A Small-Gain Co-Design Approach to Adaptive Neural Sampling Control for Uncertain Nonholonomic Systems

This article deals with adaptive event-triggering control for nonholonomic systems. Based on state feedback, we fulfill the cooperative design of control law and event-triggering strategy. The crucial method is to use the set-valued map to cover the discontinuous set of event sampling. At the same time, combining the set-valued derivative with backstepping technique to achieve adaptive event control and neural networks are used to fit the unknown functions. The nonholonomic constraints of the system are removed by state-scale systematic design. Through transforming the event-triggering control system into a cascade network with two layers of subsystems, the stability of the entire system is proved based on the input-to-state stable small-gain theorem. The proof that Zeno phenomenon does not occur works in two ways: on the one hand, it ensures that the event trigger is effective; on the other hand, it ensures that there are limited jump discontinuities so that adaptive control can be carried out. Finally, the effectiveness of the adaptive event-triggering control method based on the small-gain theorem is verified by simulation.