Fixed-time tracking control is considered for a class of nonlinear systems in this article. Different from the conventional literature on fixed-time control studies, in this article, the nonlinearities of systems are all completely unknown. Fuzzy-logic systems are utilized to model these unknown nonlinearities. To deal with the fixed-time control under the approximation errors, three steps are taken. First, a new criterion of fixed-time stability is developed; second, a new fixed-time control scheme is proposed, which is different from the existing adaptive design method; and third, to analyze the fixed-time stability of the system, two novel inequalities are established. It shows that the proposed fuzzy control scheme can guarantee system performance in a fixed time, and the upper bound of the settling time only depends on the design parameters.

In this article, we consider the leader-follower consensus control problem of uncertain multiagent systems, aiming to achieve the improvement of system steady state and transient performance. To this end, a new adaptive neural control approach is proposed with a novel design of the Lyapunov function, which is generated with a class of positive functions. Guided by this idea, a series of smooth functions is incorporated into backstepping design and Lyapunov analysis to develop a performance-oriented controller. It is proved that the proposed controller achieves a perfect asymptotic consensus performance and a tunable L₂ transient performance of synchronization errors, whereas most existing results can only ensure the stability. Simulation demonstrates the obtained results.

In this paper, the uncertain direct of the hysteretic system component will be considered. Besides, the effect of stochastic disturbance inevitably exists in many practical systems, which would cause the instability. Simultaneously, it is significant to guarantee the perfect error tracking performance for the uncertain nonlinear hysteresis systems when operation suffers the failure. To ensure the maintaining acceptable system performance in reality, the new properties of the Nussbaum function are proposed, and an auxiliary virtual controller is designed through the neural network (NN) universal approximator. Furthermore, it is challenged to save the system-limited transmutation resource for nonlinear systems, especially for stochastic nonlinear systems, with unknown hysteresis input and actuator failures. The coupling effect of the system communication resource constrains has to arise the issue of the mutual coupling function, which makes that the tracking control design is more complicated. Using the proposed event-triggered controller and back-stepping technology, a new optimization algorithm is proposed to ensure that the states of the closed-loop system and the tracking error remain bounded in probability. Finally, to illustrate the effectiveness of our proposed adaptive NN control method with the event-triggered strategy, some numerical examples are provided.

In this paper, an adaptive neural network control for stochastic nonlinear systems with uncertain disturbances is proposed. The neural network is considered to approximate an uncertain function in a nonlinear system. And computational burden in operation is reduced by handling the norm of the neural-network vector. However, it will arise chattering issue, which is a challenge to avoid it from the symbolic operation. Further, traditional schemes often view error of estimate as bounded constant, but it is a time-varying function exactly, which may lead control schemes cannot conform to practical situation and guarantee stability of systems. Thus, backstepping technology and the neural network technology combined to stabilize stochastic nonlinear systems together to handle the aforementioned issues. It is proved that the proposed control scheme can guarantee the satisfactory asymptotic convergence performance and predetermined transient tracking error performance. From simulation results, the proposed control scheme is verified that can guarantee the satisfactory effectiveness.

In this paper, the problem of event trigger Fuzzy adaptive compensation control for uncertain stochastic nonlinear system with actuator failures is considered. Although great strides have been made in accommodating nonlinear system in recent results, it is still an arduous task and challenge to design an event-triggered based controller to handle the uncertain stochastic nonlinear system with actuator failures, especially to ensure asymptotic tracking performance. In this paper, to address the actuator failures and stochastic interference, we propose a new relative event trigger adaptive Fuzzy controller established by utilizing the techniques of robust approach. It is proved that the proposed scheme guarantees the bounded of all closed-loop signals and the asymptotic convergence performance of tracking error. It is shown from simulation results that our proposed control scheme for compensating the stochastic nonlinear system guarantees the effectiveness.

Dynamic uncertainty is a potential factor destabilizing the closed-loop system. This paper aims at constructing an adaptive fuzzy output-feedback control scheme for a class of switched nonlinear systems interconnected with unmodeled dynamics. In the investigated model, the $x$ -system is interconnected with the unmodeled $z$ -dynamics. Two types of unmodeled dynamics (i.e., all modes are stable and some modes are unstable) are considered in this paper. Separate switched state observer and adaptive fuzzy controller are designed for each mode of the $x$ -system. In our control scheme, only two adaptive parameters are required to update online. With the help of multiple Lyapunov function, two lemmas are proposed to guide us how to determine the input-to-output gains of the $x$ -system and the unmodeled dynamics when the influence of switching is considered. By using the small-gain approach, the closed-loop switched nonlinear system is guaranteed to be ISpS. With the concept of ISpS, we prove that the closed-loop system's output is convergent to a small neighborhood of zero, and all the signals in the closed-loop system are bounded. Finally, three simulations are also given to illustrate the effectiveness of our main result.