An innovative parameter estimation for fractional order systems with impulse noise.

This paper investigates the problem of parameter estimation for fractional order linear systems when the output signal is polluted by impulse noise. The conventional least square error objective function is replaced by a new approximate least absolute error (ALAE) function to restrain the influence of impulse noise. Then a novel parameter estimation approach is designed based on the stochastic gradient method, the fractional order parameter update law and the ALAE criterion, which improves estimation accuracy and enhances robustness at the same time.

Observer-based adaptive backstepping control for fractional order systems with input saturation.

An observer-based fractional order anti-saturation adaptive backstepping control scheme is proposed for incommensurate fractional order systems with input saturation and partial measurable state in this paper. On the basis of stability analysis, a novel state observer is established first since the only information we could acquire is the system output. In order to compensate the saturation, a series of virtual signals are generated via the construction of fractional order auxiliary system.

A universal modified LMS algorithm with iteration order hybrid switching.

This paper presents a fractional order modified least square algorithm(FOMLMS), which involves an iteration order switch strategy. A FOMLMS scheme whose iteration order can be extended into α∈(0,2) is investigated. The performance of FOMLMS with the iteration order in different interval (0<α<1or1<α<2) is separately analyzed.