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Fractional Order Error Models With Parameter Constraints Chapter | 6  181



               TABLE 6.1 Integral of the Squared Norm of Output Errors for the Noisy
               Simulation Scenario
                                            CFOAL            NCFOAL
                 α 5 0:5       ISN1          62.2957          68.0988
                               ISN2         160.2580         142.9454
                 α 5 0:7       ISN1          37.6153          41.1030
                               ISN2          59.7030          57.7515
               α 5 0:9         ISN1          32.2745          37.8421

                               ISN2          22.5958          25.4242
               α 5 1           ISN1          35.1002          47.7553

                               ISN2          14.7588          18.1608


             of the overall adaptive system, compared to the case when classic decoupled
             fractional AL are used, under ideal conditions as well as in the presence of
             noise in the inputs.



             ACKNOWLEDGMENTS
             The results reported in this chapter have been financed by CONICYT- Chile, under the
             Basal Financing Program FB0809 “Advanced Mining Technology Center,” FONDECYT
             Project 1150488 “Fractional Error Models in Adaptive Control and Applications,” and
             FONDECYT 3150007 “Postdoctoral Program 2015.”


             REFERENCES
             Aguila-Camacho, N., Duarte-Mermoud, M.A., 2013. Fractional adaptive control for an automatic
                voltage regulator. ISA Trans. 52, 807 815.
             Aguila-Camacho, N., Duarte-Mermoud, M.A., 2015. Fractional Error Models 1 with Parameter
                Constraints. In: Proceedings of the 2015 International Symposium on Fractional Signals and
                Systems (FSS2015), Cluj-Napoca, Romania, 1-3 October, pp. 18 23.
             Aguila-Camacho, N., Duarte-Mermoud, M.A., 2016. Boundedness of the solutions for certain
                classes of fractional differential equations with application to adaptive systems. ISA Trans.
                60, 82 88.
             Aguila-Camacho, N., Duarte-Mermoud, M.A., 2017. Improved adaptive laws for Fractional
                Error Models 1 with parameter constraints. Int. J. Dynam. Control 5, 198 207.
             Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J., 2014. Lyapunov functions for frac-
                tional order systems. Commun. Nonlinear Sci. Numer. Simul. 19, 2951 2957.
             Alikhanov, A., 2010. A priori estimates for solutions of boundary value problems for fractional-
                order equations. Differ. Eq. 46, 660 666.
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