Abstract
This paper introduces a finite-time control technique for control of a class of non-autonomous fractional-order nonlinear systems in the presence of system uncertainties and external noises. It is known that finite-time control methods demonstrate better robustness and disturbance rejection properties. Moreover, finite time control methods have optimal settling time. In order to design a robust finite-time controller, a new nonsingular terminal sliding manifold is proposed. The proposed sliding mode dynamics has the property of fast convergence to zero. Afterwards, a novel fractional sliding mode control law is introduced to guarantee the occurrence of the sliding motion in finite time. The convergence times of both reaching and sliding phases are estimated. The main characteristics of the proposed fractional sliding mode technique are (1) finite-time convergence to the origin; (2) the use of only one control input; (3) robustness against system uncertainties and external noises; and (4) the ability of control of non-autonomous fractional-order systems. At the end of this paper, some computer simulations are included to highlight the applicability and efficacy of the proposed fractional control method.
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Luo, Y., Chen, Y.Q., Pi, Y.: Experimental study of fractional order proportional derivative controller synthesis for fractional order systems. Mechatronics 21, 204–214 (2011)
Aghababa, M.P.: Chaos in a fractional-order micro-electro-mechanical resonator and its suppression. Chin. Phys. B 21, 100505 (2012)
Aghababa, M.P., Aghababa, H.P.: A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs. Nonlinear Dyn. 69, 1903–1914 (2012)
Aghababa, M.P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model. 35, 3080–3091 (2011)
Aghababa, M.P., Heydari, A.: Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities. Appl. Math. Model. 36, 1639–1652 (2012)
Aghababa, M.P., Akbari, M.E.: A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances. Appl. Comput. Math. 218, 5757–5768 (2012)
Aghababa, M.P., Feizi, H.: Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs. Chin. Phys. B 21, 060506 (2012)
Aghababa, M.P., Aghababa, H.P.: Chaos suppression of a class of unknown uncertain chaotic systems via single input. Commun. Nonlinear Sci. Numer. Simul. 17, 3533–3538 (2012)
Aghababa, M.P., Feizi, H.: Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances. Trans. Inst. Meas. Control (2012). doi:10.1177/0142331211434657
Aghababa, M.P., Aghababa, H.P.: A novel finite-time sliding mode controller applied to synchronize chaotic systems with input nonlinearity. Arab. J. Sci. Eng. 34, 990–997 (2012)
Aghababa, M.P.: A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs. Chin. Phys. B 20, 090505 (2011)
Aghababa, M.P., Aghabab, H.P.: Synchronization of mechanical horizontal platform systems in finite time. Appl. Math. Model. 36, 4579–4591 (2012)
Aghababa, M.P.: Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems. Chin. Phys. B 21, 030502 (2012)
Aghababa, M.P., Aghababa, H.P.: Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs. Appl. Math. Mech. 33, 155–164 (2012)
Aghababa, M.P., Aghababa, H.P.: Chaos suppression of uncertain gyros in a given finite time. Chin. Phys. B 21, 110505 (2012)
Aghababa, M.P., Aghababa, H.P.: Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities. J. Vib. Control (2012). doi:10.1177/1077546312463715
Aghababa, M.P., Aghababa, H.P.: Adaptive finite-time synchronization of non-autonomous chaotic systems with uncertainty. J. Comput. Nonlinear Dyn. 8, 031006 (2013)
Aghababa, M.P., Aghababa, H.P.: Chaos suppression of rotational machine systems via finite-time control method. Nonlinear Dyn. 69, 1881–1888 (2012)
Aghababa, M.P., Aghababa, H.P.: Finite-time stabilization of a non-autonomous chaotic rotating mechanical system. J. Franklin Inst. 349, 2875–2888 (2012)
Aghababa, M.P., Aghababa, H.P.: Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties. Nonlinear Dyn. 67, 2689–2701 (2012)
Hamamci, S.E.: Stabilization using fractional-order PI and PID controllers. Nonlinear Dyn. 51, 329–343 (2008)
Lu, J.G.: Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal. Physica A 359, 107–118 (2006)
Aghababa, M.P.: Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov stability theory. J. Comput. Nonlinear Dyn. 7, 021010 (2012)
Aghababa, M.P.: Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Commun. Nonlinear Sci. Numer. Simul. 17, 2670–2681 (2012)
Aghababa, M.P.: Finite-time chaos control and synchronization of fractional-order chaotic (hyperchaotic) systems via fractional nonsingular terminal sliding mode technique. Nonlinear Dyn. 69, 247–261 (2012)
Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)
Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput. Appl. Math. 59, 1810–1821 (2010)
Utkin, V.I.: Sliding Modes in Control Optimization. Springer, Berlin (1992)
Diethelm, K., Ford, N.J., Freed, A.D.: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29, 3–22 (2002)
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Aghababa, M.P. A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems. Nonlinear Dyn 73, 679–688 (2013). https://doi.org/10.1007/s11071-013-0822-y
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DOI: https://doi.org/10.1007/s11071-013-0822-y