Comprehensive MPSP for Fast Optimal Control: Algorithm Development and Convergence Analysis

A computationally efficient state feedback optimal control synthesis approach, named Comprehensive Model Predictive Static Programming (C-MPSP), is presented in this paper. Using C-MPSP, one can not only handle nonlinear systems but also optimize generic cost functions and impose the necessary path and terminal constraints. It can be applied to various problems, such as terminally constrained problems, regulator problems, tracking problems, and problems with or without path constraints. A rigorous convergence analysis is presented, which, under some mild conditions, proves that the entire iterative process is guaranteed to converge within a limited number of iterations. In addition, C-MPSP is computationally very efficient owing to several key features associated with the MPSP philosophy. Because of this, the C-MPSP algorithm can be applied to synthesize state feedback optimal controllers in real-time for many practical problems. Owing to its simplicity, the algorithm can be coded easily. The applicability and efficiency of the algorithm are illustrated by applying it to optimally guide a two-wheeled differentially-driven mobile robot on a curved road to reach its destination in the presence of state constraints (road boundaries and obstacles) and control constraints.