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 time invariant 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 distributed parameter 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 well-known "Persistence of Excitation" (P.E.) and identifiability requirements arising in conventional adaptive estimation. The theoretical findings are substantiated by extensive simulation examples.