Event-Based Adaptive Sliding-Mode Containment Control for Multiple Networked Mechanical Systems With Parameter Uncertainties

The issue related to distributed containment control for multiple networked mechanical systems with inherent nonlinearities, dynamic leaders, unknown external disturbances, parameter uncertainties, and constrained network communication is investigated by designing distributed adaptive event-triggered sliding-mode controllers in this study. To lessen the number of state updates and network resource loss of networked mechanical systems, a time-varying-threshold-based adaptive event-triggered mechanism is constructed. An adaptive sliding-mode estimator is established to estimate the inaccurate states. Then, integrated with the aforementioned event-triggered strategy and adaptive sliding-mode estimator, discontinuous and continuous distributed adaptive event-triggered sliding-mode control laws without requiring each follower to get the upper bounds of the leaders’ states derivatives are, respectively, devised to compensate for the influences of nonlinearities, disturbances, and parameter uncertainties. To further attenuate the negative effects of unknown disturbances, inherent nonlinearities, and chattering, a distributed adaptive event-triggered sliding-mode control protocol with boundary layer function is designed. Eventually, the Lyapunov stability theory is utilized to testify that the adaptive error and containment error are uniformly ultimately bounded. A practical example is furnished to verify the validity of the present sliding-mode containment control strategies.
Note to Practitioners
—This work aims to develop the distributed containment control approach for multiple networked nonlinear mechanical systems, which is of great significance in the fields of deep space exploration, environment monitoring and joint rescue. We put forward an event-based adaptive estimation and containment control framework for multiple networked nonlinear mechanical systems, which solves practical problems such as transmission frequency, limited computation capability, and network resources. An adaptive sliding-mode estimator and adaptive event-triggered mechanism are, respectively, devised to estimate the inaccurate states and reduce data transmission frequency. Despite the effects of communication interruption and unknown disturbances, an event-triggered adaptive control protocol based on sliding-mode estimator is designed, which is applied to a planar manipulator with two degree-of-freedom.