Robustness analysis of gain‐scheduled Model Predictive Control for Linear Parameter Varying systems: An Integral Quadratic Constraints approach

Abstract

AbstractIn this paper, we evaluate the robustness qualities of Model Predictive Control (MPC) algorithms applied for Linear Parameter Varying (LPV) systems. Specifically, we analyze gain‐scheduled LPV MPC schemes, that is, those that use model predictions based on the LPV scheduling variables available at each sampling instant. Accordingly, we extend previous results on finite‐horizon robustness analysis of linear time‐variant (LTV) systems, employing Integral Quadratic Constraints (IQCs) to describe the input‐output behavior of prediction uncertainties. We provide two main novelties in our formulation: (i) we propose a parameter‐dependent Karush–Kuhn–Tucker (KKT) inequality to describe the existence and feasibility of the LPV MPC control inputs; and (ii) we model the uncertainties that arise due to the unavailability of the scheduling trajectory along the prediction horizon as a bounded interconnection in the form of a Linear Fractional Transformation (LFT). Accordingly, we use dissipativity arguments (‐hard IQCs) in order to compute robust induced gains of the closed‐loop system (specifically, the and ‐to‐Euclidean metrics), taking into account the MPC prediction uncertainties. We also generate the set of reachable states from a given initial condition. A benchmark example is used to illustrate the proposed analysis procedure.