Application of a Semi-Analytical Method to Model Predictive Control

Abstract

This thesis proposes a semi-analytical algorithm, named repetitive optimal open-loop control (ROC), based on the Model Predictive Control (MPC) framework to generate open-loop feedback control for solving dynamic nonlinear optimal control problems with constraints. The algorithm is developed for the continuous-time NMPC. The generated feedback law builds a semi-analytical solution between the optimal control variables and states. The resulting optimal control trajectory is well defined in a continuously varied sequence.

The optimal control problem is converted into a two-point boundary-value problem (TPBVP) form, and solved by a back-and-forth shooting method. State and output constraints are dealt with the penalty function approach. The Kalman filter is used for state estimation. Implementation of ROC algorithm is done: algorithm competency testing with a hydro-electric power plant chain experiment; and normal solution proposal for optimal control problem with an exothermic chemical reactor application. Results prove out without any doubt it is a promising optimal control algorithm for handling fairly complicated constrained nonlinear dynamic systems.

Keywords: model predictive control (MPC), repetitive optimal open-loop control (ROC), two-point boundary-value problem (TPBVP), back-and-forth shooting.