Event-Based Prescribed-Time Containment Control for Multiple Euler–Lagrange Systems via Super-Twisting Sliding Mode

Abstract

This article designs a distributed dynamic event-triggered prescribed-time sliding mode controller to tackle the containment control problem of multiple Euler–Lagrange systems (MELSs) with external disturbances and strict requirements on response speed. Unlike previous super-twisting methods that achieve finite-time control, this paper replaces the constant term in the time scaling function with a variable term and incorporates it into the design of the controller and dynamic event-triggered mechanism (DETM), achieving prescribed-time control (PTC), enhancing system robustness and reducing controller updates. Based on the sliding mode variable structure theory and PTC theory, a non-linear sliding manifold is devised for the purpose of ensuring the convergence of containment error to zero within a prescribed time. The prescribed-time super-twisting sliding mode control (PTSTC) protocol is designed to ensure the prescribed-time reachability of the sliding manifold, while attenuating chattering during the control process. The prescribed time can be set arbitrarily. To minimize the frequency of controller updates and the losses of the actuator, a DETM is deployed in the controller-to-actuator channel. Moreover, the absence of the Zeno phenomenon within a prescribed time is derived. Error signals are proven to converge to zero within a prescribed time using the Lyapunov stability theory and prescribed-time stability criteria. Ultimately, a simulation of a manipulator system indicates that the designed controller effectively drives the containment error to converge to zero. Meanwhile, the number of triggers is reduced by more than 50% when the controller framework involves DETM compared to static event-triggered mechanisms.