Observer-Based Fuzzy Adaptive Tracking Control of Nonlinear Strict-Feedback Systems via a Unique Event Triggering Approach

It is known that a controller designed via backstepping contains all virtual control signals constructed at the previous design steps. When this controller is used to generate an event-triggered control signal which is discontinuous, those virtual control signals are simultaneously triggered and the corresponding triggered virtual signals are utilized for the real control operation, they are also discontinuous. This fact results in the noncontinuity of the virtual error dynamics. This problem is ignored in the existing backstepping-based event-triggered control schemes, in which control design and stability analysis are implemented according to the continuous virtual error dynamics, namely, all the virtual control signals are required to be continuous. Based on this observation, this article focuses on the backstepping-based event-triggered fuzzy adaptive control for nonlinear strict-feedback systems with unavailable states. To do so, a concurrent event generator is first introduced, furthermore, the backstepping-based output feedback control design is given according to the discontinuous virtual error dynamics. Then, the Lyapunov approach for nonlinear impulsive systems is used to provide the closed-loop performance analysis. The results show that with the event-based fuzzy adaptive controller, all the closed-loop signals meet bounded requirements and the Zeno phenomenon is prevented. Ultimately, the proposed theoretical results are supported by two simulation examples.