Max-plus eigenvector methods for nonlinear H ∞ problems: Error analysis

SIAM Journal on Control and Optimization

Volumn 43, Issue 2, 2005, Pages 379-412

  Mceneaney, William M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dynamic programming; Max plus algebra; Nonlinear H control; Numerical methods; Partial differential equations

Indexed keywords

MAX-PLUS ALGEBRA; NONLINEAR H∞ CONTROL; STEADY STATE; TIME-HORIZON;

ALGEBRA; ALGORITHMS; DYNAMIC PROGRAMMING; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

PROBLEM SOLVING;

EID: 16244396125     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902414688     Document Type: Article

References (37)

1. ∞-Optimal Control and Related Minimax Design Problems, Birkhäuser Boston, Boston, 1991.
2. ∞ control for nonlinear plants; Connections with differential games, in Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, FL, 1989, pp. 956-962.
3. M. BARDI AND I. CAPUZZO-DOLCETTA, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser Boston, Boston, 1997.
4. F. L. BACCELLI, G. COHEN, G. J. OLSDER, AND J.-P. QUADRAT, Synchronization and Linearity, John Wiley, Chichester, UK, 1992.
5. R. K. BOEL, M. R. JAMES, AND I. R. PETERSEN, Robustness and risk sensitive filtering, in Proceedings of the 36th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 1997, pp. 2273-2278.
6. ∞ -control and filtering, in Proceedings of the 32nd IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 1993, pp. 184-189.
7. P. DUPUIS AND M. BOUÉ, Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control, SIAM J. Numer. Anal., 36 (1999), pp. 667-695.
8. P. DUPUIS AND A. SZPIRO, Convergence of the optimal feedback policies in a numerical method for a class of deterministic optimal control problems, SIAM J. Control Optim., 40 (2001), pp. 393-420.
9. L. C. EVANS, Partial Differential Equations, AMS, Providence, RI, 1998.
10. W. H. FLEMING, Functions of Several Variables, Springer-Verlag, New York, 1977.
11. W. H. FLEMING AND W. M. MCENEANEY, Robust limits of risk sensitive nonlinear filters, Math. Control Signals Systems, 14 (2001), pp. 109-142.
12. W. H. FLEMING AND W. M. MCENEANEY, A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering, SIAM J. Control Optim., 38 (2000), pp. 683-710.
13. W. H. FLEMING, Deterministic nonlinear filtering, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 4, 25 (1997), pp. 435-454.
14. W. H. FLEMING AND W. M. MCENEANEY, Risk sensitive and robust nonlinear filtering, in Proceedings of the 36th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 1997, pp. 1088-1093.
15. W. H. FLEMING AND H. M. SONER, Controlled Markov Process and Viscosity Solutions, Springer-Verlag, New York, 1993.
16. ∞ control, in Proceedings of the 38th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, pp. 3011-3016.
17. ∞ control problems with application to jet engine compressors, Control Systems Technology, (2000), pp. 98-111.
18. ∞, Control to Nonlinear Systems, SIAM, Philadelphia, 1999.
19. M. R. JAMES, A partial differential inequality for dissipative nonlinear systems, Systems Control Lett., 21 (1993) pp. 315-320.
20. V. N. KOLOKOLTSOV AND V. P. MASLOV, Idempotent Analysis and Its Application, Math. Appl. 401, Kluwer, Dordrecht, The Netherlands, 1997.
21. ∞) control and estimation, J. Math. Systems Estim. Control, 4 (1994), pp. 485-488.
22. H. J. KUSHNER AND P. DUPUIS, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag, New York, 1992.
23. G. L. LITVINOV, V. P. MASLOV, AND G. B. SHPIZ, Idempotent functional analysis: An algebraic approach, Math. Notes, 69 (2001) pp. 696-729.
24. V. P. MASLOV, On a new principle of superposition for optimization problems, Russian Math. Surveys, 42 (1987), pp. 43-54.
25. ∞, problems: Basic concepts, IEEE Trans. Automat. Control, 48 (2003), pp. 1150-1163.
26. W. M. MCENEANEY, Error analysis of a max-plus algorithm for a first-order HJB equation, in Stochastic Theory and Control, Lecture Notes in Control and Inform. Sci. 280, B. Pasik-Duncan, ed., Springer-Verlag, Berlin, 2002, pp. 335-351.
27. W. M. MCENEANEY, Convergence and error analysis for a max-plus algorithm, in Proceedings of the 39th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 2000, pp. 1194-1199.
28. W. M. MCENEANEY, Robust/game-theoretic methods in filtering and estimation, in Proceedings of the Symposium on Advances in Enterprise Control, 1999, pp. 3-10.
29. ∞ value functions, in 1999 American Control Conference, pp. 1400-1404.
30. ∞ value functions, in Proceedings of the 37th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 1998, pp. 3506-3511.
31. ∞ filtering for nonlinear systems, Systems Control Lett., 33 (1998), pp. 315-325.
32. ∞ control, Math. Control Signals Systems, 11 (1998), pp. 303-334.
33. ∞ control DPEs, in Proceedings of the Seventh International Symposium on Dynamic Games and Applications, Shonan Village, Japan, 1996, pp. 662-671.
34. R. T. ROCKAFELLAR, Conjugate Duality and Optimization, Regional Conference Series in Applied Mathematics 16, SIAM, Philadelphia, 1974.
35. R. T. ROCKAFELLAR AND R. J. WETS, Variational Analysis, Springer-Verlag, Berlin, 1998.
36. ∞ control of nonlinear systems: Differential games and viscosity solutions, SIAM J. Control Optim., 34 (1996), pp. 1071-1097.
37. ∞ control, IEEE Trans. Automat. Control, 37 (1992), pp. 770-784.