697 research outputs found
Synchronization of Fractional-order Chaotic Systems with Gaussian fluctuation by Sliding Mode Control
This paper is devoted to the problem of synchronization between
fractional-order chaotic systems with Gaussian fluctuation by the method of
fractional-order sliding mode control. A fractional integral (FI) sliding
surface is proposed for synchronizing the uncertain fractional-order system,
and then the sliding mode control technique is carried out to realize the
synchronization of the given systems. One theorem about sliding mode controller
is presented to prove the proposed controller can make the system synchronize.
As a case study, the presented method is applied to the fractional-order
Chen-L\"u system as the drive-response dynamical system. Simulation results
show a good performance of the proposed control approach in synchronizing the
chaotic systems in presence of Gaussian noise
Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems
This paper deals with the problem of pseudo-state sliding mode
control of fractional SISO nonlinear systems with model inaccuracies. Firstly,
a stable fractional sliding mode surface is constructed based on the Routh-Hurwitz conditions for fractional differential equations. Secondly, a sliding
mode control law is designed using the theory of Mittag-Leffler stability. Further,
we utilize the control methodology to synchronize two fractional chaotic
systems, which serves as an example of verifying the viability and effectiveness
of the proposed technique
Robust synchronization of fractional-order unified chaotic systems via linear control
AbstractA new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme
Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems
Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods
Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control
In this paper, we consider controlling a class of single-input-single-output
(SISO) commensurate fractional-order nonlinear systems with parametric
uncertainty and external disturbance. Based on backstepping approach, an
adaptive controller is proposed with adaptive laws that are used to estimate
the unknown system parameters and the bound of unknown disturbance. Instead of
using discontinuous functions such as the function, an
auxiliary function is employed to obtain a smooth control input that is still
able to achieve perfect tracking in the presence of bounded disturbances.
Indeed, global boundedness of all closed-loop signals and asymptotic perfect
tracking of fractional-order system output to a given reference trajectory are
proved by using fractional directed Lyapunov method. To verify the
effectiveness of the proposed control method, simulation examples are
presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics:
Systems with Minor Revision
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