Computationally efficient robust MPC using optimized constraint tightening

TL;DR

This paper introduces a robust MPC method that minimizes constraint tightening through offline optimization of disturbance-affine feedback, achieving computational efficiency comparable to nominal MPC while ensuring stability and feasibility.

Contribution

The main novelty is the offline design of a disturbance-affine feedback gain that minimizes constraint tightening via convex optimization, improving robustness and efficiency.

Findings

Computational complexity is similar to nominal MPC.

Guarantees recursive feasibility, stability, and constraint satisfaction.

Demonstrated advantages through numerical examples.

Abstract

A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed approach compared to existing robust MPC methods are demonstrated using numerical examples.