非仿射非线性系统控制综述

Control of non-affine nonlinear systems:A survey

作为仿射非线性系统更一般化的描述,非仿射非线性系统所对应的实际应用更加广泛,也更贴近实际。因此,研究非仿射非线性系统的控制问题十分重要。然而,非线性系统的非仿射特性会使控制信号以非线性函数形式出现在闭环系统中,从而带来诸如控制方向未知、奇异、过零等问题。由此,解决非仿射非线性系统的控制问题面临着巨大的挑战。基于此,介绍了仿射、严格反馈和高阶系统的相关背景知识,总结和分析了解决非仿射非线性系统控制的3种解决思路,包括函数变换法、参考模型法和数据驱动法。在已有的研究成果基础上,指出非仿射非线性系统研究领域所面临的挑战和发展趋势。

As a more general description of affine nonlinear systems,the practical applications corresponding to non-affine nonlinear systems are more comprehensive and closer to reality.Therefore,it is essential to study the control problems of non-affine nonlinear systems.However,the closed-loop system’s control signal appears as a nonlinear function due to the non-affine properties of nonlinear systems,which can lead to issues including singularity,zero-crossing,and uncertain control direction.From this point,solving control problems of non-affine nonlinear systems is a considerable challenge.This paper first introduces the relevant background knowledge of affine,strict feedback,and high-order systems,and then summarizes three solutions through literature research:function transformation method,reference model method,and data-driven method.Finally,based on existing research findings,the challenges and development trends faced in the field of non-affine nonlinear system research are proposed.