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Asynchronous Lebesgue Approximation Model for Distributed Continuous-Time Nonlinear Systems

An appropriate approximation model can significantly reduce the computational costs in model-based approaches. This paper aims to develop discrete-time models to approximate distributed continuous-time nonlinear dynamical systems, in which subsystems are physically coupled and can receive information from their neighbors. To approximate such a system, we present asynchronous Lebesgue approximation approach, where each subsystem is approximated by an individual Lebesgue approximation model (LAM). Each LAM updates its state, depending on its own state as well as the neighboring states. Different LAMs execute asynchronously. The proposed distributed LAM is cost-efficient because it can automatically adjust its iteration frequency based on state's variation. To show stability of the distributed LAM, we construct a distributed event-triggered feedback system and prove that it generates the same state trajectories as the LAM with linear interpolation. Through this specific distributed event-triggered system, we show that the distributed LAM is uniformly ultimately bounded. Finally, we carry out some simulations on a nonlinear system to show the efficiency of the proposed method.