On Finite-dimensional Risk-sensitive Estimation

In this paper, we address the finite-dimensionality issues regarding discrete-time risk-sensitive estimation for stochastic nonlinear systems. We show that for a bilinear system with an unknown parameter, finite-dimensional risk-sensitive estimates can be obtained. A necessary condition is obtained for nonlinear systems with no process noise such that one can obtain finite-dimensional risk-sensitive estimates.

[1]  Robert J. Elliott,et al.  Finite Dimensional Risk Sensitive Information States , 1995 .

[2]  P. Whittle.  Risk-sensitive linear/quadratic/gaussian control , 1981, Advances in Applied Probability.

[3]  Robert J. Elliott,et al.  Risk-sensitive generalizations of minimum variance estimation and control , 1997 .

[4]  J. Levine,et al.  Exact finite dimensional filters for a class of nonlinear discrete-time systems † , 1986 .

[5]  V. Benes.  Exact finite-dimensional filters for certain diffusions with nonlinear drift , 1981 .

[6]  S. Dey,et al.  Risk-sensitive filtering and smoothing via reference probability methods , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[7]  M. James,et al.  Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems , 1994, IEEE Trans. Autom. Control..

[8]  John B. Moore,et al.  Risk-sensitive filtering and smoothing for hidden Markov models , 1995 .

[9]  W. Wong.  New classes of finite-dimensional nonlinear filters , 1983 .

[10]  John S. Baras,et al.  Finite-dimensional optimal controllers for nonlinear plants , 1995 .

[11]  Rhodes,et al.  Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games , 1973 .

[12]  O. Zeitouni.  An extension of the Beneš filter and some identification problems solved by nonlinear filtering methods , 1984 .

[13]  J. Speyer,et al.  Optimal stochastic estimation with exponential cost criteria , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[14]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[15]  A. Bensoussan,et al.  Optimal control of partially observable stochastic systems with an exponential-of-integral performance index , 1985 .