Adaptive Event-Triggered L2−L∞ Control of Semi-Markov Jump Distributed Parameter Systems

• Published in: Applied mathematics and computation Vol. 439
• Main Authors: Mei, Yu, Wang, Guanqi, Shen, Hao
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.2023
• Subjects: Adaptive event-triggered scheme; Distributed parameter systems; Semi-Markov jump systems; Stochastic stability; Semi-Markov jump systems; Stochastic stability; Distributed parameter systems; Adaptive event-triggered scheme
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127586

•A co-design control approach under adaptive ETCS is developed to dispose of the stability problem for DPSs with spatial dimensions at the first attempt.•A comprehensive model is studied in this paper.•A novel ETCS with adaptive threshold parameters is put forward. This paper focuses on the problem of adaptive event-triggered L2−L∞ control for distributed parameter systems with semi-Markov jump parameters. An event-triggered transmission scheme, whose threshold function can be adaptively adjusted, is established to decrease the frequency of data transmission. Simultaneously, the utilization of limited network bandwidth resources is also improved due to plenty of “unnecessary” packets being discarded before accessing networks. Furthermore, the jumping of stochastic parameters in networks can be described by a semi-Markov jump model, in which the sojourn-time is considered subject to the Weibull distribution instead of the exponential distribution. Based on the aforesaid discussions, a mode-dependent controller is designed under an adaptive event-triggered scheme. Whereafter, some criteria are constructed based on the Lyapunov stability theory to guarantee stochastic stability and a prescribed L2−L∞ performance of the system. Ultimately, two simulation examples are provided to verify the feasibility of the proposed design approach.