This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

This paper addresses the finite-time tracking issue for nonlinear quantized systems with unmeasurable states. Compared with the existing researches, the finite-time quantized feedback control is considered for the first time. By proposing a new finite-time stability criterion and designing a state observer, a novel adaptive neural output-feedback control strategy is raised by backstepping technique. Under the presented control scheme, the finite-time quantized feedback control problem is coped with without limiting assumption for nonlinear functions.

This paper studies the finite-time stabilization of a class of stochastic nonlinear systems. Different from functions which are necessarily known in the conventional finite-time control of nonlinear systems, the nonlinear functions can be completely unknown in this paper. By applying fuzzy-logic systems to approximate the unknown nonlinearities, a novel adaptive finite-time control strategy is proposed. However, due to the existence of approximation errors, the existing finite-time stability criterion cannot be used to analyze the stability of stochastic nonlinear systems. To deal with this difficulty, a finite-time stability criterion, by utilizing the mean value theorem of integrals, is first established in Lemma 5, which plays a significant role in the finite-time stability analysis of stochastic nonlinear systems. Then, the finite-time mean square stability of a stochastic nonlinear system is proved by combining Lemma 3 with Jensen's inequality.

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.

This paper proposes a new finite-time tracking control strategy for a nonlinear uncertain system with actuation failures. The presented control scheme is not dependent on the exact model of system and actuation failures. By employing the approximation ability of fuzzy logic systems, an integrated adaptive controller is constructed, which accommodates for both system uncertainties and unknown actuator failures. Unlike the existing fault-tolerant control studies for actuator failures which can guarantee the system performances only if time tends to infinity, the presented control scheme can assure the system performances in finite time. By applying the Bhat and Bernstein theorem, the finite-time stability of system is proved. At last, the usefulness of the developed control scheme is illustrated by two examples.

This article is concerned with an issue of fixed time adaptive neural control for a class of uncertain nonlinear systems subject to hysteresis input and immeasurable states. The state observer and neural networks (NNs) are used to estimate the immeasurable states and approximate the unknown nonlinearities, respectively. On this foundation, an adaptive fixed time neural control strategy is developed. Technically, this control strategy is based on a novel fixed-time stability criterion. Different from the research on fixed-time control in the conventional literature, this article designs a new controller with two fractional exponential powers. In the light of the established stability criterion, the fixed-time stability of the systems is guaranteed under the proposed control scheme. Finally, a simulation study is carried out to test the performance of the developed control strategy.