Improving the control energy in model reference adaptive controllers using fractional adaptive laws

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Abstract
This paper presents the analysis of the control energy consumed in model reference adaptive control (MRAC) schemes using fractional adaptive laws, through simulation studies. The analysis is focused on the energy spent in the control signal represented by means of the integral of the squared control input (ISI). Also, the behavior of the integral of the squared control error (ISE) is included in the analysis. The orders of the adaptive laws were selected by particle swarm optimization (PSO), using an objective function including the ISI and the ISE, with different weighting factors. The results show that, when ISI index is taken into account in the optimization process to determine the orders of adaptive laws, the resulting values are fractional, indicating that control energy of the scheme might be better managed if fractional adaptive laws are used.