Risk-sensitive approach to optimal filtering and control for linear stochastic systems

International Journal of Innovative Computing, Information and Control

Volumn 5, Issue 6, 2009, Pages 1599-1613

  Alcorta García, Ma Aracelia ^a   Basin, Michael ^a   Sánchez, Yazmin Gpe Acosta ^a  

^a UNIVERSIDAD AUTÓNOMA DE NUEVO LEÓN   (Mexico)

Author keywords

Risk sensitive filtering and control; Stochastic systems

Indexed keywords

CLOSED FORM; DRIFT TERM; FILTERING ALGORITHM; FILTERING PROBLEMS; GAUSSIAN SYSTEMS; HAMILTON JACOBI BELLMAN EQUATION; INTENSITY PARAMETERS; KALMAN-BUCY FILTER; LINEAR QUADRATIC REGULATOR; LINEAR STOCHASTIC SYSTEM; MEAN-SQUARE; NUMERICAL EXAMPLE; OPTIMAL CONTROLS; OPTIMAL FILTERING; POLYNOMIAL SYSTEMS; QUADRATIC CONTROL PROBLEM; SENSITIVE ALGORITHMS; SIMULATION RESULT; VALUE FUNCTIONS;

OPTIMIZATION; RANDOM PROCESSES; STOCHASTIC CONTROL SYSTEMS;

STOCHASTIC SYSTEMS;

EID: 67649415101     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (43)

1. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, Wiley, New York, USA, 1972.
2. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, USA, 1975.
3. L. S. Pontryagin, et al., The Mathematical Theory of Optimal Processes, Fizmalit, New York, USA, 1962.
4. E. G. Albrekht, On the optimal stabilization of nonlinear systems, J. Appl. Math. Mech. vol. 25, pp. 1254-1266, 1962.
5. A. Haime and R. Hamalainen, On the nonlinear regulator problem, J. Opt. Theory and Appl., vol. 16, pp. 3-4, 1975.
6. E. B. Lee and L. Marcus, Foundations of the Optimal Control Theory Systems, Wiley, New York, USA. 1967.
7. D. L. Lukes, Optimal regulation of nonlinear dynamic systems, SIAM J. Control Opt., vol. 7, pp. 75-100, 1969.
8. A. P. Willemstein, Optimal regulation of nonlinear dynamical systems in a finite interval, SIAM J. Control Opt., vol. 15, pp. 1050-1069, 1977.
9. E. K. Boukas, Stabilization of stochastic nonlinear hybrid systems, International Journal of Innovative Computing, Information and Control, vol. 1, pp. 131-141, 2005.
10. C. S. Jeong, E. Yaz, A. Bahakeem and Y. Yaz, Nonlinear observer design with general criteria, International Journal of Innovative Computing, Information and Control, vol. 2, pp. 693-704, 2006.
11. D. H. Jacobson, Optimal Stochastic linear systems with exponential criteria and their relation to deterministic differential games, IEEE Trans. Automat. Control, AC-18, pp. 124-131, 1973.
12. M. R. James, Asymptotic analysis of nonlinear stochastic risk-sensitive control and differential games, Math. Control Signals Systems, 5, pp. 401-417, 1992.
13. ∞-norm bound and relations to risk sensivity, Systems Control Lett., 11, pp. 167-172, 1998.
14. P. Whitttle, A risk-sensitive maximum principle, Syst. Control Lett., 15, pp. 183-192, 1990.
15. P. Whitttle, A risk-sensitive maximum principle: the case of the imperfect state information, IEEE Trans. Automat. Control, 36, pp. 793-801, 1991.
16. W. H. Fleming and W.M. McEneaney, Risk-sensitive control on an infinite time horizon, SIAM, Control and Opt., vol. 33, no. 6, pp. 1881-1915, 1995.
17. W. H. Fleming et al., Robust limits of risk sensitive nonLinear filters, Math. Control Signals and Systems, vol. 14, pp. 109-142, 2001.
18. ∞ problems: Error analysis, SIAM J. Control and Opt, vol. 43, pp. 379-412, 2004.
19. ∞-control, Proc. of the 29th. IEEE CDC, Honolulu, HI, pp. 1018-1023, Dec. 1990.
20. T. Runolfsson, The equivalence between infinite horizon control of stochastic systems with exponential-of-integral performance index and stochastic differential games, Technical report JHU/ECE, pp. 91-107, Johns Hopkins University, 1991.
21. ∞ Control Theory, Lecture Notes in Control and Information Sciences, vol. 88, Springer-Verlag, New York, 1987.
22. H. Dym and H. P. McKean, Fourier Series and Integrals, Academic Press, New York, 1975.
23. ∞ Optimal Control and Related Minimax Design Problems, Birkhaäuser, Boston, 1991.
24. ∞ control for time varing systems, Proc. of the International Symposium on the Mathematical Theory of Networks and Systems, Amsterdam, Netherlands, 1989.
25. ∞ Control via measurement feedback for affine nonlinear systems, Internal Paper, Dept. Systems Science and Mathematics, Washington University, St, Louis, 1992.
26. A. Isidori, Robust regulation of nonlinear systems, MTNS Abstracts, Kobe, Japan, 1991.
27. ∞ control for nonlinear plants: connections with differential games, Proc. of the 28th IEEE Conf. Dec. Control, Tampa Fl, pp. 956-962, 1989.
28. M. James, A partial differential inequality for dissipative nonlinear systems, Systems and Control Letters.
29. W. H. Fleming and W.M. McEneaney, Risk-sensitive control and differential games, Springer Lecture Notes in Control and Info. Sci., vol. 184, Springer-Verlag, New York, pp. 185-197, 1992.
30. ∞ Control: The Non Linear Case, Doctoral Thesis, Brown University, 1993.
31. M. V. Basin and M.A Alcorta-Garcia, Optimal filtering and control for third degree polynomial systems, Dynamics of Continuous Discrete and Impulsive Systems, vol. 10, pp. 663-680, 2003.
32. M. V. Basin and M.A Alcorta-Garcia, Optimal filtering for bilinear systems and its application to terpolymerization process state, Proc. of the IFAC 13th. Symposium System Identification-SYSID-2003, pp. 467-472, 2003.
33. F. L. Lewis, Applied Optimal Control and Estimation Prentice Hall Englewood Cliffs, New Jersey, EUA, 1992.
34. V. S. Pugachev and I. N. Sinitsyn, Stochastic Systems Theory and Applications, World Scientific, Singapore, 2001.
35. S. S.-T. Yau, Finite-dimensional filters with nonlinear drift I: a class of filters including both Kalman-Bucy and Benes filters, J. Math. Systems Estimation and Control, pp. 181-203, 1994.
36. H. Zhang, M. V. Basin and M. Skliar, Optimal state estimation for continuous, stochastic, state-space system with hybrid measurements, International Journal of Innovative Computing, Information and Control, vol. 2, pp. 863-874, 2006.
37. M. V. Basin, J. Perez and R. Martinez-Zuniga, Optimal filtering for nonlinear polynomial systems over linear observations with delay, International Journal of Innovative Computing, Information and Control, vol. 2, pp. 357-370, 2006.
38. R. E. Mortensen, Maximum likelihood recursive nonlinear filtering, J. Optim. Theory Appl. pp. 386-394, 1968.
39. ∞ filtering for nonlinear systems, Systems and Control Letters, pp. 15-325, 1998.
40. M. D. Donsker and S. R. S. Varaqdhan, Asymptotic evaluation of certain Markov process expectations for large time, I, II, III, Comm. Pure Appl. Math., vol. 28, pp. 1-45, 279-301, 1975;
41. vol. 29, pp. 389-461, 1976.
42. W. McEneaney, Robust/game-theoretic methods in filtering and estimation, Proc. of the DARPA Symposium an Advances in Enterprise Control, 1999.
43. R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, ASME J. Basic Eng. Ser. D, vol. 83, 1961.