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.