In this paper, an adaptive prescribed performance controller, consisting of a novel scalarly virtual parameter adaptation (SVPA) technique, is developed for a class of single-input and single-output high-order nonlinear pure-feedback systems in the presence of model uncertain yet locally Lipschitz nonlinearities. The objective of this work is to improve the transient and steady performance of pioneering prescribed performance control (PPC) by incorporating a single SVPA mechanism into the virtual and actual controllers, therein, the unknown yet bounded parameters are defined with respect to proper composite system and virtual functions, bringing the gap between pioneering PPC and linearly parameterized approximator-based PPC schemes (including neural networks, fuzzy logic systems, etc.), that is, the computational complexity of proposed method exceeds PPC with one level (caused by introduced single adaptive law) yet maintains low level with comparison to linearly parametrized approximator-based PPC. It is guaranteed that both virtual and actual tracking errors converge transiently to small residual sets characterized by prescribed performance functions and control parameters simultaneously and ultimately converge to zero, which is also proved by rigorously mathematical analysis using Lyapunov stability theorem. The closed-loop signals are kept globally ultimately uniformly bounded, and comparative simulation results are presented to demonstrate the effectiveness and advantages of the theoretical findings.

本文针对存在模型不确定性的一类单输入单输出高阶非线性纯反馈系统，开发了一种由新型标量虚拟参数自适应（SVPA）技术组成的自适应规定性能控制器。但局部Lipschitz非线性。这项工作的目的是通过将单个SVPA机制整合到虚拟和实际控制器中，从而改善开创性规定的性能控制（PPC）的瞬态和稳定性能，其中相对于适当的复合系统定义了未知但有界的参数，并且虚拟功能，从而在先驱PPC和基于线性参数化的基于逼近器的PPC方案（包括神经网络，模糊逻辑系统等）之间拉开了差距，也就是说，与基于线性参数化逼近器的PPC相比，所提方法的计算复杂度超过了PPC一级（由引入的单个自适应定律引起），但仍保持较低水平。可以确保虚拟和实际跟踪误差都瞬时收敛到以规定的性能函数和控制参数为特征的小残差集，并最终收敛到零，这也可以通过使用Lyapunov稳定性定理进行严格的数学分析来证明。闭环信号最终在全局范围内保持均匀有界，并给出了比较仿真结果以证明理论发现的有效性和优势。