This article investigates the adaptive fuzzy output-feedback backstepping control design problem for uncertain strict-feedback nonlinear systems in the presence of unknown virtual and actual control gain functions and unmeasurable states. A fuzzy state observer is designed via fuzzy-logic systems, thus the unmeasurable states are estimated based on the designed fuzzy state observer. By constructing the logarithm Lyapunov functions and incorporating the property of the fuzzy basis functions and bounded control design technique into the adaptive backstepping recursive design, a novel observer-based adaptive fuzzy output-feedback control method is developed. The proposed fuzzy adaptive output-feedback backstepping control scheme can remove the restrictive assumptions in the previous literature that the virtual control gains and actual control gain functions must be constants. Furthermore, it can make the control system be semiglobally uniformly ultimately boundedness (SGUUB) and keep the observer and tracking errors to remain in a small neighborhood of the origin. The numerical simulation example is presented to validate the effectiveness of the proposed control scheme and theory.

In this paper, an adaptive neural finite-time event-triggered consensus tracking problem is studied for nonlinear multi-agent systems (MASs) under directed graphs. Firstly, the unknown nonlinear functions of MASs can be approximated by neural networks. Then, a distributed adaptive event-triggered control (ETC) scheme is proposed via command filter and backstepping technique. The newly designed control scheme can not only circumvent the problem of the explosion of complexity, but also remove the singularity issue typical of conventional backstepping technique. In the meanwhile, an event-triggered mechanism with a dynamic threshold is devised to reduce the waste of network resources. Moreover, by using a novel finite-time stability criterion, it can be proved that the closed-loop system is finite-time stable and the consensus tracking errors can reach zero as time approaches to infinity. Finally, a numerical example is given to validate the feasibility of the proposed scheme.

This article is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example.

This paper is concerned with the adaptive event-triggered control problem of nonlinear continuous-time systems in strict-feedback form. By using the event-sampled neural network (NN) to approximate the unknown nonlinear function, an adaptive model and an associated event-triggered controller are designed by exploiting the backstepping method. In the proposed method, the feedback signals and the NN weights are aperiodically updated only when the event-triggered condition is violated. A positive lower bound on the minimum intersample time is guaranteed to avoid accumulation point. The closed-loop stability of the resulting nonlinear impulsive dynamical system is rigorously proved via Lyapunov analysis under an adaptive event sampling condition. In comparing with the traditional adaptive backstepping design with a fixed sample period, the event-triggered method samples the state and updates the NN weights only when it is necessary. Therefore, the number of transmissions can be significantly reduced. Finally, two simulation examples are presented to show the effectiveness of the proposed control method.

This paper studies the fuzzy adaptive distributed event-based control scheme for a class of uncertain nonlinear multiagent systems in strict feedback form. A novel distributed adaptive event-trigger condition and event-triggered controller are designed simultaneously. The main advantage with respect to event-sampling states is that the controllers were updated in an aperiodic manner at the event sampled instants, saving the computation resource and transmission load. Simulation results have shown satisfactory tracking performance of the developed control scheme.