Non-linear state dynamics: computational methods and manufacturing application

摘要

Stochastic optimal control problems are considered that are non-linear in the state dynamics, but otherwise are an LQGP problem in the control, i.e. the dynamics are linear in the control vector and the costs are quadratic in the control. In addition the system is randomly perturbed by both continuous Gaussian (G) and discontinuous Poisson (P) noise. The approach to the solution is by way of computational stochastic dynamic programming using a new enhancement with a least squares equivalent LQGP problem in the state to accelerate the iterative convergence, without adding to the state space computational complexity since the LQGP coefficient equations are independent of the state. General Gauss statistics quadratures are developed to numerically handle Poisson jump integrals. The methods are illustrated for a multistage manufacturing system (MMS) with sufficient realism in an uncertain environment, together with implementation procedures needed to modify the formal general theory.