MPC with one free control action for constrained LPV systems

Based on the assumption that the parameter can be measured in real time, we propose a model predictive control (MPC) method for linear-parameter varying (LPV) systems subject to possibly asymmetric constraints which adopts the analogous framework of terminal control law, terminal set and terminal penalty of nonlinear model predictive control. The optimization problem is formulated as a convex optimization problem and, recursive feasibility and closed-loop stability are guaranteed by its feasibility at initial time. For LPV systems with symmetric constraints, we reformulate the convex optimization problem as a semi-definite program. Numerical examples demonstrate the properties of the proposed MPC design.