Dynamic event-triggered L1 control of Markov jump systems under positive constraint

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-23 DOI:10.1016/j.cnsns.2025.109076

Kai Yin , Dedong Yang , Yiming Tian , Lianjun Hu

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引用次数: 0

Abstract

This paper investigates the dynamic event-triggered

L_{1}

control of continuous-time Markov jump systems (MJSs) under positive constraint. First, we propose a novel linear dynamic event-triggered method (ETM) that not only fully addresses stringent positive constraint but also is mode-dependent. Additionally, this method prevents Zeno behavior and allows for more flexible adjustment of resource allocation by incorporating an extra state-related component. Using this dynamic ETM, we apply the linear programming (LP) approach, coupled with an interval analysis method, to guarantee the positivity of MJSs under this constraint. Moreover, by employing the interval method and constructing a copositive Lyapunov function, we derive stability criteria while ensuring

L_{1}

-gain performance. A collaborative design scheme for the controller and dynamic ETM is also introduced. All conditions adhere to the standard LP form. The paper then thoroughly analyzes the influence of dynamic ETM parameters on event-triggering frequency through numerical simulation. Finally, two numerical examples are provided to demonstrate the effectiveness and benefits of the proposed approach.

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正约束下马尔可夫跳变系统的动态事件触发L1控制

研究了正约束下连续马尔可夫跳变系统的动态事件触发L1控制问题。首先，我们提出了一种新的线性动态事件触发方法（ETM），它不仅完全解决了严格的正约束，而且与模式相关。此外，该方法可以防止Zeno行为，并通过合并额外的状态相关组件，允许更灵活地调整资源分配。利用这一动态ETM，我们采用线性规划方法，结合区间分析方法，来保证mjs在此约束下的正性。此外，通过区间方法和构造一个合成Lyapunov函数，我们得到了保证l1增益性能的稳定性判据。介绍了一种控制器与动态ETM的协同设计方案。所有条件都遵循标准LP格式。通过数值模拟，深入分析了动态ETM参数对事件触发频率的影响。最后，给出了两个数值算例，验证了该方法的有效性和优越性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.