FINITE-DIMENSIONAL OPTIMAL CONTROLLERS FOR NONLINEAR PLANTS

Optimal risk sensitive feedback controllers are now available for very general stochastic nonlinear plants and performance indices, They con sist of nonlinear static feedback of so called information states from an information state filter. In general, these filters are linear, bu t infinite dimensional, and the information state feedback gains are d erived from (doubly) infinite dimensional dynamic programming. The cha llenge is to achieve optimal finite dimensional controllers using fini te dimensional calculations for practical implementation. This paper d erives risk sensitive optimality results for finite-dimensional contro llers. The controllers can be conveniently derived for 'linearized' (a pproximate) models (applied to nonlinear stochastic systems). Performa nce indices for which the controllers are optimal for the nonlinear pl ants are revealed. That is, inverse risk-sensitive optimal control res ults for nonlinear stochastic systems with finite dimensional linear c ontrollers are generated. It is instructive to see from these results that as the nonlinear plants approach linearity, the risk sensitive fi nite dimensional controllers designed using linearized plant models an d risk sensitive indices with quadratic cost kernels, are optimal for a risk sensitive cost index which approaches one with a quadratic cost kernel, Also even far from plant linearity, as the linearized model n oise variance becomes suitably large, the index optimized is dominated by terms which can have an interesting and practical interpretation. Limiting versions of the results as the noise variances approach zero apply in a purely deterministic nonlinear H-infinity setting. Risk neu tral and continuous-time results are summarized. More general indices than risk sensitive indices are introduced with the view to giving use ful inverse optimal control results in non-Gaussian noise environments .