Finite-dimensionality of information states in optimal control of stochastic systems: A Lie algebraic approach

In this paper we introduce the sufficient statistic algebra which is respon sible for progagating the sufficient statistic, or information state, in th e optimal control of stochastic systems. Certain Lie algebraic methods wide ly used in nonlinear control theory, are then employed to derive finite-dim ensional controllers. The sufficient statistic algebra enables us to determ ine a priori whether there exist finite-dimensional controllers; it also en ables us to classify all finite-dimensional controllers.