Learning Model Predictive Control for Periodic Repetitive Tasks

TL;DR

This paper introduces a reference-free learning model predictive control method tailored for periodic repetitive tasks with time-varying dynamics and constraints, ensuring stability and cost efficiency.

Contribution

It develops a novel learning MPC approach that constructs time-varying terminal sets and costs from closed-loop data for periodic tasks.

Findings

Guarantees recursive constraint satisfaction

Ensures non-increasing open-loop cost

Achieves cost convergence at steady state

Abstract

We propose a reference-free learning model predictive controller for periodic repetitive tasks. We consider a problem in which dynamics, constraints and stage cost are periodically time-varying. The controller uses the closed-loop data to construct a time-varying terminal set and a time-varying terminal cost. We show that the proposed strategy in closed-loop with linear and nonlinear systems guarantees recursive constraints satisfaction, non-increasing open-loop cost, and that the open-loop and closed-loop cost are the same at convergence. Simulations are presented for different repetitive tasks, both for linear and nonlinear systems.