Aperiodically Delay Intermittent Control for Levy Noise Driven Highly Nonlinear Stochastic Hybrid Systems Based on Discrete-Time Observations

• 成果类型: Article
• 署名作者: Li, Wenrui; Xu, Henglei; Fei, Chen; Mao, Xuerong; Fei, Weiyin
• 署名单位: Beijing Institute of Technology; Anhui Polytechnic University; University of Strathclyde; University of Shanghai for Science & Technology; Anhui Polytechnic University; Anhui Polytechnic University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3576694
• 发表日期: 2025
• 关键词: FEEDBACK-CONTROL; differential-equations; PTH-MOMENT; stabilization; diffusion; STABILITY; state; MODEL; sure

摘要

To tackle the challenge of effectively stabilizing an inherently unstable highly nonlinear stochastic hybrid system while simultaneously minimizing costs, this article introduces a novel control strategy termed aperiodically delayed intermittent control (ADIC), grounded in discrete-time observations. Diverging from the conventional stochastic hybrid system driven by Brownian motion, we adopt Levy noise to characterize the random perturbations, which possess the capacity to capture the discontinuous, heavy tail, and peak pulse features associated with random jumps. Leveraging the Lyapunov functional approach and the strong ergodicity theory of Markov chains, we establish the mean-square exponential stability of a controlled highly nonlinear stochastic hybrid system subjected to Levy noise. Furthermore, the range of the average time rate for ADIC and the range of duration separating two consecutive observations are given. One particular note is our introduction of a novel technique for estimating the difference between the current state (or mode) and the discrete-time state (or mode). This innovation leads to less stringent conditions imposed on both the underlying system and the control function. Finally, we apply our theoretical findings to the modified FitzHugh-Nagumo models and the stochastic Gilpin-Ayala model.