and optimal control theory, IEEE Trans. Automat. Control, 43 (1998), pp. 31-45.
7. A. BRESSAN, A high order test for optimality of bang-bang controls, SIAM J. Control Optim., 23 (1985), pp. 38-48.
8. A. BRESSAN AND B. PICCOLI, A generic classification of time-optimal planar stabilizing feedbacks, SIAM J. Control Optim., 36 (1998), pp. 12-32.
9. H. BREZIS, Analyse fonctionnelle: Théorie et applications, Masson, Paris, 1983.
10. C. CASSANDRAS, D. L. PEPYNE, AND Y. WARDI, Optimal control of a class of hybrid systems, IEEE Trans. Automat. Control, 46 (2001), pp. 398-415.
11. F. H. CLARKE AND R. B. VINTER, Optimal multiprocesses, SIAM J. Control Optim., 27 (1989), pp. 1072-1091.
12. F. H. CLARKE AND R. B. VINTER, Applications of optimal multiprocesses, SIAM J. Control Optim., 27 (1989), pp. 1048-1071.
13. C. D'APICE, R. MANZO, M. GARAVELLO, AND B. PICCOLI, Hybrid optimal control: Case study of a car with gears, Internat. J. Control, 76 (2003), pp. 1272-1284.
14. B. DE SCHUTTER, Optimal control of a class of linear hybrid systems with saturation, SIAM J. Control Optim., 39 (2000), pp. 835-851.
15. M. D. DI BENEDETTO AND A. SANGIOVANNI-VINCENTELLI, EDS., Hybrid Systems: Computation and Control, Lecture Notes in Comput. Sci. 2034, Springer-Verlag, Berlin, Heidelberg, 2001.
16. G. B. FOLLAND, Real Analysis: Modern Techniques and Their Applications, John Wiley, New York, 1984.
17. S. HEDLUND AND A. RANTZER, Optimal control of hybrid systems, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999, pp. 3972-3977.
18. A. J. KRENER, The high order maximal principle and its application to singular extremals, SIAM J. Control Optim., 15 (1977), pp. 256-293.
19. A. S. MORSE, C. C. PANTELIDES, S. SASTRY, AND J. M. SCHUMACHER, EDS., Special issue on hybrid systems, Automatica J. IFAC, 35 (1999), pp. 347-536.
20. B. PICCOLI, Hybrid systems and optimal control, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 13-18.
21. B. PICCOLI, Necessary conditions for hybrid optimization, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999, pp. 410-415.
22. B. PICCOLI AND H. J. SUSSMANN, Regular synthesis and sufficient conditions for optimality, SIAM J. Control Optim., 39 (2000), pp. 359-410.
23. P. RIEDINGER, F. KRATZ, C. IUNGAND, AND C. ZANNE, Linear quadratic optimization for hybrid systems, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999, pp. 2466-2470.
24. H. SCHÄTTLER, Regularity properties of optimal trajectories: Recently developed techniques, in Nonlinear Controllability and Optimal Control, Monogr. Textbooks Pure Appl. Math. 133, Dekker, New York, 1990, pp. 351-381.
25. G. STEFANI, Higher order variations: How can they be defined in order to have good properties?, in Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control (Minneapolis, MN, 1993), IMA Vol. Math. Appl. 78, Springer, New York, 1996, pp. 227-237.
26. H. J. SUSSMANN, A maximum principle for hybrid optimal control problems, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999.
27. H. J. SUSSMANN, A nonsmooth hybrid maximum principle, in Stability and Stabilization of Nonlinear Systems (Ghent, 1999), Lecture Notes in Control and Inform. Sci. 246, Springer, London, 1999, pp. 325-354.
28. H. J. SUSSMANN, Multidifferential calculus: Chain rule, open mapping and transversal intersection theorems, in Optimal Control: Theory, Algorithms and Applications, Appl. Optim. 15, W. W. Hager and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998, pp. 436-487.
29. X. Xu AND P. J. ANTSAKLIS, A dynamic programming approach for optimal control of switched systems, in Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 1822-1827.