Fitting of experimental data using a fractional Kalman-like observer

Alegría-Zamudio, 2018, Fault tolerant system based on non-integers order observers: Application in a heat exchanger, ISA Trans, 1, 1 Podlubny, 1998 Hartley, 2003, Fractional-order system identification based on continuous order-distributions, Signal Process, 83, 2287, 10.1016/S0165-1684(03)00182-8 Sabatier, 2006, Fractional system identification for lead acid battery state of charge estimation, Signal Process, 86, 2645, 10.1016/j.sigpro.2006.02.030 Torres, 2018, A simple spectral observer, Math Comput Appl, 23, 1 Luo, 2018, Anti-oscillation and chaos control of the fractional-order brushless DC motor system via adaptive echo state networks, J Franklin Inst, 355, 6435, 10.1016/j.jfranklin.2018.07.004 Martínez-Fuentes, 2018, A novel Mittag-Leffler stable estimator for nonlinear fractional-order systems: A linear quadratic regulator approach, Nonlinear Dynam, 1, 1 Zhu, 2018, External force estimation of a piezo-actuated compliant mechanism based on a fractional order hysteresis model, Mech Syst Signal Process, 110, 296, 10.1016/j.ymssp.2018.03.012 Khan, 2018, Fractional order disturbance observer based adaptive sliding mode hybrid projective synchronization of fractional order Newton–Leipnik chaotic system, Int J Dyn Control, 6, 1136, 10.1007/s40435-017-0370-2 Yang, 2018, Generation of fractional-order Chua’s chaotic system and it’s synchronization, vol. 1, 1 Coronel-Escamilla, 2017, Design of a state observer to approximate signals by using the concept of fractional variable-order derivative, Digit Signal Process, 69, 127, 10.1016/j.dsp.2017.06.022 Sierociuk, 2006, Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation, Int J Appl Math Comput Sci, 16, 129 Malti, 2008, Advances in system identification using fractional models, J Comput Nonlinear Dyn, 3, 1 Podlubny, 2012, Fitting of experimental data using mittag-leffler function, 578 Gao, 2018, System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay, ISA Trans, 79, 62, 10.1016/j.isatra.2018.04.012 Naghibolhosseini, 2018, Fractional-order modelling and simulation of human ear, Int J Comput Math, 95, 1257, 10.1080/00207160.2017.1404038 Leyden, 2018, Fractional-order system identification for health monitoring, Nonlinear Dynam, 92, 1317, 10.1007/s11071-018-4128-y Gabano, 2011, Identification of a thermal system using continuous linear parameter-varying fractional modelling, IET Control Theory Appl, 5, 889, 10.1049/iet-cta.2010.0222 Chen, 2004, Fractional order disturbance observer for robust vibration suppression, Nonlinear Dynam, 38, 355, 10.1007/s11071-004-3766-4 Lu, 2006, Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal, Physica A, 359, 107, 10.1016/j.physa.2005.04.040 Senejohnny, 2012, Active sliding observer scheme based fractional chaos synchronization, Commun Nonlinear Sci Numer Simul, 17, 4373, 10.1016/j.cnsns.2012.03.004 Kong, 2017, Observer design for a class of nonlinear fractional-order systems with unknown input, J Franklin Inst B, 354, 5503, 10.1016/j.jfranklin.2017.06.011 Dadras, 2011, A new fractional order observer design for fractional order nonlinear systems, vol. 1, 403 Dadras, 2011, Fractional sliding mode observer design for a class of uncertain fractional order nonlinear systems, vol. 1, 6925 Boroujeni, 2012, Non-fragile nonlinear fractional order observer design for a class of nonlinear fractional order systems, Signal Process, 92, 2365, 10.1016/j.sigpro.2012.02.009 Luo, 2018, Observer-based adaptive stabilization of the fractional-order chaotic MEMS resonator, Nonlinear Dynam, 92, 1079, 10.1007/s11071-018-4109-1 Meléndez-Vázquez, 2018, Reduced-order fractional integral observer for synchronisation and anti-synchronisation of fractional-order chaotic systems, IET Control Theory Appl, 12, 1755, 10.1049/iet-cta.2017.1117 Chen, 2004, Fractional order disturbance observer for robust vibration suppression, Nonlinear Dyn, 38, 355, 10.1007/s11071-004-3766-4 Boroujeni, 2012, Observer based control of a class of nonlinear fractional order systems using LMI, World Acad Sci, Eng Technol, 61, 779 Taghvafard, 2011, Phase and anti-phase synchronization of fractional order chaotic systems via active control, Commun Nonlinear Sci Numer Simul, 16, 4079, 10.1016/j.cnsns.2011.02.015 Aghababa, 2013, A switching fractional calculus-based controller for normal non-linear dynamical systems, Nonlinear Dynam, 75, 577, 10.1007/s11071-013-1087-1 Boukal, 2017, Robust H∞ observer-based control of fractional-order systems with gain parametrization, IEEE Trans Automat Control, 10.1109/TAC.2017.2690140 Belkhatir, 2017, High-order sliding mode observer for fractional commensurate linear systems with unknown input, Automatica, 82, 209, 10.1016/j.automatica.2017.04.035 Kaczorek, 2016, Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems, Fract Calc Appl Anal, 19, 775, 10.1515/fca-2016-0041 Petrás, 2018, An introduction to class of fractional-order extremal control: First results, vol. 1, 1 Soltan, 2018, Fractional order PID system for suppressing epileptic activities, vol. 1, 1 Dabiri, 2018, Integration of divide-and-conquer algorithm with fractional order controllers for the efficient dynamic modeling and control of multibody systems, 1, 1 Chaudhary, 2018, Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems, Appl Math Model, 55, 698, 10.1016/j.apm.2017.11.023 Hostetter, 1980, Recursive discrete fourier transformation, IEEE Trans Acoust Speech Signal Process, 28, 184, 10.1109/TASSP.1980.1163389 Bitmead, 1982, On recursive discrete fourier transformation, IEEE Trans Acoust Speech Signal Process, 30, 319, 10.1109/TASSP.1982.1163868 Yang, 2014, Cuckoo search: Recent advances and applications, Neural Comput Appl, 24, 169, 10.1007/s00521-013-1367-1 Abdel-Basset, 2016, A comprehensive study of cuckoo-inspired algorithms, Neural Comput Appl, 1, 1 Yang, 2010, Engineering optimisation by Cuckoo Search, Int J Math Model Numer Optimisation, 1, 330, 10.1504/IJMMNO.2010.035430 Chauvin, 2010, Reconstruction of the fourier expansion of inputs of linear time-varying systems, Automatica, 46, 354, 10.1016/j.automatica.2009.11.001 Chauvin, 2010, Asymptotic reconstruction of the Fourier expansion of inputs of linear time-varying systems with applications, vol. 1, 1 Reif, 1998, An ekf-based nonlinear observer with a prescribed degree of stability, Automatica, 34, 1119, 10.1016/S0005-1098(98)00053-3 2007 Petras, 2011 Yang, 2009, Cuckoo search via lévy flights, 210 Ma, 2013, Parameter estimation of photovoltaic models via cuckoo search, J Appl Math, 10.1155/2013/362619 Siderskiy, 2015, Chua’s circuit for experimenters using readily available parts from a hobby electronics store, vol. 26, 1 Wyglinski, 2009 Andrzejak, 2001, Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state, Phys. Rev. E, 64, 10.1103/PhysRevE.64.061907 de Lathauwer, 2000, Fetal electrocardiogram extraction by blind source subspace separation, IEEE Trans Biomed Eng, 47, 567, 10.1109/10.841326 Callaerts, 1989 Chua, 1993, Chaos synchronization in Chua’s circuit, J Circuits Syst Comput, 3, 93, 10.1142/S0218126693000071