Predictive Control for Polynomial Systems Subject to State and Input Constraints

We present a nonlinear model predictive control (NMPC) approach to design optimal feedback controllers for the class of continuous-time input affine polynomial systems subject to state and input constraints. The corresponding feedback law is obtained via the solution of an efficient to solve convex optimization problem subject to sum of squares (SOS) constraints. To serve the conflicting requirements of performance and computational costs in various applications, the approach comes in three different control schemes which differ in how many times the (updated) optimization problem has to be solved, and whether this is done on- or offline. Each of the proposed control schemes minimizes an upper bound on the cost functional while guaranteeing closed-loop stability and satisfaction of input and state constraints. Finally, simulations of an example system show the applicability and the effectiveness of the proposed controllers.