Adaptive control of linearly parameterized nonaffine nonlinear systems via dynamic matching

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.