论文标题
Razumikhin和Krasovskii进行安全稳定的方法
Razumikhin and Krasovskii Approaches for Safe Stabilization
论文作者
论文摘要
本文研究了非线性时间延迟系统的稳定和安全问题。遵循Razumikhin和Krasovskii的方法，我们提出了新颖的控制Lyapunov功能/功能，以解决稳定问题，以及用于安全问题的新型控制屏障功能/功能。拟议的控制Lyapunov和屏障功能/功能将现有的功能从无延迟情况扩展到时间延迟案例，并允许在封闭形式中设计稳定和安全控制器。由于难以实现时间延迟最佳控制问题的分析解决方案，因此开发了基于滑动模式控制的方法来合并所提出的控制Lyapunov和障碍功能/功能。基于滑动表面功能，建立了反馈控制定律，以同时研究稳定和安全目标。特别是，分析了滑动表面功能的性能，并进一步讨论了如何构建滑动表面功能。最后，通过两个数值示例从汽车系统的连接巡航控制问题和多代理系统的同步问题中说明了所提出的方法。
This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be achieved, a sliding mode control based approach is developed to merge the proposed control Lyapunov and barrier functions/functionals. Based on the sliding surface functional, a feedback control law is established to investigate the stabilization and safety objectives simultaneously. In particular, the properties of the sliding surface functional are analyzed, and further how to construct the sliding surface functional is discussed. Finally, the proposed approaches are illustrated via two numerical examples from the connected cruise control problem of automotive systems and the synchronization problem of multi-agent systems.
