A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering

SIAM Journal on Control and Optimization

Volumn 38, Issue 3, 2000, Pages 683-710

  Fleming, Wendell H ^a   McEneaney, William M ^b  

^a BROWN UNIVERSITY   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

H ; Max plus algebra; Nonlinear filtering; Nonlinear HJB equations; Robust

Indexed keywords

EID: 0000873359     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012998332433     Document Type: Article

References (32)

1. ∞-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, 2nd ed., Birkhäuser, Basel, 1995.
2. M. BARDI AND F. DA LIO, On the Bellman equation for some unbounded control problems, NoDEA Nonlinear Differential Equations Appl., 4, (1997), pp. 491-510.
3. F. L. BACCELLI, G. COHEN, G. J. OLSDER, AND J.-P. QUADRAT, Synchronization and Linearity, John Wiley, New York, 1992.
4. E. N. BARRON AND R. JENSEN, Generalized viscosity solutions for Hamilton-Jacobi equations with time-measurable Hamiltonians, J. Differential Equations, 69 (1987), pp. 10-21.
5. R. K. BOEL, M. R. JAMES, AND I. R. PETERSEN, Robustness and risk-sensitive filtering, submitted.
6. M. H. A. DAVIS, Lectures on Stochastic Control and Nonlinear Filtering, Tata Inst. Fund. Res. Lectures on Math. and Phys. 75, Springer-Verlag, New York, 1984.
7. F. DA LIO AND W. M. MCENEANEY, Finite time-horizon risk-sensitive control and the robust limit under a quadratic growth assumption, SIAM J. Control Optim., submitted.
8. W. H. FLEMING, Functions of Several Variables, Springer-Verlag, New York, 1977.
9. W. H. FLEMING, Deterministic nonlinear filtering, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24 (1997), pp. 435-454.
10. W. H. FLEMING AND W. M. MCENEANEY, Risk sensitive and robust nonlinear filtering, in Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, 1997, pp. 1088-1093.
11. W. H. FLEMING AND E. PARDOUX, Optimal control of partially observed diffusions, SIAM J. Control Optim., 20 (1982), pp. 261-285.
12. O. J. HIJAB, Minimum Energy Estimation, Ph.D. thesis, University of California, Berkeley, CA, 1980.
13. ∞-Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives, SIAM, Philadelphia, 1999.
14. H. ISHII, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Bull. Fac. Sci. Engrg. Chuo Univ. Ser. I Math., 28 (1985), pp. 33-77.
15. H. ISHII, Comparison results for Hamilton-Jacobi equations without a growth condition on solutions from above, Appl. Anal., to appear.
16. K. ITO, Approximation of the Zakai equation for nonlinear filtering, SIAM J. Control Optim., 34 (1996), pp. 620-634.
17. ∞ control, SIAM J. Control Optim., 34 (1996), pp. 1342-1364.
18. A. J. KRENER AND A. DUARTE, A hybrid computational approach to nonlinear estimation, in Proceedings of the 35th IEEE Conference on Decision and Control, Japan, 1996.
19. H. KUNITA, Stochastic Partial Differential Equations Connected with Nonlinear Filtering, Lecture Notes in Math. 972, Springer-Verlag, New York, 1982.
20. G. L. LITVINOV AND V. P. MASLOV, Correspondence principle for idempotent calculus and some computer applications, in Idernpotency, J. Gunawardena, ed., Publ. Newton Inst. 11, Cambridge University Press, Cambridge, UK, 1998, pp. 420-443.
21. S. LOTOTSKY, R. MIKULEVICIUS, AND B. L. ROZOVSKII, Nonlinear filtering revisited: A spectral approach, SIAM J. Control Optim., 35 (1997), pp. 435-461.
22. P. L. LIONS AND B. PERTHAME, Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians, Nonlinear Anal., 11 (1987), pp. 613-621.
23. V. P. MASLOV, On a new principle of superposition for optimization problems, Russian Math. Surveys, 42 (1987), pp. 43-54.
24. ∞ filtering for nonlinear systems, Systems Control Lett., 33 (1998), pp. 315-325.
25. W. M. MCENEANEY, Uniqueness for viscosity solutions of nonstationary Hamilton-Jacobi-Bellman equations under some a priori conditions (with applications), SIAM J. Control Optim., 33 (1995), pp. 1560-1576.
26. W. M. MCENEANEY, Robust control and differential games on a finite time horizon, Math. Control Signals Systems, 8 (1995), pp. 138-166.
27. ∞ control, in Proceedings of the IFAC 13th World Congress, Vol. E, San Francisco, 1996, pp. 401-406.
28. S. K. MITTER, Lectures on Nonlinear Filtering and Stochastic Control, Lecture Notes in Math. 972, Springer-Verlag, New York, 1982.
29. R. E. MORTENSEN, Maximum likelihood recursive nonlinear filtering, J. Optim. Theory Appl., 2 (1968), pp. 386-394.
30. R. T. ROCKAFELLAR, Conjugate Duality and Optimization, CBMS-NSF Regional Conf. Ser. in Appl. Math. 16, SIAM, Philadelphia, 1974.
31. R. T. ROCKAFELLAR AND R. J. WETS, Variational Analysis, Springer-Verlag, New York, 1997.
32. P. SORAVIA, Evolution operators and viscosity solutions of Hamilton-Jacobi equations, Boll. Un. Mat. Ital. B (7), 2 (1988), pp. 571-600.