Efficient offline model predictive control of constrained nonlinear periodic systems*

We propose an offline model predictive control approach for nonlinear periodically time-varying systems subject to state and input constraints. Under the assumption that the nonlinear system can be approximated using a periodic linear differential inclusion, we offline calculate a set of ellipsoids and associated feedback matrices by the solution of a semi-definite program. Online, the smallest ellipsoid containing the current state is determined, and the corresponding control law is applied to the system. The approach relaxes the conditions of existing approaches applicable to the considered system class. The effectiveness of the proposed controller is demonstrated by its application to a magnetic satellite attitude control problem.