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An Enlarged Framework of Event-Triggered Control for Stochastic Systems

机译：用于随机系统的事件触发控制的放大框架

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This article aims to enlarge the applicability of event-triggered control for stochastic systems, and is particularly concerned with event-triggered stabilization for stochastic systems with control-dependent diffusion term. Roughly treating stochastic noises as unfavorable factors for system stability, the related works are based on Lyapunov-type conditions for ISS property with respect to sampling error as those in the nonstochastic context. The conditions imply the existence of a twice-differentiable Lyapunov function with negative-definite infinitesimal under continuous-time control, and indeed exclude many familiar stochastic systems with control-dependent diffusion term which are continuously stabilizable while no such Lyapunov function exists. As the main contribution of this article, an enlarged framework of event-triggered stabilization is established for stochastic systems with control-dependent diffusion term, starting from the system stability under continuous-time control, rather than from Lyapunov-type conditions for ISS property. Specifically, with moment exponential stability assumed under continuous-time control, elementary event-triggering mechanisms are proposed with an enforced minimum inter-execution interval, under which the event-triggered controller can render the system exponentially stable both in the sense of expectation and in the almost sure sense. Particularly, a distinctive analysis of closed-loop stability is performed via delicate comparison between the solutions under the event-triggered, and continuous-time controls. Within the framework, inclusive Lyapunov-type conditions incorporating the underlying positive effects of stochastic noises are presented for event-triggered exponential stabilization of the stochastic systems, where the candidate Lyapunov function involved is weakened to be nondifferentiable at the origin and, even, to allow non-negative infinitesimal under continuous-time control.
机译：本文旨在扩大事件触发控制对随机系统的适用性，特别关注具有控制依赖性扩散项的随机系统的事件触发稳定性。粗略地将随机噪声视为系统稳定性的不利因素，相关工程基于Lyapunov型条件的ISS属性，相对于非转换背景下的采样误差。条件意味着在连续时间控制下存在两次不同的Lyapunov函数，在连续时间控制下具有负定向无限的功能，并且确实排除了许多熟悉的随机系统，其具有控制依赖性扩散项，其连续稳定，而不存在这种情况。作为本文的主要贡献，为具有控制相关扩散项的随机系统建立了事件触发稳定的扩大框架，从连续时间控制下的系统稳定性开始，而不是来自ISS属性的Lyapunov型条件。具体地，在连续时间控制下假设的时刻指数稳定性，提出了具有强制执行最小执行间隔的基本事件触发机制，在该执行中，事件触发的控制器可以在期望和中呈现对数字稳定的系统稳定几乎肯定的感觉。特别地，通过在事件触发的溶液和连续时间控制下的溶液之间的微小比较来进行闭环稳定性的独特分析。在框架内，提供了包含随机噪声的底层积极效果的包容性Lyapunov型条件，用于随机系统的事件触发的指数稳定，其中所涉及的候选Lyapunov功能被削弱到原点，甚至是允许的在连续时间控制下的非负无穷小。

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