Nonlinear State Dynamics, Computational Approximations and Multistage Manufacturing System Application

In this paper, we treat stochastic optimal control problems that are nonlinear in the state, but otherwise are a Linear-Quadratic-Gaussian-Poisson problem in the control (LQGP/U), such that the dynamics are linear in the control with quadratic costs in control. The uncertainty in the environment is modeled by Gaussian noise for continuous background uctuations and discrete random jumps by Pois-son noise. Computational approximations in the dynamic programming approach include least squares equivalent LQGP problems in the state for a state independent approximation to solutions, modiied Gauss quadrature to handle arbitrary jump distributions, and multidimensional linear interpolation for Poisson functional terms. The approximations are applied to a multistage manufacturing system (MMS) in an uncertain environment, along with implementation procedures needed to modify the formal theory for hybrid systems.