基于连续反演算法的时滞补偿控制综述

在实际系统的工作过程中，时滞现象普遍存在，如控制信号的采集与传输、控制器的构建与实施、事件的决策与处理等。考虑并有效处理时滞特性的影响有助于提升系统的性能。基于连续反演算法的时滞补偿控制策略是一种有效的控制方法且取得很多研究成果。该时滞补偿控制的主要思路是将具有时滞特性的常微分方程或偏微分方程变换为不具有时滞特性的常微分方程?偏微分方程/常微分方程?偏微分方程(ODE?PDE/PDE?PDE)级联系统。进一步地，基于变换的级联系统，结合连续反演算法提出相应的控制策略。该方法具有系统的稳定性证明简单，鲁棒性强，易于求取闭环系统精确解等优点。详细论述了连续反演算法的基本原理，并针对基于连续反演算法的时滞补偿控制算法在处理输入、输出、状态等类型时滞特性的最新研究进展做简单的阐述和总结。最后，开放式地论述了时滞系统的未来研究方向。 

A survey of delay compensation and control based on continuum backstepping control algorithms for time-delay systems

In practical control systems, time delays inevitably occur when sensors need to measure and require the system’s data for decision making as well as when microcontrollers (or other devices) compute and implement control signal processes. The time-delay phenomenon is common in network systems because information (e.g., plant output and control input) is exchanged via a network among control system components and communication delays inevitably arise. Time delays usually affect the dynamic performance of a system, such as the response time and operation accuracy of the system, and may even lead to system instability. Therefore, considering the effects of time delays and effectively compensating for them will improve the performance of a system. Recently, considerable attention has been paid to the study of time-delay problems based on a continuum backstepping control algorithm for its superiority on stability analysis. The design process mainly comprises three steps. First, the original system is transformed into an ordinary differential equation (ODE)–partial differential equation (PDE) or PDE–PDE cascaded system wherein a first-order hyperbolic transport-PDE is introduced to describe the time-delay phenomenon. Thereafter, the cascaded system is turned into a stable system using a Volterra transformation. Finally, a corresponding time-delay compensated control law is developed based on the proposed Volterra transformation. The algorithm based on the continuum backstepping control algorithm is robust, has an inverse optimal control, and exhibits great potential for explicit exact control laws. Moreover, the stability analysis and exact solutions of closed-loop systems are obtained easily. This survey summarizes the basic principle and design procedure of the time-delay compensation method and control law based on the continuum backstepping control algorithm. Further, the recent works of the time-delay compensation control based on this algorithm are introduced for time-delay systems covering the aspects of input, output, and state. Finally, the future works of the time-delay compensation control based on the continuum backstepping control algorithm are discussed.