H∞ Control for Oscillator Systems With Event-Triggering Signal Transmission of Internet of Things

Abstract

This article proposes to design a distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> optimal control algorithm for Van der Pol oscillators with unknown internal dynamics, input constraints and external disturbances, via event-triggering signal transmission of the Internet of Things (IoT). First, the graph theory for the IoT is introduced. Second, the dynamics of Van der Pol oscillators are transformed into the tracking dynamics which cooperate via the IoT network. Third, unlike the existing online optimal control algorithms using adaptive dynamic programming, we design an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> optimal control algorithm employing an event-triggering signal transmission mechanism to reduce the burden of communication resource and computation bandwidth of the IoT network. As the triggering condition and approximation parameter update policies are appropriately designed, the algorithm guarantees that the Zeno phenomenon is free, the consensus errors are uniformly ultimately bounded, and the external disturbance is compensated. Finally, numerical simulation results with comparison to the time-triggering algorithms confirm the effectiveness of the proposed algorithm.