Adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties

The paper considers adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties. The time‐varying uncertainties do not need to be differentiable, but their variation amplitudes are required to be known. Such uncertainties appear not only in the system nonlinearities but also as the control coefficient. We pursue a tight design scheme by combining tuning functions and the congelation of variables method, thereby avoiding the overuse of dominations and obtaining a less conservative controller. In view of the essence of the control problem, we don't design a continuous controller first and then search for a complex and suitable event‐triggering mechanism, as emulation methods done in the literature. In contrast, we adopt a simple event‐triggering mechanism with the relative threshold, while seeking a complex and appropriate adaptive controller which contains the new adaptive treatment for execution error due to the unknown time‐varying control coefficient. Note that there are three parameter dynamic compensators in the adaptive controller, and one is specialized to the execution error, which is not required in the continuous feedback context. It is shown that with the proposed adaptive event‐triggered controller, all the closed‐loop signals are bounded, the system state converges to zero, and no Zeno behavior occurs. A comparative simulation is provided to verify the theoretical results.