The command filtered adaptive fuzzy backstepping control method has been proposed in this study. By using the command filter, it is not only the states, the actuator constraints, and the problem of 'explosion of complexity' in conventional backstepping have been solved, but also the calculation of partial derivatives is unnecessary, so that control law and update law become succinct. Fuzzy logic systems, designed in this study, are utilised in real-time identification of the uncertain non-linear functions. Throughout the process of controller design, the transformed style and Butterworth low-pass filter are applied to solve the problem of unknown control directions. Using the Lyapunov theorem, it has been shown that the approach can guarantee all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, an application of the method has been made to the controller design of the attack angle of a hypersonic vehicle. The simulation results are given to prove the effectiveness of the method presented in this study. IntroductionIn the past few years, adaptive fuzzy backstepping method has made much progress and became one of the most popular robust and practical control methods for uncertain non-linear systems (see and references therein). Yang and Zhou [1] and Mohammad and Hamid [2] presented adaptive fuzzy backstepping methods for single input single output (SISO) systems. Sui et al. [3] and Xu et al. [4] proposed the fault-tolerant controllers by using adaptive fuzzy backstepping methods. To overcome unknown backlash-like hysteresis properties of the actuators and the time delay which are common in the control systems, Boulkroune et al. [5] and Shahnazi et al. [6] presented the stable adaptive fuzzy controllers for the interconnected uncertain non-linear systems. However, the approaches proposed in [5, 6] are limited to be suitable for the controlled plants which must satisfy matching conditions. Li et al. [7], motivated by the aforementioned literatures, presented an output-feedback control approach for time-delay systems. It is not only the unknown backlash-like hysteresis properties of the actuators has been taken into account, but also can be applied for the complicated systems whose states are not measured and that do not satisfy the matching conditions. It is known that the phenomenon of the physical saturation of the actuators, which often degrades the performance of the systems or even severely damages the stability, is inevitable in the controllers design process. The analysis and designations of the systems with input saturations have been well studied in [8, 23] and references therein. Li et al. [8] presented a direct adaptive fuzzy backstepping approach. The hyperbolic tangent and Nussbaum gain functions are applied effectively to handle the non-linearities aroused by the input saturations. Chen et al. [23] proposed the scheme to handle the unknown control directions. However, it requires some details of the systems. For example, the control coefficient ma...

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