Adaptive Parameter Estimation in LTI Systems

An adaptive algorithm solving the on-line parameter estimation problem for a broad class of linear systems is proposed. The approach can be applied to systems with delay, distributed-parameter systems, fractional-order systems, and others that are stable or stabilized by linear feedback. The proposed scheme can be applied to simultaneously track sufficiently slow changes in process gains, delays, time constants, diffusivity, and other parameters. The proposed method is gradient-based, and it yields a relatively efficient numerical implementation. Convergence and robustness of the algorithm are investigated through Lyapunov analysis, yielding explicit convergence conditions that generalize the well-known “persistence of excitation” and identifiability requirements arising in conventional adaptive estimation. The method is illustrated by several examples.