  High-order tuners are algorithms that show promise in achieving greater
efficiency than classic gradient-based algorithms in identifying the parameters
of parametric models and/or in facilitating the progress of a control or
optimization algorithm whose adaptive behavior relies on such models. For
high-order tuners, robust stability properties, namely uniform global
asymptotic (and exponential) stability, currently rely on a persistent
excitation (PE) condition. In this work, we establish such stability properties
with a novel analysis based on a Matrosov theorem and then show that the PE
requirement can be relaxed via a concurrent learning technique driven by
sampled data points that are sufficiently rich. We show numerically that
concurrent learning may greatly improve efficiency. We incorporate reset
methods that preserve the stability guarantees while providing additional
improvements that may be relevant in applications that demand highly accurate
parameter estimates at relatively low additional cost in computation.
