Lie algebraic methods in optimal control of stochastic systems with exponential-of-integral cost

The purpose of this paper is to formulate and study the optimal control of partially observed stochastic systems with exponential-of-integral-sample c ost, known as risk-sensitive problems, using Lie algebraic tools. This lead s to the introduction of the sufficient statistic algebra, L-s, through whi ch one can determine a priori the maximum order of the controller. When dim (L-s) < infinity, the construction of the control laws is addressed through extensions of the Wei-Norman method, as in nonlinear filtering problems. A side from specific known finite-dimensional examples which are studied in o rder to delineate the application of the Lie algebraic tools, new classes o f finite-dimensional controllers are identified as well. In addition, relat ions with minimax dynamic games are explored to best assess the importance and generality of the finite-dimensional control systems. (C) 1999 Elsevier Science B.V. All rights reserved.