具有乘性噪声的随机系统事件触发控制研究

Event-triggered control has become a research hotspot in the field of sampling control due to its characteristics of improving resource utilization in resource-constrained systems. However, the current research mainly focuses on deterministic systems. Since the theory of stochastic hybrid systems is not perfect, there are few studies involving event-triggered control of stochastic systems, and much work remains to be done. This project will study event-triggered control for stochastic systems with multiplicative noise. First, based on the covariance matrix of the states of the augmented system, we will give a continuous event-triggering condition for linear stochastic systems with multiplicative noise, and analyze the stability of the corresponding closed-loop systems. Secondly, periodic event-triggered control mechanisms depending on linear quadratic functions will be given for linear stochastic systems with multiplicative noise by using the delay system approach and the impulsive system approach, respectively. Finally, we will discuss the problem of event-triggered control of nonlinear stochastic systems with multiplicative noise and establish a continuous event-triggered mechanism based on waiting time. The project will reveal the law of multiplicative noise in the design of event-triggered control strategies and provide theoretical support for engineers to design event-triggered control algorithms under random noise.

事件触发控制因其在资源受限系统中具有提高资源利用率的特性，已成为采样控制领域的研究热点。但目前的研究主要集中于确定性系统，由于随机混杂系统理论尚不完善，涉及随机系统事件触发控制的研究较少，仍需大量工作。本项目将针对具有乘性噪声的随机系统开展事件触发控制研究。首先，考虑具有乘性噪声的线性随机系统，拟通过求解增广系统状态协方差矩阵给出连续事件触发条件和相应闭环控制系统的稳定性分析；其次，针对相同的线性随机系统，拟通过时滞系统方法和脉冲系统方法分别给出依赖线性二次型函数的周期事件触发控制；最后，拟讨论具有乘性噪声的非线性随机系统的事件触发控制问题，建立基于等待时间的连续事件触发机制。本项目将揭示乘性噪声在事件触发控制策略设计过程中的作用规律，并为工程人员在随机噪声下设计事件触发控制算法提供理论支撑。

该项目围绕非线性系统采样控制问题，在充分考虑外部乘性噪音、传感器性能和系统非线性等多方面因素的情况下，对非线性系统事件触发控制机制设计问题进行了深入的探索研究。在经典的事件触发控制框架下，基于李雅普诺夫函数，提出了一种优于传统的连续静态事件触发和动态连续事件触发机制的连续事件触发机制；在非输入到状态稳定性的条件下，利用经典的扰动理论和泰勒展开定理提出了一种新颖的自触发控制机制；通过定义一个自变量为采样误差和系统状态的特定函数，并求解得到此特定函数的一个上界函数，利用此上界函数的解析性质，建立了一种转化传统的连续事件触发控制系统为周期事件触发控制系统的策略；通过把非线性随机采样控制系统建模为相应的增广脉冲系统，并结合增广系统李雅普诺夫稳定性条件给出随机采样控制系统稳定的时间域，依据此时间域构造了一种带有等待时间的事件触发控制机制。本项目所获得的成果将对事件触发控制系统的应用提供理论指导。