Periodic event-triggered targeted shape control of Lagrangian systems with discrete-time delays

Periodic event-based sliding mode tracking control of Euler-Lagrange systems with dynamic triggering

In this article, we propose the design of a robust tracking controller of perturbed Euler-Lagrange systems (ELSs) based on dynamic event-triggered (DET) sliding mode control (SMC) with periodic evaluation of triggering rule. To ensure robustness, we employ the SMC technique and introduce a dynamic periodic event-triggering strategy to reduce communication frequency significantly. This strategy involves the incorporation of an auxiliary dynamic variable to formulate the event-triggering condition, leading to the generation of sparser triggering instants. An upper bound of the sampling period is also obtained in this design to facilitate the periodic assessment of the event-triggered strategy, alleviating the need for continuous verification of the event condition. This technique is more economical with respect to communication resources and practical than its continuous counterpart due to the relaxation of continuous measurements. The stability of the closed loop system is established using Lyapunov analysis within the dynamically triggered event-based SMC framework. The necessary switching gain for maintaining the stable motion of the sliding variable is derived with the help of Lyapunov analysis. The tracking error is shown to be ultimately bounded, and Zeno-behaviour is excluded to ensure finite sampling. A comparative analysis based on simulation results is included to highlight the effectiveness of the proposed scheme, especially in reducing the network usage in the transient phase of the response while achieving comparable steady-state behaviour. Ultimately, we validate the effectiveness of the proposed algorithm by simulating a two-link manipulator and experimentally implementing it with a one-link manipulator.

Adaptive Neural Coordinated Control for Multiple Euler-Lagrange Systems With Periodic Event-Triggered Sampling

This article addresses the event-triggered coordinated control problem for multiple Euler-Lagrange systems subject to parameter uncertainties and external disturbances. Based on the event-triggered technique, a distributed coordinated control scheme is first proposed, where the neural network-based estimation method is incorporated to compensate for parameter uncertainties. Then, an input-based continuous event-triggered (CET) mechanism is developed to schedule the triggering instants, which ensures that the control command is activated only when some specific events occur. After that, by analyzing the possible finite-time escape behavior of the triggering function, the real-time data sampling and event monitoring requirement in the CET strategy is tactfully ruled out, and the CET policy is further transformed into a periodic event-triggered (PET) one. In doing so, each agent only needs to monitor the triggering function at the preset periodic sampling instants, and accordingly, frequent control updating is further relieved. Besides, a parameter selection criterion is provided to specify the relationship between the control performance and the sampling period. Finally, a numerical example of attitude synchronization for multiple satellites is performed to show the effectiveness and superiority of the proposed coordinated control scheme.

Observer-based event-triggered leader-following consensus of multi-agents with generalized Lipschitz nonlinear dynamics

This paper discusses a leader-following consensus problem for nonlinear multi-agent systems (MASs) subjected to generalized Lipschitz-type nonlinearity using output feedback. An event-triggered (ET) leader-following control scheme, based upon estimated states using observers, is proposed for efficient bandwidth utilization by application of invariant sets. Distributed observers are designed to estimate the states of the followers because actual states are not always readily available. Besides, in order to reduce unnecessary data communication among the followers, an ET strategy has been formulated which excludes Zeno behavior as well. Under this proposed scheme, sufficient conditions are formulated using Lyapunov theory. These conditions not only guarantee the asymptotic stability of estimation error, but also ensure the tracking consensus of nonlinear MASs. Further, a simple and less conservative design approach using a decoupling scheme for assuring necessity and sufficiency for the main design approach has also been explored. The decoupling scheme is similar to separation principle for linear systems. Contrary to the existing works, the nonlinear systems considered in this study cover a wide family of Lipschitz nonlinearities, including both globally and locally Lipschitz systems. Moreover, the proposed approach is more efficient in handling ET consensus. Finally, the obtained results are verified with single link robots and modified Chua's circuits.