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In this article, the adaptive fuzzy tracking control problem for a class of uncertain strict-feedback systems with unknown nonlinearities is investigated with particular emphasis on global stability. The proposed control scheme is designed by integrating the barrier Lyapunov functions (BLFs) with the techniques of fuzzy approximation and backstepping. The novel integral BLFs (iBLFs) are introduced to overcome the design difficulties induced by the virtual control coefficients and determine a priori the compact set for guaranteeing the validity of fuzzy approximation. Compared with existing approximation-based control results, the developed controller not only guarantees global stability without requiring prior information of system nonlinearities and assumptions on the time derivatives of virtual control coefficients, but also prevents the ``explosion of complexity'' issue without attaching additional filters. The simulation results further confirm the effectiveness of the theoretical findings.

Summary This paper contributes to dynamic surface asymptotic tracking for a class of uncertain nonlinear systems in strict-feedback form. By utilizing the nonlinear filters with a positive time-varying integral function, an adaptive state feedback controller is explicitly designed via a dynamic surface approach, where the compensating term with the estimate of an unknown bound is introduced to eliminate the effect raised by the boundary layer error at each step. Compared with the existing results in the literature, the proposed control scheme not only avoids the issue of “explosion of complexity” inherent in the backstepping procedure but also holds the asymptotic output tracking. Finally, simulation results are presented to verify the effectiveness of the proposed methodology.

In this study, the authors consider the problem of adaptive tracking control for a class of non-linear uncertain systems in the presence of input saturation. To tackle the effects of the non-smooth saturation non-linearity, a novel approximate saturation model is constructed, which can smoothly approximate the real saturation with arbitrarily prescribed precision. By utilising dynamic surface control approach with the modified linear filters, a robust adaptive control scheme is explicitly designed via the adding an integrator technique. The proposed controller can eliminate not only the ‘explosion of complexity’ issue inherent in the backstepping design but also the coupling terms with respect to the surface errors and the boundary layer errors. In addition, the stability analysis shows that all the resulting closed-loop signals are semi-global uniformly ultimately bounded. Finally, simulation results are presented to demonstrate the performance of the developed method.

Summary This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the problem of universal control for a class of second order nonlinear systems with unknown dynamics. Without utilizing function approximators, a universal adaptive control scheme is developed via backstepping approach, where the system nonlinearities are adaptively compensated at each step. Based on Lyapunov stability theory, it is proven that, for any initial system condition, all the resulting closed loop signals are globally uniformly ultimately bounded. Finally, simulation results are presented to validate the effectiveness of the proposed design method.

This paper investigates the problem of output tracking for a class of nonlinear uncertain systems in strict feedback form. By utilizing the nonlinear filters with a common compensator, a robust adaptive control scheme is proposed via dynamic surface approach. Compared with the existing results in the literature, the proposed control scheme not only avoids the issue of "explosion of complexity" in the recursive procedure, but also eliminates the effects raised by boundary layer errors. Finally, a numerical example is presented to verify the effectiveness of the proposed methodology.

In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes.

Summary This paper concerns the global output tracking for uncertain pure-feedback systems. By adding an integrator, the original systems with nonaffine-in-control are transformed into the augmented affine-in-control systems. Through a novel change of coordinates, an adaptive control scheme is proposed via backstepping approach, which eliminates the need of overparametrization. It is proven that the proposed control scheme is sufficient to ensure the global asymptotic tracking, as well as the boundedness of all the closed-loop signals. An illustrative example is provided to demonstrate the feasibility of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with the problem of dynamic surface asymptotic tracking for a class of uncertain nonlinear systems preceded by a hysteresis input nonlinearity, where the hysteresis is described by the Bouc-Wen model. By utilizing the modified nonlinear filters and a positive time-varying integral function, a smooth adaptive controller is designed via dynamic surface approach, where the compensating terms with the estimate of unknown bounds are employed to eliminate the effects of given continuous functions on a certain compact, unknown hysteresis and external disturbance. It is shown that all the resulting closed loop signals are semiglobally bounded, and the output tracking error converges to zero asymptotically. Finally, simulation results are presented to validate the effectiveness of the proposed methodology.

This paper is concerned with the problem of tracking control for strict feedback nonlinear systems in the presence of input saturation. A transformation nonlinear function is employed to guarantee the saturation constraint. Then, to deal with the transformed system with nonaffine structure, an auxiliary integrator is introduced such that the use of backstepping is feasible in the control design. It is rigorously proven that the proposed control scheme can ensure that all closed loop signals are globally bounded, and the tracking error is asymptotically converge to zero. The effectiveness of the proposed approach is verified through a numerical example.

The output tracking problem for a class of uncertain strict-feedback nonlinear systems with unknown Duhem hysteresis input is investigated. In order to handle the undesirable effects caused by unknown hysteresis, the properties in respect to Duhem model are used to decompose it as a nonlinear smooth term and a nonlinear bounded “disturbance-like” term, which makes it possible to deal with the unknown hysteresis without constructing inverse in the controller design. By combining robust control and dynamic surface control technique, an adaptive controller is proposed in this paper to avoid “the explosion complexity” in the standard backstepping design procedure. The negative effects caused by the unknown hysteresis can be mitigated effectively, and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is obtained. The effectiveness of the proposed scheme is validated through a simulation example.

In this paper, the tracking problem for a class of uncertain nonlinear systems preceded by unknown Coleman-Hodgdon hysteresis is investigated. By analysing the hysteresis conditions, an important property is given, and hence Coleman-Hodgdon hysteresis can be decomposed as a nonlinear smooth term and a nonlinear bounded distrubance-like term. In order to remove the difficulty arising from the nonlinear smooth term, mean value theorem and a Nussbaum function lemma are introduced. Then following backstepping design procedure, a novel adaptive controller is developed without constructing a hysteresis inverse. The proposed controller not only doesn't need any assumptions on the uncertain system parameters within a known compact and a priori knowledge on the bound of the external disturbance, but also can guarantee global uniformly ultimately boundedness of all signals in the closed-loop system. Simulations performed on a nonlinear system illustrate and clarify the proposed scheme.

Focusing on a class of pure-feedback nonlinear time-delay systems with unknown hysteresis input, an adaptive control method is discussed in this paper. For such nonlinear systems, the nonaffine structure and the non-smooth hysteresis nonlinearities are the major challenges for the controller design. To deal with the nonaffine problem of pure-feedback systems, mean-value theorem is adopted to transform the systems as affine form, and neural network approximator is utilized to estimate the unknown system functions. For the unknown preceded hysteresis nonlinearities, the Backlash-like model is utilized as an illustration to show the way dealing with the unknown hysteresis input. Following the backstepping design procedure, a dynamic surface control approach is investigated to avoid the complexity of controller by applying the low-pass filters at each step, and the semiglobal uniform ultimate boundedness of the signals in the closed-loop system is ensured. The proposed control method explores the validity mitigating the negative effects caused by the unknown hysteresis, and the simulation results validate the effectiveness of the proposed design scheme.

In this paper, the tracking problem for a class of uncertain perturbed strict-feedback nonlinear systems with unknown Duhem hysteresis input is investigated. Different with the conventional nonlinear systems, the existence of the unknown preceded hysteresis will affect the system performance and bring a challenge for the controller design. To overcome the difficulties caused by the unknown hysteresis, the Duhem model is used to describe the hysteresis in this paper. The properties of the Duhem model are utilized to get the explicit expression of the hysteresis output, which makes it possible to deal with the unknown hysteresis input. Following the conventional backstepping design procedure, a dynamic surface control method in each step is used to avoid "the explosion complexity" in the backstepping design, and the Nussbaum function method is used to solve the time-varying coefficient problem in the explicit expression of the Duhem model. Under the proposed control approach, the semiglobal uniform ultimate boundedness of all the signals in the close-loop system is guaranteed. The effectiveness of the proposed design scheme is validated through a simulation example.