Discrete feedback stabilization of semilinear control systems

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 1, Issue , 1996, Pages 207-224

  Grüne, Lars ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Discounted optimal control problems; Discrete feedback control; Lyapunov exponents; Semilinear control systems; Stabilization

Indexed keywords

EID: 84996128593     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:1996106     Document Type: Article

References (23)

1. A. Bacciotti: Local Stabilizability of Nonlinear Control Systems, World Scientific, Singapore, 1992.
2. R. W. Brockett: Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, R.W. Brockett, R.S. Millman, and H.J. Sussmann, eds., 181191, Birkhàuser, Boston, 1983.
3. I. Capuzzo Dolcetta and M. Falcone: Discrete dynamic programming and viscosity solutions of the Bellman equation, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 6 (supplément), 1989, 161-184.
4. I. Capuzzo Dolcetta and H. Ishii: Approximate solutions of the Bellman equation of deterministic control theory, Appl. Math. Optim., 11, 1984, 161-181.
5. R. Chabour, G. Sallet, and J. Vivalda: Stabilization of nonlinear systems: A bilinear approach, Math. Control Signals Syst., 6, 1993, 224-246.
6. F. Clarke, Y. Ledyaev, E. Sontag, and A. Subbotin: Asymptotic controllability and feedback stabilization, in Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ, 1996. To appear, full version submitted.
7. B. D. Coller, P. Holmes, and J. L. Lumley: Control of bursting in boundary layer models, Appl. Mech. Rev., 47, 1994, 139-143.
8. F. Colonius and W. Kliemann: Linear control semigroups acting on projective space, J. Dyn. Differ. Equations, 5, 1993, 495-528.
9. F. Colonius and W. Kliemann, Maximal and minimal Lyapunov exponents of bilinear control systems, J.Differ. Equations, 101, 1993, 232-275.
10. F. Colonius and W. Kliemann, Asymptotic null controllability of bilinear systems, in Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications Vol. 32, Warsaw, 1995, 139-148.
11. M. Falcone: A numerical approach to the infinite horizon problem of deterministic control theory, Appl. Math. Optim., 15, 1987, 1-13. Corrigenda, 23, 1991, 213214.
12. M. Falcone and R. Ferretti: Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations, Numer. Math., 67, 1994, 315-344.
13. L. Grüne: An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation, Numer. Math., 1996. To appear.
14. L. Grüne, Numerical stabilization of bilinear control systems, SIAM J. Control Optim.,1996. To appear.
15. H. Hermes: On stabilizing feedback attitude control, J. Optimization Theory Appl., 31, 1980, 373-384.
16. H. Hermes, On the synthesis of stabilizing feedback control via Lie algebraic methods, SIAM J. Control Optim., 18, 1980, 352-361.
17. A. Isidori: Nonlinear Control Systems: An Introduction, Springer Verlag, Berlin, 1989.
18. N.N. Krasovskii and A.I. Subbotin: Game-Theoretical Control Problems, Springer Verlag, New York, 1988.
19. P.-L. Lions: Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982.
20. E.D. Sontag: Nonlinear regulation: The piecewise linear approach, IEEE Trans. Autom. Control, AC-26, 1981, 346-358.
21. E.D. Sontag: Feedback stabilization using two-hidden-layer nets, IEEE Trans. Neural Networks, 3, 1992, 981-990.
22. N. Sri Namachchivaya and H.J. Van Roessel: Maximal Lyapunov exponents and rotation numbers for two coupled oscillators driven by real noise, J. Stat. Phys., 71, 1993, 549-567.
23. J. Stoer and R. Bulirsch: Introduction to Numerical Analysis, Springer Verlag, New York, 1980.