Data-Driven Inference of Passivity Properties via Gradient Flows and Finite-Time Stabilization

Abstract

In this paper, we address the problem of computing passivity indices-quantitative measures of a system's passivity-due to their significance in controller design. In practical scenarios, the explicit input-output relationship of a system is often unavailable, and only input-output data from simulations or experiments can be accessed. We focus on determining the passivity indices of a discrete linear time-invariant system using optimal input-output samples tailored to the specific property being assessed. Here, passivity indices are formulated as an objective function of an optimization problem. To compute these indices, we introduce prescribed-time gradient flows, which has the property of guaranteed convergence, within a prior chosen time. Notably, the proposed method is data-driven and does not require knowledge of the system's mathematical model, as it relies solely on gradients computed from data. Furthermore, we leverage the feedback interconnection properties of passive systems to ensure both asymptotic and finite-time stability of the discrete-time system, using only the computed passivity indices. Specifically, stabilization is achieved by employing input feedforward passive and output feedback passive systems as controllers, again without requiring the explicit model of the system. Simulation results for the coupled tank system shows the effectiveness of the proposed approach.