Compensation-based Asymptotic Adaptive Stabilization for Time-Varying Nonlinear Systems

Note that classical adaptive control methods often impose restrictive assumptions on uncertainty dynamics, such as the persistence of excitation conditions, and the assumption of known basis functions. To relax these stringent assumptions while ensuring asymptotic stability, sliding mode techniques and integral bounded function designs have been developed for general nonlinear time-varying systems. However, sliding mode control’s reliance on the sign function often introduces controller oscillations, and integral function designs may result in high-gain or high-frequency feedback, both of which degrade transient performance. In response to these challenges, this paper proposes a novel compensation-based adaptive control scheme. The proposed design incorporates a dynamic compensation mechanism, eliminating the need for high-gain feedback and sliding mode-like terms, while still achieving asymptotic stabilization. The method is further applied to high-order nonlinear systems with unknown control coefficients. A simulation of an Euler-Lagrange system is provided to demonstrate the superior asymptotic stability performance.