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Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems

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Abstract

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi , 110 025, India

    Ayub Khan & Arti Tyagi

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  1. Ayub Khan
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  2. Arti Tyagi
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Correspondence to Arti Tyagi.

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Khan, A., Tyagi, A. Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems. Pramana - J Phys 90, 67 (2018). https://doi.org/10.1007/s12043-018-1555-8

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  • DOI: https://doi.org/10.1007/s12043-018-1555-8

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