SUBOPTIMAL CONTROL OF NONLINEAR STOCHASTIC-SYSTEMS

Theoretical procedures are developed for comparing the performance of arbitrarily selected admissible feedback controls among themselves wit h the optimal solution of a nonlinear optimal stochastic control probl em. Iterative design schemes are proposed for successively improving t he performance of a controller until a satisfactory design is achieved . Specifically, the exact design procedure is based on the generalized Hamilton-Jacobi-Bellman equation of the cost function of nonlinear st ochastic systems, and the approximate design procedure for the infinit e-time nonlinear stochastic regulator problem, is developed by using t he upper and lower bounds of the cost functions. Stability of this pro blem is also considered. For a given controller, both the upper and lo wer bounds to its cost function can be obtained by solving a partial d ifferential inequality. These bounds, constructed without actually kno wing the optimal controller, are used as measure to evaluate the accep tability of suboptimal controllers. These results establish an approxi mation theory of optimal stochastic control and provide a practical pr ocedure for selecting effective practical controls for nonlinear stoch astic systems. An Entropy reformulation of the Generalized Hamilton-Ja cobi-Bellman equation is also presented.