Inverse optimality in robust stabilization

SIAM Journal on Control and Optimization

Volumn 34, Issue 4, 1996, Pages 1365-1391

  Freeman, R A ^a   Kokotovic, P V ^a  

^a University of California   (United States)

Author keywords

Control Lyapunov functions; Differential games; Input to state stability; Nonlinear systems; Robust stabilization

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; FEEDBACK; GAME THEORY; LYAPUNOV METHODS; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

ARTSTEIN THEOREM; CONTINUOUS STATE FEEDBACK; DIFFERENTIAL GAMES; HAMILTON-JACOBI-ISAACS EQUATION; ROBUST CONTROL LYAPUNOV FUNCTION; ROBUST STABILIZATION;

OPTIMIZATION;

EID: 0030191874     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012993258732     Document Type: Article

References (40)

1. B. D. O. ANDERSON AND J. B. MOORE, Linear Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1971.
2. Z. ARTSTEIN, Stabilization with relaxed controls, Nonlinear Anal., 7 (1983), pp. 1163-1173.
3. J.-P. AUBIN, Contingent Isaacs equations of a differential game, in Differential Games and Applications, T. Basar and P. Bernhard, eds., Springer-Verlag, Berlin, 1989, pp. 51-61.
4. J.-P. AUBIN AND A. CELLINA, Differential Inclusions, Springer-Verlag, Berlin, 1984.
5. J.-P. AUBIN AND H. FRANKOWSKA, Set-Valued Analysis, Birkhäuser, Boston, 1990.
6. B. R. BARMISH, M. J. CORLESS, AND G. LEITMANN, A new class of stabilizing controllers for uncertain dynamical systems, SIAM J. Control Optim., 21 (1983), pp. 246-255.
7. Y. H. CHEN, A new matching condition for robust control design, in Proc. 1993 American Control Conference, San Francisco, CA, June 1993, pp. 122-126.
8. Y. H. CHEN AND G. LEITMANN, Robustness of uncertain systems in the absence of matching assumptions, Int. J. Control, 45 (1987), pp. 1527-1542.
9. F. H. CLARKE, Optimization and Nonsmooth, Analysis, Society for Industrial and Applied Mathematics, Philadelphia, 1990.
10. M. J. CORLESS, Robust stability analysis and controller design with quadratic Lyapunov functions, in Variable Structure and Lyapunov Control, A. Zinober, ed., Springer-Verlag, Berlin, 1993.
11. M. J. CORLESS AND G. LEITMANN, Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Trans. Automat. Control, 26 (1981), pp. 1139-1144.
12. R. A. FREEMAN AND P. V. KOKOTOVIC, Design of "softer" robust nonlinear control laws, Automatica, 29 (1993), pp. 1425-1437.
13. _, Optimal nonlinear controllers for feedback linearizable systems, in Proc. Workshop on Robust Control via Variable Structure & Lyapunov Techniques, Benevento, Italy, September 1994, pp. 286-293.
14. S. T. GLAD, Robustness of nonlinear state feedback - a survey, Automatica, 23 (1987), pp. 425-435.
15. S. GUTMAN, Uncertain dynamical systems - Lyapunov min-max approach, IEEE Trans. Automat. Control, 24 (1979), pp. 437-443.
16. D. H. JACOBSON, Extensions of Linear-Quadratic Contol, Optimization and Matrix Theory, Academic Press, London, 1977.
17. R. E. KALMAN, When is a linear control systems optimal?, Trans. ASME Ser. D J. Basic Engrg., 86 (1964), pp. 1-10.
18. J. L. KELLEY, General Topology, D. Van Nostrand Company, Princeton, NJ, 1955.
19. M. KISIELEWICZ, Differential Inclusions and Optimal Control, PWN - Polish Scientific Publishers, Warszawa, Poland, 1991.
20. A. LEITMANN, Guaranteed ultimate boundedness for a class of uncertain linear dynamical systems, IEEE Trans. Automat. Control, 23 (1978), pp. 1109-1110.
21. Y. LIN, Lyapunov Function Techniques for Stablization, Ph.D. thesis, Rutgers, The State University of New Jersey, 1992.
22. Y. LIN AND E. D. SONTAG, Further universal formulas for Lyapunov approaches to nonlinear stabilization, in Proc. Conference on Information Science and Systems, Johns Hopkins University, March 1991, pp. 541-546.
23. _, A universal formula for stabilization with bounded controls, Systems Control Lett., 16 (1991), pp. 393-397.
24. Y. LIN, E. D. SONTAG, AND Y. WANG, Recent results on Lyapunov-theoretic techniques for nonlinear stability, in Proc. 1994 American Control Conference, Baltimore, MD, June 1994, pp. 1771-1775.
25. R. MARINO AND P. TOMEI, Robust stabilization of fedback linearizable time-varying uncertain nonlinear systems, Automatica, 29 (1993) pp. 181-189.
26. F. MAZENC AND L. PRALY, Adding an integration and global asymptotic stabilization of feedforward systems, IEEE Trans. Automat. Control, to appear.
27. L. PRALY AND Z. P. JIANG, Stabilization by output feedback for systems with ISS inverse dynamics, Systems Control Lett., 21 (1993), pp. 19-33.
28. Z. QU, Global stabilization of nonlinear systems with a class of unmatched uncertainties, Syst. Control Lett., 18 (1992), pp. 301-307.
29. _, Robust control of nonlinear uncertain systems under generalized matching conditions, Automatica, 29 (1993), pp. 985-998.
30. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
31. M. A. ROTEA AND P. P. KHARGONEKAR, Stabilization of uncertain systems with norm bounded uncertainty: A control Lyapunov function approach, SIAM J. Control Optim., 27 (1989), pp. 1462-1476.
32. J. J. E. SLOTINE AND K. HEDRICK, Robust input-output feedback linearization, Int. J. Control, 57 (1993), pp. 1133-1139.
33. E. D. SONTAG, Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control, 34 (1989), pp. 435-443.
34. _, A 'universal' construction of Artstein's theorem on nonlinear stabilization, Systems Control Lett., 13 (1989), pp. 117-123.
35. _, Feedback stabilization of nonlinear systems, in Robust Control of Linear Systems and Nonlinear Control, M. A. Kaashoek, J. H. van Schuppen, and A. C. M. Ran, eds., Birkhäuser, Boston, 1990, pp. 61-81.
36. _, Further facts about input to state stabilization, IEEE Trans. Automat. Control, 35 (1990), pp. 473-476.
37. A. R. TEEL, A nonlinear small gain theorem for the analysis of control systems with saturation, IEEE Trans. Automat. Control, to appear.
38. A. R. TEEL AND L. PRALY, Tools for semiglobal stabilization by partial state and output feedback, SIAM J. Control Optim., 33 (1995), pp. 1443-1488.
39. J. TSINIAS, Sufficient Lyapunov-like conditions for stabilization, Math. Control Signals Systems, 2 (1989), pp. 343-357.
40. _, Sontag's 'input-to-state stability condition' and global stabilization using state detection, Systems Control Lett., 20 (1993), pp. 219-226.