Robust data-driven state-feedback design

Abstract

We consider the problem of designing robust statefeedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single openloop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closedloop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the H∞-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.

An Extended Kalman Filter for Data-Enabled Predictive Control

“…and linear-quadratic tracking for deterministic LTI systems in a behavioral setting [14], [15]. This has resulted in a growing stream of literature dealing with data-driven analysis [16], [17] and control problems [18]- [21].…”

“…Unlike earlier methods, recent data-driven approaches based on the Fundamental Lemma have devoted little attention to stochastic systems. Some approaches adopt a "robust control" perspective and treat the uncertainty as a deterministic and bounded sequence [18], [20], [26], sometimes affecting just the output. The focus of the present paper is to extend the DeePC algorithm to stochastic LTI systems and design methods for including more data to improve closed-loop performance, without increasing the computational load of the optimization.…”

A geometric framework for constraints and data: from linear systems to convex processes

“…The first results building on Willems' lemma were developed in a behavioral context by Markovsky and Rapisarda [111,112]. More recently, the work was brought into the context of state space systems in for instance [15,23,30,42,72,83,118]. Also data-driven analysis has benefited from the development of the fundamental lemma.…”

“…A study of data-driven control problems in this situation is particularly interesting, because system identification is less straightforward. We note that data-driven stabilization under measurement noise has been studied in [42] and under unknown disturbances in [23]. Additionally, the data-driven LQR problem is popular in the machine learning community, where it is typically assumed that the system is influenced by (Gaussian) process noise, see e.g.…”

“…The idea is that control laws can be obtained directly from data, with the underlying mechanism that the system is represented implicitly by the so-called Hankel matrix of a measured trajectory. This framework has led to several interesting control strategies, first in a behavioral setting [111,112,114], and more recently in the context of state-space systems [22,23,41,42,83,143].…”