Improved Quasi-Min-Max MPC for Constrained LPV Systems via Nonlinearly Parameterized State Feedback Control

We consider the regulation problem of linear parameter varying systems with input and state constraints. It is assumed that the time-varying parameters are available at the current time, but their future behavior is unknown and contained in a polytopic set. The aim is to design a new stabilizing quasi-min-max MPC algorithm via a nonlinearly parameterized state feedback control law. It is shown that the use of such a control law leads to less conservative results compared to those derived from linearly parameterized state feedback control laws. At each time instant, a convex semi-definite optimization problem is required to solved. Two numerical examples, including a non-quadratically stabilizable system, are given with comparison to earlier solutions from the literature to illustrate the effectiveness of the proposed approaches.