Predictive control for polynomial systems subject to constraints using sum of squares

This paper presents a computationally attractive nonlinear model predictive control approach for the class of continuous-time input affine polynomial systems. The control law is obtained via the repeated solution of an efficient to solve convex optimization problem subject to sum of squares (SOS) constraints. Closed-loop stability and satisfaction of input and state constraints are guaranteed by the feasibility of the SOS conditions at initial time. Further, the initial solution supplies - as a byproduct - a rational feedback law guaranteeing constraint satisfaction for all times. The applicability and effectiveness of the proposed controller is shown by means of simulation of an example system.