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Uniform Asymptotic Convergence of an Adaptive Algorithm with Diminishing Persistent Excitation

Abstract Conventional adaptive systems algorithms require persistent excitation (p.e.) for exponential convergence, in turn important for robustness. A recently proposed algorithm for localizing a target by a moving agent that can measure its distance from the target, reduces to the same error model. In this case persistent excitation requires the agent's velocity vector to be p.e.. Yet in many control tasks e.g. where an agent must dock on a target at an unknown location, by measuring its distance from the target, such a p.e. condition cannot be met. In this paper we propose a notion of an excitation condition where the degree of p.e. declines with the quality of estimate and prove uniform asymptotic convergence under this condition.