Adaptive event-triggered stabilization without overparametrization for a class of nonlinear hyperbolic ODE–PDE–ODE systems

This paper is devoted to the event-triggered stabilization of a class of nonlinear hyperbolic ODE–PDE–ODE systems. The system under investigation is remarkably characterized by the unknown nonlinear terms involved in the boundary actuator which are not necessarily linearly grow or parameterized by unknown constants, and hence imply more serious uncertainties and nonlinearities than those of the related literature. Such a feature results into the incapability of the traditional schemes on this topic and then deserves a powerful one for the investigated control problem. For this, a novel adaptive control method is proposed by combining the infinite- and finite-dimensional backstepping method with the adaptive dynamic compensation technique, which brings an explicit state-feedback controller. Particularly, by a smart redefinition of the unknown parameter and the introduction of certain tuning functions, only one dynamic compensator is needed for the compensation of the serious uncertainties, and hence removes the overparametrization in the related literature. A rigorous proof procedure shows the boundedness of the signals of the resulting closed-loop system and the convergence of the original system states, together with the exclusion of the Zeno phenomenon. Finally, a simulation example is provided to validate the effectiveness of the proposed theoretical results.