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Implementation of Continuous-time MPC Using B-spline Functions

In this paper some implementation aspects of the continuous-time stabilizing model predictive control (MPC) based on B-spline functions are addressed. Specifically, two problems are discussed: (a) suitable parametrization of control variables and (b) intersample satisfaction of constraints. The proposed solution relies on B-spline functions parametrization of the control variable during a continuous-time cost function minimization. The close relation between B-spline curves and their control polygons is utilized for the intersample satisfaction of constraints. Stability of the closed-loop system is standardly ensured through a quasi-infinite horizon approach by means of a terminal cost, a terminal constraint set, and an auxiliary (local) controller.