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Combining adaptive fuzzy sliding mode control with fuzzy or variable universe fuzzy switching technique, this study develops two novel direct adaptive schemes for a class of MIMO nonlinear systems with uncertainties and external disturbances. The proposed control schemes consist of fuzzy equivalent control terms, fuzzy switching control terms (in scheme one) or variable universe fuzzy switching control terms (in scheme two), and compensation control terms. The compensation control terms are used to relax the assumption on fuzzy approximation error. Based on Lyapunov stability theory, the parameters update laws are adaptively tuned online and the global asymptotic stability of the closed-loop system can be guaranteed. The major contribution of this study is to develop a novel framework for designing direct adaptive fuzzy sliding mode control scheme facing model uncertainties and external disturbances. The derived schemes can effectively solve the chattering problem and the equivalent control calculation in that environment. Simulation results performed on a two-link robotic manipulator demonstrate the feasibility of the proposed control schemes.

This paper presents a new hyperchaotic system by introducing an additional state variable into Lorenz system. The system’s characteristics, including the dissipativity, equilibrium, and Lyapunov exponents, are studied. A controller is developed which consists of an active control term and a variable universe adaptive fuzzy system. By using this controller, the synchronization of the new hyperchaotic systems with uncertain linear part is accomplished according to Lyapunov’s direct method. Simulation results illustrate the effectiveness of the proposed method.

This paper presents an adaptive nonsingular terminal sliding mode control approach for the attitude control of a hypersonic vehicle with parameter uncertainties and external disturbances based on Chebyshev neural networks (CNNs). First, a new nonsingular terminal sliding surface is proposed for a general uncertain nonlinear system. Then, a nonsingular sliding mode control is designed to achieve finite-time tracking control. Furthermore, to relax the requirement for the upper bound of the lumped uncertainty including parameter uncertainties and external disturbances, a CNN is used to estimate the lumped uncertainty. The network weights are updated by the adaptive law derived from the Lyapunov theorem. Meanwhile, a low-pass filter-based modification is added into the adaptive law to achieve fast and low-frequency adaptation when using high-gain learning rates. Finally, the proposed approach is applied to the attitude control of the hypersonic vehicle and simulation results illustrate its effectiveness.

A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output (SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.

In this study, the problem of fractional-order (FO) output feedback controller design for FO Takagi-Sugeno (TS) fuzzy systems with deterministic parameters and unmeasurable premise variables has been investigated, and the FO is in the range of 0 to 2. First, the FO TS fuzzy system is changed to an equivalent FO system with uncertain parameters. Then, a FO output feedback controller for the equivalent FO uncertain parameter system can be designed. In terms of linear matrix inequality, an explicit expression for the designed FO output feedback controller is found. Consequently, the FO TS fuzzy system is shown to be stabilized by the designed FO output feedback controller. Examples are included to demonstrate the effectiveness of the proposed method.

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