Composite learning control with modular backstepping and high-order tuners

Abstract

Adaptive control of strict-feedback nonlinear systems with mismatched uncertainties remains challenging because high-order derivatives of parameter estimates can degrade transient tracking, while parameter convergence typically requires the stringent condition of persistent excitation (PE). This paper proposes a composite learning backstepping control (CLBC) strategy based on modular backstepping and high-order tuners to achieve closed-loop exponential stability without high-gain feedback and PE. A novel composite learning mechanism that maximizes the staged excitation strength is designed for parameter estimation, enabling exponential convergence of the full set of unknown parameters under interval excitation (IE) and exponential convergence of the excited parameter components under partial IE, both of which are strictly weaker than PE. An extra prediction error is employed in the adaptive law to ensure transient performance without high-gain feedback. Simulations have demonstrated the effectiveness and superiority of the proposed CLBC in both parameter estimation and control compared to state-of-the-art methods.

arXiv commentSubmitted to 2026 China Automation Congress