On key properties of the Lion's and Kreisselmeier's adaptation algorithms

Abstract The paper revises properties of two identification/adaptation algorithms proposed by Lion (1967) and Kreisselmeier (1977) more than 40 years ago to accelerate parametric convergence under regressor persistency of excitation (PE) condition. First, being motivated by paper Aranovskiy et al. (2017) it is demonstrated that these algorithms can provide asymptotic (not exponential) parametric convergence under simple condition which is weaker than requirement of PE. Second, it is shown that via some condition these schemes can be used for generating the high order time derivatives (HOTD) of the adjustable parameters that are necessary for solution of a wide range of problems of identification and adaptive control including backstepping design procedure.

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