Linear convex stochastic optimal control with applications in production planning

Abstract

Linear stochastic systems with convex performance criteria and convex, compact control regions are studied. The admissible control region is assumed to be a continuous function of the (perfectly) observed state. Optimal feedback controls are shown to exist within the class of Borel measurable functions of past states. In fact, they are shown to be continuous functions of the present state. Using dynamic programming the optimal return function is shown to be convex. Generalization of the results to quasi-convex cost functions is discussed and asymptotic results for stable systems are derived. These results are then used to explore several problems in aggregate production and workforce planning. Computational aspects of the results in the context of the smoothing problem are discussed.