The role of information state and adjoint in relating nonlinear output feedback risk-sensitive control and dynamic games

This paper employs logarithmic transformations to establish relations between continuous-time nonlinear partially observable risk-sensitive control problems and analogous output feedback dynamic games. The first logarithmic transformation is introduced to relate the stochastic information state to a deterministic information state. The second logarithmic transformation is applied to the risk-sensitive cost function using the Laplace-Varadhan lemma. In the small noise limit, this cost function is shown to be logarithmically equivalent to the cost function of an analogous dynamic game.

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

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

[3]  W. Fleming,et al.  Optimal Control for Partially Observed Diffusions , 1982 .

[4]  Ioannis Karatzas,et al.  On the Relation of Zakai’s and Mortensen’s Equations , 1983 .

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

[6]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[7]  M. James,et al.  Nonlinear filtering and large deviations:a pde-control theoretic approach , 1988 .

[8]  P. Whittle.  A risk-sensitive maximum principle , 1990 .

[9]  P. Whittle.  A risk-sensitive maximum principle: the case of imperfect state observation , 1991 .

[10]  Matthew R. James,et al.  Asymptotic analysis of nonlinear stochastic risk-sensitive control and differential games , 1992, Math. Control. Signals Syst..

[11]  W. Fleming,et al.  Risk sensitive optimal control and differential games , 1992 .

[12]  M. James,et al.  Output feedback risk-sensitive control and differential games for continuous-time nonlinear systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[14]  Kevin L. Moore,et al.  Solvable risk-sensitive control problems with output feedback , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[15]  Charalambos D. Charalambous,et al.  Remarks on the explicit solutions for nonlinear partially observable stochastic control problems and relations to H/sup /spl infin// or robust control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[16]  Robert J. Elliott,et al.  General finite-dimensional risk-sensitive problems and small noise limits , 1996, IEEE Trans. Autom. Control..

[17]  Finite Dimensional Observers and Controllers for Nonlinear Systems , 1996 .

[18]  Charalambos D. Charalambous.  Partially observable nonlinear risk-sensitive control problems: dynamic programming and verification theorems , 1997, IEEE Trans. Autom. Control..