Stochastic Control Problems

Abstract

A stochastic control problem is to determine a control law within a rather general set of control laws such that the closed-loop system meets prespecified control objectives. A stochastic control problem is motivated by control problem of engineering, economics, or other areas of the sciences. The concepts of an information pattern, a control law, and of a closed-loop stochastic system are defined. The main control objectives are stability, optimization of performance, and robustness in case of changes in the control system. Control synthesis at a theoretic level is described. Statistical decision problems are treated as elementary stochastic control problems in which there is no dynamics.