Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

TL;DR

This paper introduces a scalable robust model predictive control method for uncertain linear systems using ellipsoidal sets, ensuring constraint satisfaction and stability with linear computational complexity.

Contribution

It presents a novel ellipsoidal tube MPC approach that handles dynamic uncertainties efficiently, with offline design and linear online complexity.

Findings

Guarantees constraint satisfaction and recursive feasibility.

Ensures closed-loop stability.

Demonstrates effectiveness through simulation studies.

Abstract

This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of the system. The design of the state tube is formulated as an offline optimization problem, which offers flexibility to impose desirable features such as robust invariance on the terminal set. This contrasts with most existing tube MPC strategies using polytopic sets in the state tube, which are difficult to design and whose complexity grows combinatorially with the system order. The algorithm guarantees constraint satisfaction, recursive feasibility, and stability of the closed loop. The advantages of the algorithm are demonstrated using two simulation studies.