Learning Robustness with Bounded Failure: An Iterative MPC Approach

TL;DR

This paper introduces an iterative MPC method that learns disturbance support sets from data to robustly satisfy constraints in linear systems, reducing conservativeness and bounding violation probability.

Contribution

It presents a novel iterative MPC framework that uses confidence support sets to adaptively learn disturbance support, improving robustness without excessive conservativeness.

Findings

Confidence support sets converge to true disturbance support with more data

The approach bounds the probability of constraint violation

Numerical example demonstrates effectiveness of the method

Abstract

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain the true support of the disturbance distribution with a given probability. As more data is collected, the Confidence Supports converge to the true support of the disturbance. This enables design of an MPC controller that avoids conservative estimate of the disturbance support, while simultaneously bounding the probability of constraint violation. The efficacy of the proposed approach is then demonstrated with a detailed numerical example.