Data‐Driven Control of Discrete‐Time Two‐Dimensional Systems With Noisy Data

Abstract

This paper considers the stabilization issue of unknown two‐dimensional (2‐D) Fornasini–Marchesini (FM) systems with noisy data. Note that existing results on 2‐D systems require accurate system models, which are almost impossible to be obtained in practice. Within this context, a robust data‐based control strategy for unknown 2‐D FM systems is put forward herein. First, based on the data collection of 2‐D input and state measurements, the data‐based representation is established for a set of 2‐D FM systems consistent with these sampled data, leading to the purpose of stabilizing such a set of data‐consistent 2‐D dynamics with robustness. Then, the noisy data embedded in the set of data‐consistent 2‐D dynamics is expressed by virtue of a matrix ellipsoid, which motivates the potential of applying Petersen's lemma to cope with the noise impacts in the closed loop. Next, data‐driven sufficient conditions on ensuring the stability of 2‐D FM systems are developed, and the feasibility of such convex programming leads to the control strategy synthesis with data informativity. Finally, the effectiveness and applicability of the developed data‐based 2‐D control scheme are verified by the case study of the Darboux equation.