Optimization Algorithms In Stochastic Model Predictive Control Based On Monte Carlo Methods

The difference between Stochastic Model Predictive Control (SMPC) and Standard Model Predictive Control is that the former one deals with uncertainties systematically,while the later one compensate the uncertainties with feedback. In Stochastic Model Predictive Control, chance constraints are presented and the objective function is an mathematical expectation. As a result, stochastic programming is carried out in a receding horizon mode. Monte Carlo methods are preferred in solving stochastic programming problems.This thesis deeply studied the stochastic optimization based on Monte Carlo methods and their application in SMPC. The production fluctuation and demand uncertainties always exist in the supply chain systems. To reduce the cost brought by uncertainties in supply chain management (SCM), based on the previous work on the model predictive control of supply chain management pioneered by researchers, we formed a SMPC framework for SCM and take advantage of MCMC to obtain the control signal. We propose two modes according to different inventory level: MCMC and Chance-constraints, which are verified by simulation study that they perform better than standard MPC in restrain inventory variation and production variation respectively. Besides, in order to reduce the overall cost in the long run, we build a switching scheme for the two modes. We prove the existence of a optimal switching bound and find the bound based on game theory. Also the simulation results show its optimality.As to the Non-linear No-Gaussian model, this thesis demonstrates the state estimation and solution of control law based on Sequential Monte Carlo. We propose an integration of state estimation and control law. The particles of control law are marginalized by Rao-Blackwell theory, and the prediction of the state is based on the current state estimation. Then the problem is solved by Sequential Monte Carlo.