This paper presents an approximate prescribed performance control for a class of uncertain discrete-time nonlinear strict-feedback systems with full state constraints. The observation of the states is taken with a set of independent random measurement noises. The approximate prescribed performance control is proposed as follows. In the tracking error equations on the adaptive fuzzy backstepping control, the future virtual controls are replaced as the current virtual controls to obtain the actual control in a simple structure. The nonlinear uncertainties included in the systems are approximated as the fuzzy logic systems, and the number of the fuzzy IF–THEN rules is reduced based on the simplified extended single input rule modules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the proposed approximate estimator. The estimation errors are proved to be uniformly ultimately bounded. The effectiveness of the proposed approach is indicated by the simulation experiment of a simple numerical system.

中文翻译：

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不确定离散时间非线性严格反馈系统规定性能控制的近似设计

本文提出了一类具有全状态约束的不确定离散时间非线性严格反馈系统的近似规定性能控制。状态的观察是通过一组独立的随机测量噪声进行的。大致规定的性能控制建议如下。在自适应模糊反步控制的跟踪误差方程中，将未来的虚拟控制替换为当前的虚拟控制，以获得结构简单的实际控制。系统中包含的非线性不确定性近似为模糊逻辑系统，并在简化扩展的单输入规则模块的基础上减少了模糊IF-THEN规则的数量。不可测量状态和可调参数的估计是通过使用建议的近似估计器获得的。证明估计误差是一致最终有界的。一个简单的数值系统的仿真实验表明了所提出方法的有效性。