  Adaptive backstepping control provides a feasible solution to achieve
asymptotic tracking for mismatched uncertain nonlinear systems. However,
input-to-state stability depends on high-gain feedback generated by nonlinear
damping terms, and closed-loop exponential stability with parameter convergence
involves a stringent condition named persistent excitation (PE). This paper
proposes a composite learning backstepping control (CLBC) strategy based on
modular backstepping and high-order tuners to compensate for the transient
process of parameter estimation and achieve closed-loop exponential stability
without the nonlinear damping terms and the PE condition. A novel composite
learning mechanism that maximizes the staged exciting strength is designed for
parameter estimation, such that parameter convergence can be achieved under a
condition of interval excitation (IE) or even partial IE that is strictly
weaker than PE. An extra prediction error is employed in the adaptive law to
ensure the transient performance without nonlinear damping terms. The
exponential stability of the closed-loop system is proved rigorously under the
partial IE or IE condition. Simulations have demonstrated the effectiveness and
superiority of the proposed method in both parameter estimation and control
compared to state-of-the-art methods.
