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In this paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples. [ABSTRACT FROM PUBLISHER]

In this paper, an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems. The controlled systems are in a strict-feedback frame and contain unknown functions and nonsymmetric dead-zone. For this class of systems, the control objective is to design a controller, which not only guarantees the stability of the systems, but achieves the optimal control performance as well. This immediately brings about the difficulties in the controller design. To this end, the fuzzy logic systems are employed to approximate the unknown functions in the systems. Based on the utility functions and the critic designs, and by applying the backsteppping design technique, a reinforcement learning algorithm is used to develop an optimal control signal. The adaptation auxiliary signal for unknown dead-zone parameters is established to compensate for the effect of nonsymmetric dead-zone on the control performance, and the updating laws are obtained based on the gradient descent rule. The stability of the control systems can be proved based on the difference Lyapunov function method. The feasibility of the proposed control approach is further demonstrated via two simulation examples. [ABSTRACT FROM PUBLISHER]

In this study, we investigate an adaptive fuzzy controller design for a class of nonlinear multi-input multi-output (MIMO) systems in interconnected form. The systems considered comprise n subsystems and an unknown interconnection term is included in every equation for each subsystem. The interconnection term is a function of all the states from the first to the ( n − 1 ) th subsystems. Moreover, the effects of dead-zone models are considered in each subsystem of the systems. These properties of the systems cause the difficulties and add further complexity to the design. In order to overcome these difficulties, we use the following methods: (1) the fuzzy logic systems are employed to approximate the appropriate unknown functions of the systems, (2) a novel backstepping design procedure is constructively designed, and (3) compensative adaptation laws are provided to compensate for the effects of the dead-zone inputs. We show that all the signals in the closed-loop system are bounded and that the outputs converge to a compact set by using the Lyapunov analysis theorem. Simulated examples are presented that validate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

An adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper. The considered systems are of the discrete-time form in a triangular structure and include the backlash and the external disturbance. By using the prediction function of future states, the systems are transformed into an n-step ahead predictor. The fuzzy logic systems (FLSs) are used to approximate the unknown functions, unknown backlash, and backlash inversion, respectively. A discrete-time tuning algorithm is developed to estimate the optimal fuzzy parameters. Compared with the previous works for the discrete-time systems with backlash, the main contributions of the paper are that 1) the rigorous restriction for the functional estimation error is removed, and 2) the external disturbance is bounded, but the bound is not required to be known. A novel controller and the adaptation laws are constructed by using the discrete Taylor series expansion and the difference Lyapunov analysis, and thus, those limitations in the previous works are overcome. It is proven that all the signals in the closed-loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set. A simulation example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi-input–multi-output (MIMO) systems in the discrete-time form. The considered MIMO systems are composed of n subsystems with the couplings of inputs and states among subsystems. In order to solve the noncausal problem and decouple the couplings, it needs to transform the systems into a predictor form. The higher order neural networks are utilized to approximate the desired controllers. By using Lyapunov analysis, it is proven that all the signals in the closed-loop system is the semi-globally uniformly ultimately bounded and the output errors converge to a compact set. In contrast to the existing results, the advantage of the scheme is that the number of the adjustable parameters is highly reduced. The effectiveness of the scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

Abstract: The universal approximation theorem of the fuzzy logic systems (FLS) is utilized to develop an adaptive control scheme for a class of nonlinear MIMO systems by the backstepping technique. The MIMO systems consist of some subsystems and each subsystem is able to be reputed as non-affine pure-feedback structure. The external disturbances appear in each equation of each subsystem and the disturbance coefficients are assumed to be unknown functions rather than constant one. The two main advantages of the developed scheme are that (1) it does not require a priori knowledge of the signs of the control gains and (2) only one parameter is needed to be adjusted online in controller design procedure for each subsystem. It is proven that, under the appropriate assumptions, the developed scheme can achieve that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. Effectiveness of the developed scheme is illustrated by the simulation example. [Copyright &y& Elsevier]