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Data-Driven Control of Linear-Threshold Network Dynamics

This paper studies the data-driven stabilization of linear-threshold network models. Our goal is to design a linear state feedback controller to stabilize the system to the origin purely based on data samples, instead of a parametric model. To achieve this, we first establish a data-based representation for the linear-threshold network in an open-loop form. This is done by introducing a map that represents the state-input pair as a transformation of data matrices. We then employ a linear feedback controller in the formulation of the map and obtain a closed-loop data-based representation for the system. To facilitate the design of the feedback gain matrix, we rewrite the dynamics as a switched linear system relying on the special structure of linear thresholding. The design problem then becomes equivalent to solving a system of linear matrix inequalities (LMIs). We analyze the associated computational complexity and, to reduce it, we introduce a different set of LMIs that act as a sufficient condition to obtain the linear control design. Simulations demonstrate the effectiveness of the proposed approach.