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

TL;DR

This paper introduces an indirect-adaptive model predictive control method for linear systems with polytopic uncertainty, ensuring robust constraint satisfaction and stability through quadratic programming.

Contribution

It presents a novel MPC algorithm that handles polytopic uncertainties with guaranteed robustness and recursive feasibility using parameter-dependent Lyapunov functions.

Findings

Ensures robust constraint satisfaction for uncertain systems.

Achieves recursive feasibility and input-to-state stability.

Requires only quadratic program solutions online.

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.