Adaptive connectivity-preserving formation control with a dynamic event-triggering mechanism

Connectivity preservation for real-life multi-agent systems is key to designing an effective and reliable control algorithm to achieve desired objectives. But the coexistence of system nonlinearities and uncertainties makes it difficult for the algorithm design, and especially in the event-triggered setting, such difficulty becomes severer due to the demand for integration of multiple ingredients. This paper focuses on proposing an adaptive connectivity-preserving formation control strategy that incorporates a dynamic event-triggering mechanism, in the scenario of the unknown control directions and intrinsic nonlinearities coupling with parameter uncertainties. First, a cluster of potential functions serving as control barrier functions are given to maintain the prescribed connectivity of communication graph. Second, two types of dynamic gains (one type is based on a Nussbaum function) are introduced for agents to cope with the system nonlinearities, uncertainties and the adverse effect of the execution error. As such, an adaptive event-triggered formation protocol is constructed such that the desired formation with connectivity preservation is achieved while a positive minimum inter-execution interval is ensured for each agent to avoid Zeno behavior. Particularly, the threshold in the developed event-triggering mechanism is dynamically adjusted online, rather than static, which better improves resource efficiency. A simulation example is given to demonstrate the effectiveness and advantage of the proposed strategy.