On Fractional Order Adaptive Observer

This article derives a new scheme to an adaptive observer for a class of fractional order systems. Global asymptotic convergence for joint state-parameter estimation is established for linear time invariant single-input single-output systems. For such fractional order systems, it is proved that all the signals in the resulting closed-loop system are globally uniformly bounded, the state and parameter estimation errors converge to zero. Potential applications of the presented adaptive observer include online system identification, fault detection, adaptive control of fractional order systems, etc. Numerical simulation examples are presented to demonstrate the performance of the proposed adaptive observer.