Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Abstract

The development of control methods based on data has seen a surge of interest in recent years. When applying data-driven controllers in real-world applications, providing theoretical guarantees for the closedloop system is of crucial importance to ensure reliable operation. In this review, we provide an overview of data-driven model predictive control (MPC) methods for controlling unknown systems with guarantees on systems-theoretic properties such as stability, robustness, and constraint satisfaction. The considered approaches rely on the Fundamental Lemma from behavioral theory in order to predict input-output trajectories directly from data. We cover various setups, ranging from linear systems and noise-free data to more realistic formulations with noise and nonlinearities, and we provide an overview of different techniques to ensure guarantees for the closed-loop system. Moreover, we discuss avenues for future research that may further improve the theoretical understanding and practical applicability of data-driven MPC.

Data-Driven Tests for Controllability

“…This result has been utilized in developing identification algorithms [4,Chapter 8] and in data-driven simulation and control [5]. Recently, the fundamental lemma has received considerable attention due to growing interest in data-driven control problems [6], [7], [8], [9], [10], [11], [12], [13]. A weakness of the fundamental lemma, however, is that it requires an a priori assumption that the system under consideration is controllable.…”

Data-driven model predictive control: closed-loop guarantees and experimental results

“…Another promising approach for designing MPC schemes using only measured data stems from a result from behavioral systems theory: In [22], it is shown that one input-output trajectory of an unknown linear timeinvariant (LTI) system can be used to parametrize all trajectories, assuming that the corresponding input is persistently exciting. By replacing the standard state-space model with this data-dependent parametrization, it is simple to design MPC schemes which use input-output data instead of prior model knowledge [23,11,7]. Such MPC schemes have successfully been applied to challenging realworld examples, compare [13], and open-loop robustness properties have been established [12].…”

Data-Driven Model Predictive Control of DC-to-DC Buck-Boost Converter

“…The popularity of the data-driven model predictive control (DDMPC) scheme has recently increased due to it being naturally suitable for achieving the objectives in model predictive control (MPC), which can handle non-linear system dynamics and hard constraints, whilst taking performance criterion into account. An attractive characteristic of DDMPC is that an accurate model of the plant is dispensable as it instead utilises the plant's observational data to learn an optimal policy and make informed predictive decisions using the control feedback mechanism [1]. In contrast, model-based predictive control schemes require accurate modelling of the physical model of the considered plant using first principles, which may either be infeasible or even if these models are available, they may be intractable for controller designs due to their complexity.…”