Data-Driven Model Predictive Control (MPC) with Stability and Robustness Guarantees

This repository is an implementation of the robust data-driven model predictive control (MPC) scheme presented in the paper "Data-Driven Model Predictive Control With Stability and Robustness Guarantees" by Julian Berberich, Johannes Köhler, Matthias A. Müller, and Frank Allgöwer. The methodology is based on a data-driven approach utilizing behavioral systems theory and does not require a prior identification step, only an initially measured input-output trajectory and an upper bound on the system's order.

Abstract

The authors propose a robust data-driven MPC scheme for controlling linear time-invariant systems. The scheme relies on an implicit model description based on past measured trajectories. In the absence of measurement noise, the paper establishes the exponential stability of a nominal data-driven MPC scheme with terminal equality constraints. Furthermore, for bounded additive output measurement noise, the authors propose a robust modification including a slack variable with regularization in the cost. The robust MPC scheme leads to practical exponential stability of the closed-loop with respect to the noise level, marking the first theoretical analysis of the closed-loop properties of such a purely data-driven MPC scheme.

Before Implementation

    pip3 install control cvxpy

Implementation Files

This repository contains the following Python scripts which simulate the control scheme as described in the paper:

• Compute_init_cond.py: Script to compute initial conditions for MPC simulations.
• henkel_r.py: Module for handling Hankel matrix operations.
• MDL_sim_prestab.py: Script to simulate the model with pre-stabilization.
• Robust_DD_MPC.py: The main script implementing the robust data-driven MPC algorithm.

Results

Included in this repository are the results demonstrating the closed-loop properties achieved by the data-driven MPC scheme. These results validate the robustness and stability guarantees of the algorithm and are key to understanding the practical applications of the proposed control scheme.

Citing This Work

J. Berberich, J. Köhler, M. A. Müller and F. Allgöwer, "Data-Driven Model Predictive Control With Stability and Robustness Guarantees," in IEEE Transactions on Automatic Control, vol. 66, no. 4, pp. 1702-1717, April 2021, doi: 10.1109/TAC.2020.3000182.