Abstract
This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented.
Highlights
In recent years, fractional calculus has attracted an increasing interest among mathematicians, and among physicists and engineers
This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems
We prove that the proposed sliding manifold is adapted for the fractional systems in the presence of uncertainties and external disturbances
Summary
Fractional calculus has attracted an increasing interest among mathematicians, and among physicists and engineers. The first approach relies on the concept of a fractional integration operator characterized by a continuous frequency distributed model It involves two steps: firstly converting FDEs into exactly equivalent infinite dimensional ODEs, secondly applying the traditional indirect Lyapunov approach. It is potentially a convenient way to propose the stability analysis for nonlinear FDEs. In this paper, our main objective is to propose adaptive sliding control design for a class of commensurate fractionalorder chaotic systems based on the newly discovered property of Caputo operator. Our main objective is to propose adaptive sliding control design for a class of commensurate fractionalorder chaotic systems based on the newly discovered property of Caputo operator For this end, we firstly introduce a fractional integral sliding manifold for these nominal systems.
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