网络振荡系统中失同步的事件触发稳定控制
Event-Triggered Stabilisation of Desynchronisation in Networked Oscillatory Systems
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中文总结 AI 辅助
针对网络振荡系统资源约束下的失同步稳定问题，提出事件触发控制框架，结合伪相位构造实现无需持续控制的失同步稳定，排除芝诺行为，经数值验证有效鲁棒。
中文摘要 AI 辅助
病理性神经元同步为研究网络振荡系统中的稀疏失同步控制提供了实际动机，尤其适用于执行器和通信受资源约束的应用场景，如深部脑刺激。受此挑战驱动，我们研究如何在耦合振荡动力系统中稳定失同步状态，无需持续更新控制，即使振荡器相位不可用。我们开发了一种通用的事件触发控制框架，用于稳定耦合极限环振荡动力系统的失同步状态。我们的分析建立了统一的理论结果，表明多种稀疏作用且仅依赖序参数可观测量的反馈控制器可实现失同步。所提出的控制器具有梯度下降解释，可稳定一般相位约简振荡器网络的失同步状态。我们进一步证明，事件触发机制下的受控系统具有严格正的事件间驻留时间下界，排除了芝诺行为。为解决精确相位约简的实际不可用性，我们引入伪相位构造，仅从状态测量中产生可计算的序参数。对代表性振荡器网络的数值研究证明了所提框架的有效性和鲁棒性。
英文摘要
Pathological neuronal synchrony provides one practical motivation for studying sparse desynchronisation control in networked oscillatory systems, particularly in applications where actuation and communication are resource constrained, as in deep brain stimulation. Motivated by this challenge, we study how to stabilise desynchronisation in coupled oscillatory dynamical systems without continuously updated control, even when the oscillators' phase is unavailable. We develop a general event-triggered control framework for stabilising the desynchronised state of coupled limit-cycle oscillatory dynamical systems. Our analysis establishes a unified theoretical result showing that desynchronisation can be achieved by various feedback controllers that act sparsely and depend only on an order parameter observable. The proposed controllers admit a gradient-descent interpretation and stabilise the desynchronisation state of general phase-reduced oscillator networks. We further prove the controlled systems under event-triggered mechanisms possess a strictly positive lower bound of the inter-event dwell-time, excluding Zeno behaviour. To address the practical unavailability of exact phase reductions, we introduce a pseudo-phase construction that yields a computable order parameter from state measurements alone. Numerical studies on representative oscillator networks demonstrate the effectiveness and robustness of the proposed framework.
