A Semi-Definite Programming Approach to Robust Adaptive MPC under State Dependent Uncertainty

TL;DR

This paper introduces a robust adaptive MPC method for uncertain linear systems with state-dependent uncertainties, utilizing semi-definite programming and set membership techniques for online uncertainty estimation and constraint satisfaction.

Contribution

It presents a novel semi-definite programming based adaptive MPC framework that handles state-dependent uncertainties with online envelope refinement.

Findings

Guarantees robust constraint satisfaction under uncertainty.

Effectively refines uncertainty estimates with data.

Demonstrates efficacy through a numerical example.

Abstract

We propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known Lipschitz constant. We use a non-parametric technique for online identification of the system uncertainty by approximating its graph via envelopes defined by quadratic constraints. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction for the closed loop system for all possible values of system uncertainty modeled by the envelope. The uncertainty envelope is refined with data using Set Membership Methods. We highlight the efficacy of the proposed framework via a detailed numerical example.