期刊
PRAMANA-JOURNAL OF PHYSICS
卷 90, 期 5, 页码 -出版社
INDIAN ACAD SCIENCES
DOI: 10.1007/s12043-018-1555-8
关键词
Fractional-order financial system; incommensurate fractional-order systems; commensurate fractional-order systems; fractional-order disturbance observer; hybrid projective synchronisation; adaptive sliding mode control
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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