This paper presents a novel adaptive fuzzy backstepping dynamic surface control (DSC) scheme for a class of single-input-single-output (SISO) strict-feedback fractional order uncertain nonlinear systems. The controlled systems contain unknown nonlinear functions and unknown external disturbances. Fuzzy logic systems (FLSs) are employed for approximating the unknown nonlinear functions. Further, an auxiliary function is introduced into the control function with the aim to simultaneously compensate the unknown external disturbance and the approximation error caused by fuzzy approximation, which erases the possible chattering phenomenon in the existing results. Meanwhile, a new DSC method based on the fractional order filter is proposed to avoid the issue of explosion of complexity inherent in the backstepping procedure, which releases the limitation that the fractional order derivative of the intermediate control function need be complete known in the existing references. Under certain assumptions, the stability of the closed-loop system is proved by using the fractional order Lyapunov function stability criterion. Finally, contrastive simulation results are provided to validate the effectiveness of our proposed control strategy.

In this paper, an adaptive fuzzy fault-tolerant control approach is proposed for a class of non-triangular structure nonlinear systems, which contain immeasurable states and unknown actuator faults (actuator loss-of-effectiveness and bias fault). It should be noted that if existing approaches are employed for non-triangular structure nonlinear systems, the algebraic loop problem may occur. In this study, fuzzy systems are employed to approximate unknown nonlinear functions, and a fuzzy state observer is designed to estimate immeasurable states. In the proposed approach, based on the property of performance function and simple barrier Lyapunov function design method, the prescribed output tracking error dynamic performance and the corresponding stability is guaranteed. By using the parameter estimation technique, a new fault compensation strategy is developed to relax the requirement that the efficiency indicator must be known. The stability of the closed-loop system is proved by using the Lyapunov function stability theory. Finally, a simulation example is given to validate the effectiveness of the proposed control strategy.

This paper presents two adaptive fuzzy outputfeedback dynamic surface control (DSC) schemes for single input-single-output (SISO) strict-feedback fractional-order uncertain nonlinear systems under the complete smooth nonlinearity and partial piecewise-smooth nonlinearity, respectively. For the former, complete smooth nonlinear functions are approximated by employing fuzzy logic systems (FLSs), based on which a novel fractional-order reduced-order observer is constructed to estimate the un-measurable states. For the latter, a new switched approximation and estimate strategy is proposed to deal with the problem of piecewise-smooth nonlinearity. Meanwhile, radial basis function property is utilized to eliminate the assumption requirement that the nonlinear functions must satisfy the Lipschitz condition inherent in the output-feedback control, which is suitable for two cases. Under certain assumptions, the stability of two closed-loop systems are proved via fractional-order Lyapunov function stability criterion. Specifically, the stability proof of the second case is built on the foundation of common Lyapunov function method. Finally, two diverse Chua's circuit simulation examples are provided to respectively validate the effectiveness of the proposed two control strategy.

This paper presents an adaptive fuzzy output- feedback dynamic surface control (DSC) for the nonlinear systems with dead-zone output nonlinearity. First, a novel smooth approximation of the output dead zone is given to conveniently fuse with the backstepping technique. After that, a nonlinear fuzzy state observer is constructed to estimate the unmeasurable states, by employing the fuzzy logic systems (FLSs) for identifying the unknown compounded nonlinear functions, which releases the limitation in the existing references that the state observer needs to be linear in the presence of dead-zone output nonlinearity. Then, to reduce the effect of unknown dead-zone coefficients, an adaptive compensation mechanism is introduced by using the characteristic of hyperbolic tangent function, which can replace the widely used Nussbaum-type function-based control strategy. Further, a novel DSC method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complex- ity inherent in the backstepping procedure, but also improves the system control performance. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed control method is rigorously verified by a single-link robot arm simulation example.

The problem of adaptive decentralized fault-tolerant control is investigated in this paper for the pure-feedback nonlinear switched large-scale systems. The considered systems possess the unknown compounded nonlinearities (unknown nonlinear functions, unknown interconnected terms, unknown nonlinear function faults, and unknown actuator dead-zone nonlinearity). The radial basis function neural networks are utilized for identifying the unknown compounded nonlinear functions so that the problems of unknown nonlinearities can be solved. A switched neural networks k-filter observer is constructed to estimate the unmeasurable states, deal with the unknown actuator dead-zone nonlinearity and compensate the nonlinear function faults simultaneously. Then, by combining the average dwell time theory, adaptive decentralized control method, and under the framework of backstepping design, an adaptive output-feedback fault compensation control method is presented. Under the certain assumptions, the stability of the closed-loop system is proved by use of Lyapunov function stability theory. Finally, the applicability of the proposed controller is well carried out by a double-inverted-pendulums simulation example.

This paper presents a nonlinear filters-based adaptive fuzzy control design for strict-feedback nonlinear systems with unknown asymmetric dead-zone output and virtual control coefficients. First, a novel smooth approximation of the non-smooth asymmetric output dead-zone nonlinearity is constructed to improve the approximation performance and speed. Then, to dilute the effects of unknown dead-zone and virtual control coefficients, an adaptive compensation mechanism is presented by utilizing projection operators techniques and the properties of fuzzy basis functions and hyperbolic tangent functions. Further, a novel adaptive backstepping control design method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also completely compensates the effects of the boundary errors generated by the introduced filters in spite of unknown virtual control coefficients. From the properties of the smooth projection operator, and based on Lyapunov synthesis, it is shown that all closed-loop signals are ensured uniformly bounded. Finally, the applicability of the proposed control method is rigorously verified by a example of one-link manipulator with a brushed dc motor. Note to Practitioners —Strict-feedback nonlinear systems can be utilized to model many practical engineering systems, such as one-link manipulator, permanent magnet synchronous motor, robots with flexible joints, spacecrafts, etc. Due to the physical limitations and other factors, non-smooth dead-zone nonlinearity often presents in system components, which will influence the control performance and threat the operation security. Therefore, this paper considers the control design problem for strict-feedback nonlinear systems with unknown asymmetric dead-zone output nonlinearity, and the proposed control algorithm is successfully applied to one-link manipulator with a brushed dc motor. In addition, the virtual control coefficients are often assumed to be known constants or known nonlinear functions with known bounds in the existing results, which is unrealistic on account of the economic costs and environmental factors. To erase such limitation, this paper presents a novel adaptive compensation mechanism based on smooth auxiliary function dependent on the property of tanh-function and the projection operator technique.