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This article studies the adaptive backstepping control problem for a class of fractional-order (FO) nonlinear systems subject to input quantization and unknown control directions by combining with an indirect FO Lyapunov stability method, and a command filter-based FO dynamic surface control (FODSC) technique. First, a modified FODSC method is utilized to reduce the computational complexity existing in the conventional recursive procedure in which an FO command filter is designed to obtain the command signals and their FO derivatives. Furthermore, the Nussbaum function and neuro-fuzzy networks (NFNs) are adopted to deal with the problem of the unknown control directions and unknown nonlinear functions existing in the system. Moreover, by introducing the compensation and prediction mechanism to controller design, the adaptive controllers, and adaptive laws are constructed to ensure that all the signals of the controlled systems are bounded. Finally, two examples are given to show the validity of the developed control method. [ABSTRACT FROM AUTHOR]

This article investigates the issue of neuro-fuzzy-based adaptive dynamic surface control (DSC) for uncertain fractional-order (FO) nonlinear systems in strict-feedback form where input constraint is considered in the systems. In the recursive steps, the neuro-fuzzy network systems are employed to deal with the unknown nonlinear terms existing in systems. Furthermore, based on a DSC scheme, a modified FO filter is constructed to overcome the problem of explosion of complexity caused by the traditional backstepping design. Moreover, according to the FO Lyapunov stability theory, a neuro-fuzzy-based adaptive controller is designed to guarantee all the signals of FO closed-loop systems tend to be bounded. Finally, the three examples are provided to verify the validity and superiority of the presented control scheme. [ABSTRACT FROM AUTHOR]

This paper studies the issue of adaptive hybrid fuzzy output feedback control for a class of commensurate fractional-order (FO) nonlinear systems with time-varying delays and input saturation. First, a hybrid fuzzy state observer is designed to estimate the unmeasured system states, where the neuro-fuzzy network systems (NFNSs) are introduced to handle the unknown nonlinear functions. Furthermore, based on DSC technique, a modified FO filter is designed to avoid the issue of the "explosion of complexity" generated by the traditional backstepping control design approach. Moreover, based on the recursive technique and an indirect Lyapunov method, an adaptive controller is constructed to ensure that all the signals of FO closed-loop systems are bounded. Finally, the simulation results are presented to demonstrate the effectiveness of the presented control scheme. [ABSTRACT FROM AUTHOR]