Learning to Satisfy Unknown Constraints in Iterative MPC

TL;DR

This paper introduces an iterative control method for linear systems that learns to satisfy unknown constraints over repeated tasks, providing guarantees and balancing safety with performance.

Contribution

It presents a novel iterative learning approach to estimate and satisfy unknown environment constraints using data-driven MPC with probabilistic guarantees.

Findings

The method guarantees constraint satisfaction with high probability.

It effectively balances safety and performance in control tasks.

Demonstrated robustness and safety in numerical simulations.

Abstract

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a detailed numerical example.