Event-Triggered Control with Time Delays

随着在线通信、万维网和计算技术的迅速发展，控制系统在动态网络中得到了广泛的应用。网络由大量的动态节点组成，每个节点都有自己的属性。研究网络时延对网络化控制系统设计和综合的影响，开发有效的控制机制以减少网络节点间的通信负荷，具有十分重要的意义。减少信息传输的传统方法是将两次连续通信限制在一个时间限制内。因此，所有的通信都是可预测的，这样的策略很容易实现。然而，这些可预测的信息传输是不安全和保守的，因为可能会进行不必要的通信，这是一种通信能量的浪费。在需要时激活网络节点之间的通信是理想的。因此，事件触发控制的发展是为了提高通信效率，同时保证网络控制系统的预期性能。事件触发控制的思想是，只有当系统违反预先设计的性能阈值时才激活通信。在本研究中，我们重点研究了时延系统的事件触发控制及其在各种网络控制系统中的应用。我们的目标包括：(1)开发事件触发控制算法，以确保时滞系统的期望性能，如稳定性、有界性和吸引力，并从控制系统中排除芝诺行为（在有限周期内无限次控制更新）；(2)为时滞系统开发有效的事件触发脉冲控制算法，以保证期望的性能水平，并确保两个连续脉冲时间间隔最小的停留时间；(3)将所得结果应用于实际问题，如网络控制系统的一致性和同步问题；(4)发展时间尺度上脉冲泛函微分方程的基本理论，并将其应用于调度问题和数值方法。本文的研究成果将为一般非线性时滞系统提供新的事件触发控制机制，降低通信成本的新的一致性和同步准则，时间尺度上脉冲系统的基本理论，以及有效的调度策略和自适应数值方法。由于拟议研究计划的跨学科性质，HQP培训将包括撰写科学论文，目标是在顶级控制期刊上，掌握对行业进一步就业很重要的技术和方法。其成果将有助于加拿大在时滞系统和控制领域的科学和技术发展。

With the rapid development of online communication, the World Wide Web, and computation, control systems have been widely implemented in dynamical networks. A network consists of a large number of dynamical nodes each of which possesses its own attributes. It is very important to investigate the effects of network-induced time delays on the design and synthesis of the networked control systems and develop efficient control mechanisms to reduce the communication load among the network nodes. A traditional way to reduce the information transmission is to restrict two successive communications to less than a time constraint. Hence, all the communications are predictable, and such a strategy is easy to implement. However, these predictable information transmissions are insecure and conservative in the sense that unnecessary communications may be conducted, which is a waste of communication energy. It is ideal to activate the communication among network nodes when needed. Therefore, event-triggered control has been developed to improve communication efficiency while still guaranteeing the desired performance of networked control systems. The idea of event-triggered control is to activate the communication only when the system violates a predesigned performance threshold. In this research, we focus on event-triggered control for time-delay systems and applications on various networked control systems. Our objectives include: (1) to develop event-triggered control algorithms to ensure the desired performance of time-delay systems, such as stability, boundedness, and attractivity, and rule out Zeno behavior (infinitely many control updates over a finite period) from the control system; (2) to develop efficient event-triggered impulsive control algorithms for time-delay systems to guarantee the desired performance level and also ensure two consecutive impulse times are separated by a minimum dwell-time; (3) to apply the obtained results to practical problems, such as consensus and synchronization problems of networked control systems; (4) to develop the fundamental theory for impulsive functional differential equations on time scales with applications to scheduling problems and numerical methods. The outcomes of this research will result in new event-triggered control mechanisms for general nonlinear time-delay systems, new consensus and synchronization criteria with reduced communication cost, fundamental theory for impulsive systems on time scales, and efficient scheduling strategies and adaptive numerical methods. Due to the interdisciplinary nature of the proposed research program, HQP training will be involving writing scientific papers, aimed at the top control journals, with mastering techniques and methods important for further employment in the industry. The outcomes will contribute to the scientific and technological development of Canada in the area of time-delay systems and control.