Improved Design of Nonlinear Model Predictive Controllers

One way to ensure recursive feasibility, stability and performance of Nonlinear Model Predictive Control is the combined use of a terminal region and a terminal cost. However, finding suitable combinations of the terminal cost and terminal region that guarantee closed-loop stability for nonlinear systems is in general challenging. Most existing methods are either based on the linearized system dynamics and a linear feedback, or assume that a control Lyapunov function for the system close to the origin is know. This paper proposes the use of higher order approximations of the optimal feedback and optimal cost of the infinite horizon problem via Al’brekht’Method to determine a suitable terminal region for polynomial systems. To do so, the stability conditions are reformulated in terms of a sumof-squares problem which is iteratively used to determine the terminal region. For a nonlinear chemical reactor example it is shown that the proposed approach leads to a larger terminal region and an improved performance compared to existing approaches.