Continuous-time Stochastic Control Research Articles

Linear discrete stochastic control with a reduced-order dynamic compensator

In continuous-time linear stochastic control with a fixed structure, reduced-order, dynamic compensator one obtains a quasisingular problem whereby part of the structure is arbitrary. The dual of this problem in discrete time is considered with a more general formulation. Using a quadratic performance index, the Hamiltonian for obtaining the necessary conditions is obtained which may be used to define the optimal linear reduced-order dynamic compensator and the controller gain. It is shown that the discrete problem does not have the quasisingular property of the continuous-time case as is seen by consideration of the Hamiltonian.

Production Planning for a Stochastic Demand Process

This paper deals with planning production of a single good over a prescribed finite interval of time [0, T]. The costs considered within the problem are production and holding costs; holding costs are incurred for negative inventory (caused by backlogged sales) and positive inventory (caused by production in excess of demand). The demand for the product is treated as a stochastic process. Problem formulation and optimization use tools from continuous-time stochastic variational calculus and control theory. Among its results, the paper proves the uniqueness of the optimal solution and provides an algorithm for the problem.