This article studies an adaptive control problem for nonaffine nonlinear systems with linear parametric uncertainty. Inspired by the affine system case, the studied nonaffine nonlinear systems are specified such that the ideal control input is implicitly defined by a matching equation stemming from a Lyapunov‐based analysis. The core idea of control design is to solve the matching equation in a dynamic manner. Toward this end, a dynamic state‐feedback law, together with an adaptation law for the unknown parameters, is developed such that global asymptotic stabilization is theoretically guaranteed. The proposed method is validated on a Duffing‐Holmes oscillator with a nonaffine input and a multi‐input numerical example.

中文翻译：

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动态匹配的线性参数化非仿射非线性系统的自适应控制

本文研究具有线性参数不确定性的非仿射非线性系统的自适应控制问题。受仿射系统案例启发，指定了研究的非仿射非线性系统，从而使理想控制输入由基于Lyapunov分析的匹配方程式隐式定义。控制设计的核心思想是以动态方式求解匹配方程。为此，开发了动态状态反馈定律以及未知参数的自适应定律，从而在理论上保证了全局渐近稳定。所提出的方法在具有非仿射输入和多输入数值示例的Duffing-Holmes振荡器上得到了验证。