Computational linear and nonlinear stochastic optimal control with applications

Continuous time stochastic optimal control problems are considered that are linear (called LQGP) and nonlinear (called LQGP/U) in the state dynamics, but both are linear in the control dynamics. These problems are subject to a quadratic (Q) cost functional of the control. The cases for unconstrained (regular) and constrained control are considered. Additionally, the system is randomly perturbed by both Gaussian (G) and Poisson (P) noise. A feature of this work is that the Poisson noise can be dependent on the state or the control and introduces discrete random jumps into the value of the system. The method employed to determine a solution is computational dynamic stochastic programming.; In the LQGP formulation, a closed form solution to the Hamilton-Jacobi-Bellman (HJB) equation, which is the partial differential equation of stochastic dynamic programming, is found that requires a solution to a system of nonlinear ordinary differential equations. The form of the solution is a state-time decomposition, in which only the evolution of a coefficient space that is temporally dependent needs to be determined.; For the LQGP/U problem a numerical predictor-corrector method is used. A least squares equivalent LQGP problem in the state is used to accelerate the iterative convergence of the method which does not increase the state space computational complexity. A statistics type Gauss quadrature is developed to evaluate the Poisson integral terms that arise. These are particular features of this method.; A multistage manufacturing system (MMS) is used to illustrate both the LQGP and LQGP/U problems. The MMS considered is subject to a random environment in terms of small fluctuations in production, modeled by Gaussian noise, as well as large jumps in production due to workstation repair and failure or labor strikes, modeled by Poisson noise.