Continuous-Time Adaptive Control with Dynamic Adaptation Gain

This paper investigates a class of continuous-time parameter identifiers with the so-called “dynamic adaptation gain (DAG)”, inspired by its discrete-time counterpart [1]. A modular control law is first presented: this helps re-parametrize the system and highlight the required properties for the identifier. Then, a dynamic adaptation gain is constructed using a strictly passive system, strengthened by a feedthrough path: the resulting DAG is input strictly passive. Analysis shows that the identifier with the proposed DAG satisfies specific signal properties. An integrated analysis of both the control law and the identifier establishes boundedness of all closedloop signals and state convergence. The convergence of the parameter estimate is also established under a persistence of excitation condition. Finally, an example inspired by a pathfollowing problem demonstrates the convergence improvement achieved by the proposed DAG.