Robust MPC for constrained LPV systems with guaranteed ISS and finite L2-gain

The paper presents a robust model predictive control (MPC) algorithm for linear parameter-varying (LPV) systems subject to constraints on the state and control, and uncertain disturbance including model uncertainty and unknown but bounded disturbances. A finite horizon cost function on states, controls and disturbances is defined and the min-max optimization problem of robust MPC is reduced to a convex minimization problem involving linear matrix inequalities (LMI) constraints. In order to improve potential performance, a parameter-dependent MPC controller is developed so that it becomes self-scheduling via time-varying parameters measured in real-time. The notions of the input-to-state stability and finite L₂-gain are introduced to achieve the closed-loop robustness of the obtained MPC controller. Finally, an example of classical angular positioning system is used to illustrate the effectiveness of results obtained here.