Adaptive unit-vector law with time-varying gain for finite-time parameter estimation in LTI systems

A continuation of previous authors' work on adaptive parameter estimation for linear dynamical systems having irrational transfer function is presented in this work. An original modification of the gradient algorithm, inspired by the variable structure control techniques and additionally featuring a time-varying adaptation gain, is presented and analyzed using Lyapunov techniques. The exposition is illustrated by several numerical examples which illustrate the effectiveness of the proposed algorithm

Adaptive parameter estimation for infinite-dimensional LTI systems with finite-time convergence

A novel adaptive algorithm to address the on-line identification of constant uncertain parameters in linear timeinvariant dynamical systems is proposed. The approach can be applied to a broad class of linear dynamical processes including, e.g., delay systems, fractional-order systems, and distributedparameter systems. The proposed scheme takes advantage of a nonlinear adaptation rule inspired by the unit-vector variable-structure control strategy and provides the finite-time parameter estimation. Convergence properties of the algorithm are investigated through Lyapunov analysis, that constructively yields explicit convergence conditions which generalize the wellknown Persistence of Excitation (P.E.) and identifiability requirements arising in conventional adaptive estimation. The theoretical findings are substantiated by extensive simulation examples