On the Robustness Properties of Gain-scheduled Unconstrained MPC for LPV Systems

Abstract

In this brief paper, we assess the robustness qualities of gain-scheduled Model Predictive Control (MPC) algorithms for Linear Parameter Varying (LPV) systems. We consider unconstrained MPC schemes that rely on the scheduling signal from the current sampling instant (thus gain-scheduled). Accordingly, we generalise previous results on finite-horizon robustness analysis of linear time-variant processes, describing the input-output behaviour of the uncertainties through Integral Quadratic Constraints (IQCs). Uncertainties arise due to the unavailability of the future scheduling behaviour, resulting in model-process mismatches, which are represented as the interconnection of a known gain-scheduled system and a nonlinear feedback. We provide the robust closed-loop induced gains (L2 and L2-to-Euclidean) and reachable state sets, conceived through dissipativity arguments. A benchmark example is provided in order to illustrate the analysis procedure. The proposed framework can be directly used for robust gain-scheduled MPC synthesis, without requiring terminal ingredients.