Adaptive and Optimal Control of Stochastic Dynamical Systems.

摘要

A number of results have been obtained for problems of stochastic control and stochastic differential games. Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise processes that are arbitrary fractional Brownian motions or more generally square integrable continuous processes. Linear-quadratic control problems for stochastic partial differential equations with fractional Brownian motions having the Hurst parameter in the interval (1/2,1), which includes the long range dependent processes, are solved. A direct method for solving stochastic control problems is given that does not require the solution of Hamilton-Jacobi-Bellman equations or the solution of backward stochastic differential equations. Both of these latter methods present serious difficulties for solutions. A stochastic control problem is explicitly solved for a system that evolves in the two-sphere which is useful for applications. Linear exponential quadratic Gaussian control problems for both continuous and discrete time systems are solved in a simple direct way. Linear exponential-quadratic control problems for stochastic partial differential equations are explicitly solved. Discrete time linear quadratic control problems for systems with correlated noise are explicitly solved. Linear-quadratic stochastic differential games are explicitly solved for systems with arbitrary noise. Stochastic differential games for stochastic partial differential equations with fractional Brownian motions are explicitly solved. Ergodic control problems for linear exponential quadratic control for stochastic partial differential equations with fractional brownian motions are explicitly solved. Stochastic differential games that evolve in spheres are explicitly solved. Various aspects of stochastic adaptive control are described. Some linear quadratic control problems with state dependent noise are explicitly solved.