Indirect-adaptive Model Predictive Control for Linear Systems with Polytopic Uncertainty

Abstract

We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but unknown. Robust constraint satisfaction is obtained by constraints enforcing a robust control invariant. The terminal cost and set are constructed from a parameter-dependent Lyapunov function and the associated control law. The proposed design ensures robust constraint satisfaction and recursive feasibility, is input-to-state stable with respect to the parameter estimation error and it only requires the online solution of quadratic programs.