Direct Data-Driven Computation of Polytopic Robust Control Invariant Sets and State-Feedback Controllers

Abstract

This paper presents a direct data-driven approach for computing robust control invariant (RCI) sets and their associated state-feedback control laws. The proposed method utilizes a single state-input trajectory generated from the system, to compute a polytopic RCI set with a desired complexity and an invariance-inducing feedback controller, without the need to identify a model of the system. The problem is formulated in terms of a set of sufficient LMI conditions that are then combined in a semi-definite program to maximize the volume of the RCI set while respecting the state and input constraints. We demonstrate through a numerical case study that the proposed data-driven approach can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. Under the assumption of persistency of excitation of the data, the proposed algorithm guarantees robust invariance even with a small number of data samples. Overall, the direct data-driven approach presented in this paper offers a reliable and efficient counterpart to the model-based methods for RCI set computation and state-feedback controller design.Comment: 9 pages, 4 figures, preprint submitted to 62nd IEEE Conference on Decision and Control 202