Robust Control of Constrained Sector Bounded Lur’e Systems with Applications to Nonlinear Model Predictive Control

We consider the problem of controlling continuous-time sector bounded Lur’e systems subject to state and input constraints. First, we derive a linear static feedback law which stabilizes Lur’e systems with uncertain nonlinearities. The approach is then used to calculate the terminal region and the terminal penalty term for quasi-infinite horizon nonlinear model predictive control (NMPC). The results are further extended to a robustly stabilizing NMPC scheme and finally to an NMPC approach with low online computational demand which is based on the offline calculation of a set of ellipsoids and associated feedback laws. All controllers are calculated by solving linear matrix inequalities and satisfy state and input constraints. To illustrate their effectiveness the controllers are applied to a flexible link robotic arm and their properties are discussed by means of the obtained simulation results.