Improved adaptive laws for fractional error models 1 with parameter constraints

This paper presents the analysis of two fractional adaptive systems described by the so called fractional error model 1. The true unknown parameters of each error model are, however, not independent, but linearly related. The analytical results show that it is possible to find coupled fractional adaptive laws, such that the overall adaptive system is globally stable, when the fractional order is in the interval α∈ (0 , 1). Although no analytical results are provided for the case α∈ (1 , 2) , simulations studies are carried out using fractional orders in the whole interval α∈ (0 , 2). The results indicate that using coupled fractional adaptive laws can lead to better parameter estimation than when using independent adaptive laws without incorporating the information contained in the constraint. These conclusions hold for simulation studies under ideal conditions and in the presence of noise in the inputs.