Stochastic Adaptive Event‐Triggered Control With Almost Sure Convergence Guarantee

ABSTRACT

This paper addresses event‐triggered control for stochastic systems with large parametric uncertainties. The uncertainties necessitate adaptive compensation which needs to organically coordinate with event triggering. As such, intricate interaction of nonlinearities and discontinuities would be induced, thereby complicating the analysis in the stochastic context. As the main contribution, a framework of adaptive event‐triggered stabilization is established for the stochastic systems. Particularly, an adaptive event‐triggering mechanism is exerted, where the signal of parameter estimation is incorporated to online adjust the suspension time of state evaluation. This enables timely execution for adaptive compensation while ensuring a positive minimum inter‐execution time for almost every sample path. Recognizing the inapplicability of LaSalle theorem, a sophisticated analysis pattern of almost sure convergence is conducted. Crucially, by excavating underlying martingale properties, the coupling effect of diffusion term and parameter estimation is delicately treated for execution error assessing. On this basis, the boundedness and integrability of system state is elaborately exploited to validate the desired convergence. As the consequence within the established framework, the control synthesis of adaptive event‐triggered stabilization is fulfilled for a typical class of uncertain stochastic systems.