Backstepping control is effective for integer-order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to fractional-order nonlinear systems as the fractional-order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a fractional order is approximated by a fuzzy logic system, and a virtual control law is designed based on the fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.

In this paper, an adaptive fuzzy predefined time and accuracy tracking control scheme is proposed for strict-feedback nonlinear systems. A sufficient condition that can be used to determine whether the tracking error converges to a predefined region within a predefined time is first derived based on the definition of predefined time stability. Under the proposed stability criterion, an adaptive fuzzy controller is developed by applying the backstepping technique, and the stability time and convergence accuracy of the tracking error can be set previously, which facilitates the engineering application with requirements for convergence time and accuracy. Especially, to reduce chattering and decrease energy consumptions on the premise of ensuring the stability of the system, an inequality is introduced to construct a continuous term which can replace the sign function. Finally, a practical example is presented to illustrate the feasibility of main results.

Backstepping control for fractional-order nonlinear systems (FONSs) requires the analytic calculation of fractional derivatives of certain complicated stabilizing functions, which becomes prohibitive as the order of the system increases. This article aims to facilitate the adaptive neural network (NN) backstepping control design for FONSs with actuator faults whose parameters and patterns are fully unknown. A fractional filtering approach, which obviates the requirement of analytic fractional differentiation, is used to generate command signals together with their fractional derivatives. Compensated tracking errors that can eliminate approximation errors of command signals are generated by fractional filters. The proposed adaptive NN command filtered backstepping control (ANNCFBC) approach, together with fractional adaptive laws, guarantees not only the boundedness of all involved variables but also the convergence of both the tracking error and the compensated tracking error to a sufficiently small region. Finally, simulation studies are given to indicate the effectiveness of the proposed control method.

In fibrotic liver, connective tissue growth factor (CTGF) is constantly expressed in activated hepatic stellate cells (HSCs) and acts downstream of TGF-β to modulate extracellular matrix production. Distinct from other cell types in which Smad signaling plays major role in regulating CTGF production, TGF-β stimulated CTGF expression in activated HSCs is only in part dependent on Smad3. Other signaling molecules like MAPKs and PI3Ks may also participate in this process, and the underlying mechanisms have yet to be clarified. In this study, we report involvement of Stat3 activation in modulating CTGF production upon TGF-β challenge in activated HSCs. Stat3 is phosphorylated via JAK1 and acts as a critical ALK5 (activin receptor-like kinase 5) downstream signaling molecule to mediate CTGF expression. This process requires de novo gene transcription and is additionally modulated by MEK1/2, JNK, and PI3K pathways. Cell-specific knockdown of Smad3 partially decreases CTGF production, whereas it has no significant influence on Stat3 activation. The total CTGF production induced by TGF-β in activated HSCs is therefore, to a large extent, dependent on the balance and integration of the canonical Smad3 and Stat3 signaling pathways.