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Adaptive control for discontinuous variable-order fractional systems with disturbances. (English) Zbl 1517.93052


MSC:

93C40 Adaptive control/observation systems
34A36 Discontinuous ordinary differential equations
34A08 Fractional ordinary differential equations
93C73 Perturbations in control/observation systems
Full Text: DOI

References:

[1] Luo, W.; Liu, Y.; Ma, T., Consensus of fractional-order multi-agent systems with impulsive disturbance, IFAC Pap. On Line, 52, 174-178 (2019) · doi:10.1016/j.ifacol.2019.12.402
[2] Li, Y.; Zhao, D.; Chen, Y.; Podlubny, I.; Zhang, C., Finite energy Lyapunov function candidate for fractional order general nonlinear systems, Commun. Nonlinear Sci. Numer. Simul., 78, 104886 (2019) · Zbl 1479.34121 · doi:10.1016/j.cnsns.2019.104886
[3] Alessandretti, A.; Pequito, S.; Pappas, G.; Aguiar, A., Finite-dimensional control of linear discrete-time fractional-order systems, Automatica, 115, 108512 (2020) · Zbl 1436.93048 · doi:10.1016/j.automatica.2019.108512
[4] Butzer, P.; Westphal, U., An Introduction to Fractional Calculus (2000), Singapore: World Scientific, Singapore · Zbl 0987.26005 · doi:10.1142/9789812817747_0001
[5] Wu, C.; Liu, X., Lyapunov and external stability of Caputo fractional order switching systems, Nonlinear Anal. Hybrid Syst., 34, 134-146 (2019) · Zbl 1434.93071 · doi:10.1016/j.nahs.2019.06.002
[6] Zambrano-Serrano, E.; Campos-Cantón, E.; Muñoz-Pacheco, J., Strange attractors generated by a fractional order switching system and its topological horseshoe, Nonlinear Dyn., 83, 1629-1641 (2016) · Zbl 1351.34011 · doi:10.1007/s11071-015-2436-z
[7] Soczkiewicz, E., Application of fractional calculus in the theory of viscoelasticity, Mol. Quantum Acoust., 23, 397-404 (2002)
[8] Hilfer, R., Applications of Fractional Calculus in Physics (2001), Hackensack, NJ: World Scientific, Hackensack, NJ · Zbl 0998.26002
[9] Meng, R.; Yin, D.; Drapaca, C., A variable order fractional constitutive model of the viscoelastic behavior of polymers, Int. J. Non-Linear Mech., 113, 171-177 (2019) · doi:10.1016/j.ijnonlinmec.2019.04.002
[10] Bhrawy, A.; Zaky, M., Numerical algorithm for the variable-order Caputo fractional functional differential equation, Nonlinear Dyn., 85, 1815-1823 (2016) · Zbl 1349.65505 · doi:10.1007/s11071-016-2797-y
[11] Samko, S.; Ross, B., Integration and differentiation to a variable fractional order, Integral Transforms Spec. Funct., 1, 277-300 (1993) · Zbl 0820.26003 · doi:10.1080/10652469308819027
[12] Sheng, H.; Sun, H.; Coopmans, C.; Chen, Y.; Bohannan, G., A physical experimental study of variable-order fractional integrator and differentiator, Eur. Phys. J. Spec. Top., 193, 93-104 (2011) · doi:10.1140/epjst/e2011-01384-4
[13] Ramirez, L.; Coimbra, C., On the variable order dynamics of the nonlinear wake caused by a sedimenting particle, Phys. D Non-linear Phenom., 240, 1111-1118 (2011) · Zbl 1219.76054 · doi:10.1016/j.physd.2011.04.001
[14] Tolba, M.; Saleh, H.; Mohammad, B.; Al-Qutayri, M., Enhanced FPGA realization of the fractional-order derivative and application to a variable-order chaotic system, Nonlinear Dyn., 99, 3143-3154 (2020) · doi:10.1007/s11071-019-05449-w
[15] Zhang, L.; Yu, C.; Liu, T., Control of finite-time anti-synchronization for variable-order fractional chaotic systems with unknown parameters, Nonlinear Dyn., 86, 1967-1980 (2016) · Zbl 1371.93096 · doi:10.1007/s11071-016-3008-6
[16] Razminiaa, A.; Dizajib, A.; Majda, V., Solution existence for non-autonomous variable-order fractional differential equations, Math. Comput. Modell., 55, 1106-1117 (2012) · Zbl 1255.34008 · doi:10.1016/j.mcm.2011.09.034
[17] Zhang, S., Existence result of solutions to differential equations of variable-order with nonlinear boundary value conditions, Commun. Nonlinear Sci. Numer. Simul., 18, 3289-3297 (2013) · Zbl 1344.34022 · doi:10.1016/j.cnsns.2013.05.003
[18] Xu, Y.; He, Z., Existence and uniqueness results for Cauchy problem of variable-order fractional differential equations, Int. J. Appl. Math. Comput. Sci., 43, 295-306 (2013) · Zbl 1296.34041
[19] Jiang, J.; Chen, H.; Guirao, J.; Cao, D., Existence of the solution and stability for a class of variable fractional order differential systems, Chaos Solitons Fractals, 128, 269-274 (2019) · Zbl 1483.34014 · doi:10.1016/j.chaos.2019.07.052
[20] Jiang, J.; Cao, D.; Chen, H., Sliding mode control for a class of variable-order fractional chaotic systems, J. Frankl. Inst., 357, 10127-10158 (2020) · Zbl 1450.93004 · doi:10.1016/j.jfranklin.2019.11.036
[21] Du, H.; Wen, G.; Wu, D.; Cheng, Y.; Lü, J., Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems, Automatica, 113, 1-11 (2020) · Zbl 1440.93232 · doi:10.1016/j.automatica.2019.108797
[22] Liu, X.; Ho, D.; Song, Q.; Cao, J., Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances, Nonlinear Dyn., 90, 2057-2068 (2017) · Zbl 1380.93194 · doi:10.1007/s11071-017-3782-9
[23] Wu, Y.; Jiang, B.; Lu, N., A descriptor system approach for estimation of incipient faults with application to high-speed railway traction devices, IEEE Trans. Syst. Man Cybern. Syst., 49, 2108-2118 (2019) · doi:10.1109/TSMC.2017.2757264
[24] Wu, Y.; Jiang, B.; Wang, Y., Incipient winding fault detection and diagnosis for squirrel-cage induction motors equipped on CRH trains, ISA Trans., 99, 488-495 (2020) · doi:10.1016/j.isatra.2019.09.020
[25] Peng, X.; Wu, H.; Cao, J., Global nonfragile synchronization in finite time for fractional-order discontinuous neural networks with nonlinear growth activations, IEEE Trans. Neural Netw. Learn. Syst., 30, 2123-2137 (2019) · doi:10.1109/TNNLS.2018.2876726
[26] Wang, X.; Wu, H.; Cao, J., Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth, Nonlinear Anal. Hybrid Syst., 37, 100888 (2020) · Zbl 1478.93645 · doi:10.1016/j.nahs.2020.100888
[27] Liu, Y.; Arimoto, S.; Parra-Vega, V.; Kitagaki, K., Decentralized adaptive control of multiple manipulators in cooperations, Int. J. Control, 67, 649-674 (1997) · Zbl 0882.93054 · doi:10.1080/002071797223938
[28] Dydek, Z.; Annaswamy, A.; Lavretsky, E., Adaptive control of quadrotor UAVs: a design trade study with flight evaluations, IEEE Trans. Control Syst. Technol., 21, 1400-1406 (2013) · doi:10.1109/TCST.2012.2200104
[29] Yoerger, D., Slotine, J.: Adaptive sliding control of an experimental underwater vehicle. In: IEEE International Conference on Robotics and Automation, pp. 2746-2751. IEEE, Sacramento, California (1991)
[30] Chen, Y.; Wei, Y.; Liang, S.; Wang, Y., Indirect model reference adaptive control for a class of fractional order systems, Commun. Nonlinear Sci. Numer. Simul., 39, 458-471 (2016) · Zbl 1510.93139 · doi:10.1016/j.cnsns.2016.03.016
[31] Gong, P.; Lan, W., Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies, Automatica, 92, 92-99 (2018) · Zbl 1388.93052 · doi:10.1016/j.automatica.2018.02.010
[32] Jmal, A., Naifar, O., Makhlouf, A.Ben, Derbel, N., Hammami, M.: Adaptive stabilization for a class of fractional order systems with nonlinear uncertainty. Arab. J. Sci. Eng. 4, 2195-2203 (2020) · Zbl 1447.93171
[33] Wang, J.; Shao, C.; Chen, Y., Fractional order sliding mode control via disturbance observer for a class of fractional order systems with mismatched disturbance, Mechatronics, 53, 8-19 (2018) · doi:10.1016/j.mechatronics.2018.05.006
[34] Valrio, D.; Costa, J., Variable-order fractional derivatives and their numerical approximations, Signal Process., 91, 470-483 (2011) · Zbl 1203.94060 · doi:10.1016/j.sigpro.2010.04.006
[35] Xu, L.; Wang, X., Mathematical Analysis Methods and Examples (1983), Beijing: Higher Education Press, Beijing
[36] Gronwall, T., Gronwall-Bellman note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Annu. Math., 20, 292-296 (1919) · JFM 47.0399.02 · doi:10.2307/1967124
[37] Bellman, R., The stability of solutions of linear differential equations, Duke Math. J., 10, 643-647 (1943) · Zbl 0061.18502 · doi:10.1215/S0012-7094-43-01059-2
[38] Filippov, A., Differential Equations with Discontinuous Right-Hand Sides (1988), Dordrecht: Kluwer, Dordrecht · Zbl 0664.34001 · doi:10.1007/978-94-015-7793-9
[39] Aubin, J.; Cellina, A., Differential Inclusions (1984), Berlin: Springer, Berlin · Zbl 0538.34007 · doi:10.1007/978-3-642-69512-4
[40] Forti, M., Nistri, P.: Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50, 1421-1435 (2003) · Zbl 1368.34024
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