Switching in Sliding Mode Control: A Spatio-Temporal Perspective

Sliding mode control (SMC) is a widely adopted control technology known for its robustness and simplicity. The essence of SMC is to use discontinuous control to drive a system into a pre-defined motion, called the sliding mode, which is designed with desirable dynamical properties. In the sliding mode, the controlled system is insensitive to the matched uncertainties and disturbances. Most SMC theory and methods have been developed based on the dynamical systems in the continuous-time domain, where switching functions play a critical role. Ideal switching is supposed to be instantaneous, activating as soon as the switching condition is met. However, in practice, switching mechanisms are affected by imperfections such as time delays, unmodeled dynamics, defects, digitization effects, and actuation limitations, which can degrade the salient properties of SMC. Understanding these effects and developing mitigation strategies are essential for industrial applications. Furthermore, the advent of networked control environments presents new challenges like limited communication bandwidth, latency and cyberattack, which have seen the emergence of the event-triggered SMC recently. Despite these significant advances, there is a lack of comprehensive studies which examine the commonalities and distinctions of utilizing switching in SMC across the continuous-time and discrete-time domains and beyond. This paper investigates the role of switching in SMC from a spatio-temporal perspective, considering both state-space and time aspects. The aim is to facilitate better understanding of its effects and misbehaviors, and to unlock its full potential for future applications. The interplay between SMC methods in the continuous-time and discrete-time domains is analyzed, and their shared principles and unique challenges are identified. Furthermore, important technical issues relating to switching across these time domains are explored, and several myths and pitfalls in their theory and applications are depicted. The relationships of SMC with other switching-based control systems such as switched control systems, fuzzy control systems, and event-triggered control systems are discussed. The impact of networked control environments on SMC in the continuous-time and discrete-time domains is also examined. Finally, key challenges and opportunities are outlined for future work in SMC and beyond.