Offline NMPC for continuous-time systems using sum of squares

Abstract

An offline nonlinear model predictive control (NMPC) approach for continuous time nonlinear systems subject to input and state constraints is presented. The approach deals with nonlinear systems which can be represented by polynomial parameter-varying systems. Since the applicability of NMPC is often limited by the speed at which an optimization problem can be solved online, we propose an NMPC scheme with drastically reduced online computational burden. The basic idea involves the offline computation of nested invariant sets and associated feedback laws by solving a convex optimization problem subject to sum of squares (SOS) constraints via semidefinite programming (SDP). Online, a search algorithm is executed to determine the feedback law suitable for the current state. The resulting offline NMPC controller guarantees stability and constraint satisfaction. Its applicability and effectiveness is shown by means of simulation of an example system.

A new switched off‐line NMPC approach for nonlinear systems with a switching performance index using an extended modal series method

“…In recent years, in order to design an NMPC with mitigated online computational burden, several off‐line approaches have been designed, ie, the approaches based on the linear matrix inequality technique for Lur'e systems and polynomial control systems . In the work of Deroo et al, these approaches are extended to the general affine‐input nonlinear systems by using polynomial parameter‐varying system representations. Unfortunately, this approach considerably increases the computational burden by increasing the nested invariant set and inserting state‐dependent time‐varying parameters.…”