State constrained feedback stabilization

SIAM Journal on Control and Optimization

Volumn 42, Issue 2, 2003, Pages 422-441

  Clarke, F H ^a   Stern, R J ^b  

^a UNIVERSITÉ LYON 1   (France)

^b Dept of Electrical and Computer Engineering   (Canada)

Author keywords

Asymptotic controllability; Constraint removal; Feedback; Robustness; Semiconcave control Lyapunov function; State constraint

Indexed keywords

ASYMPTOTIC CONTROLLABILITY; CONSTRAINT REMOVAL; SEMICONCAVE CONTROL LYAPUNOV FUNCTIONS; STATE CONSTRAINTS;

ASYMPTOTIC STABILITY; CONSTRAINT THEORY; FEEDBACK; FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); THEOREM PROVING;

NONLINEAR CONTROL SYSTEMS;

EID: 1942510309     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301290240453X     Document Type: Article

References (38)

1. F. ANCONA AND A. BRESSAN, Patchy vector fields and asymptotic stabilization, ESAIM Control Optim. Calc. Var., 4 (1999), pp. 445-471.
2. A. BACCIOTTI, Local Stabilizability of Nonlinear Systems, World Scientific, River Edge, NJ, 1992.
3. M. BARDI AND I. CAPUZZO-DOLCETTA, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser Boston, Boston, 1997.
4. R. W. BROCKETT, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, and H. J. Sussmann, eds., Birkhäuser Boston, Boston, 1983, pp. 181-191.
5. F. H. CLARKE, Optimization and Nonsmooth Analysis, Classics Appl. Math. 5, SIAM, Philadelphia, 1990.
6. F. H. CLARKE, Methods of Dynamic and Nonsmooth Optimization, CBMS-NSF Regional Conf. Ser. in Appl. Math. 57, SIAM, Philadelphia, 1989.
7. F. H. CLARKE, Yu. S. LEDYAEV, L. RIFFORD, AND R. J. STERN, Feedback stabilization and Lyapunov functions, SIAM J. Control Optim., 39 (2000), pp. 25-48.
8. F. H. CLARKE, Yu. S. LEDYAEV, E. D. SONTAG, AND A. I. SUBBOTIN, Asymptotic controllability implies control feedback stabilization, IEEE Trans. Automat. Control, 42 (1997), p. 1394.
9. F. H. CLARKE, Yu. S. LEDYAEV, R. J. STERN, AND P. R. WOLENSKI, Qualitative properties of trajectories of control systems: A survey, J. Dynam. Control Systems, 1 (1995), pp. 1-48.
10. F. H. CLARKE, Yu. S. LEDYAEV, AND R. J. STERN, Complements, approximations, smoothings and invariance properties, J. Convex Anal., 4 (1997), pp. 189-219.
11. F. H. CLARKE, Yu. S. LEDYAEV, R. J. STERN, AND P. R. WOLENSKI, Nonsmooth Analysis and Control Theory, Grad. Texts in Math. 178, Springer-Verlag, New York, 1998.
12. F. H. CLARKE, L. RIFFORD, AND R. J. STERN, Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var., 7 (2002), pp. 97-134.
13. F. H. CLARKE AND R. J. STERN, Inner approximation of state constrained optimal control problems, in Advances in Convex Analysis and Global Optimization, N. Hadjisavvas and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 1-11.
14. 2 property, J. Convex Anal., 2 (1995), pp. 117-145.
15. J.-M. CORON, Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5 (1992), pp. 295-312.
16. J.-M. CORON AND L. ROSIER, A relation between continuous time-varying and discontinuous feedback stabilization, J. Math. Systems Estim. Control, 4 (1994), pp. 67-84.
17. F. FORCELLINI AND F. RAMPAZZO, On nonconvex differential inclusions whose state is constrained in the closure of an open set. Applications to dynamic programming, Differential Integral Equations, 12 (1999), pp. 471-497.
18. H. FRANKOWSKA AND F. RAMPAZZO, Filippov's and Filippov-Wazewski's theorems on closed domains, J. Differential Equations, 161 (2000), pp. 449-478.
19. H. HERMES, Discontinuous vector fields and feedback control, in Differential Equations and Dynamic Systems, J. K. Hale and J. P. LaSalle, eds., Academic Press, New York, 1967.
20. H. HERMES, Resonance, stabilizing feedback controls, and regularity of Hamilton-Jacobi-Bellman equations, Math. Control Signals Systems, 9 (1996), pp. 59-72.
21. C. M. KELLETT AND A. R. TEEL, Uniform asymptotic controllability to a set implies locally Lipschitz control-Lyapunov function, in Proceedings of the 39th IEEE Conference on Decision and Control, Vol. 4, IEEE Press, Piscataway, NJ, 2000, pp. 3994-3999.
22. P. V. KOKOTOVIO AND H. J. SUSSMANN, A positive real condition for stabilization of nonlinear systems, Systems Control Lett., 13 (1989), pp. 125-134.
23. N. N. KRASOVSKIǏ AND A. I. SUBBOTIN, Game-Theoretical Control Problems, Springer-Verlag, New York, 1988.
24. P. LOEWEN, Optimal Control via Nonsmooth Analysis, CRM Proc. Lecture Notes 2, AMS, Providence, RI, 1993.
25. C. PRIEUR, A robust globally asymptotically stabilizing feedback: The example of the Artstein's circles, in Nonlinear Control in the Year 2000, A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, eds., Lectures Notes in Control and Inform. Sci. 258, Springer-Verlag, London, 2000, pp. 279-300.
26. C. PRIEUR, Uniting local and global controllers with robustness to vanishing noise, Math. Control Signals Systems, 14 (2000), pp. 143-172.
27. L. RIFFORD, Problémes de Stabilisation en Théorie du Contrôle, Doctoral thesis, Univ. Claude Bernard-Lyon 1, France, 2000.
28. L. RIFFORD, Stabilisation des systèmes globalement asymptotiguement commandables, C. R. Acad. Sci. Paris Sér. I. Math., 330 (2000), pp. 211-216.
29. L. RIFFORD, Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim., 39 (2000), pp. 1043-1064.
30. n, Nonlinear Anal., 3 (1979), pp. 145-154.
31. R. T. ROCKAFELLAR, Favorable classes of Lipschitz continuous functions in subgradient optimization, in Nondifferentiable Optimization, E. Nurminski, ed., Permagon Press, New York, 1982.
32. E. P. RYAN, On Brockett's condition for smooth stabilizability and its necessity in a context of nonsmooth feedback, SIAM J. Control Optim., 32 (1994), pp. 1597-1604.
33. H. M. SONER, Optimal control with state-space constraint I, SIAM J. Control Optim., 24 (1986), pp. 552-561.
34. E. D. SONTAG, A Lyapunov-like characterization of asymptotic controllability, SIAM J. Control Optim., 21 (1983), pp. 462-471.
35. E. D. SONTAG, Clock and insensitivity to small measurement errors, ESAIM Control Optim. Calc. Var., 4 (1999), pp. 537-557.
36. E. D. SONTAG AND H. J. SUSSMAN, Remarks on continuous feedback, in Proceedings of the 19th IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 1980, pp. 916-921.
37. A. R. TEEL AND L. PRALY, A smooth Lyapunov function from a class-Kℒ estimate involving two positive semidefinite functions, ESAIM Control Optim. Calc. Var., 5 (2000), pp. 313-367.
38. R. B. VINTER, Optimal Control, Birkhäuser Boston, Boston, 2000.