Abstract
In this paper we consider a finite horizon, nonlinear, stochastic, risk-sensitive optimal control problem with complete state information, and show that it is equivalent to a stochastic differential game. Risk-sensitivity and small noise parameters are introduced, and the limits are analyzed as these parameters tend to zero. First-order expansions are obtained which show that the risk-sensitive controller consists of a standard deterministic controller, plus terms due to stochastic and game-theoretic methods of controller design. The results of this paper relate to the design of robust controllers for nonlinear systems.
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Research supported in part by the 1990 Summer Faculty Research Fellowship, University of Kentucky.
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James, M.R. Asymptotic analysis of nonlinear stochastic risk-sensitive control and differential games. Math. Control Signal Systems 5, 401–417 (1992). https://doi.org/10.1007/BF02134013
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DOI: https://doi.org/10.1007/BF02134013