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

A note on the multi-stage spectral relaxation method for chaos control and synchronization

In this study, we present and apply a new, accurate and easy to implement numerical method to realize and verify the synchronization between two identical chaotic Lorenz, Genesio-Tesi, Rössler, Chen and Rikitake systems. The proposed method is called the multi-stage spectral relaxation method (MSRM). We utilize the active control technique for the synchronization of these systems. To illustrate the effectiveness of the method, simulation results are presented and compared with results obtained using the Runge-Kutta (4, 5) based MATLAB solver, ode45

Synchronization of two fractional-order chaotic systems via nonsingular terminal Fuzzy Sliding Mode Control

La sincronización de dos sistemas caóticos complejos de orden fraccional se discute en este documento. El parámetro incertidumbre y la perturbación externa se incluyen en el modelo del sistema, y la sincronización de los sistemas considerados caóticos se implementa en base al concepto de tiempo finito. Primero, se propone una nueva superficie deslizante terminal no singular de orden fraccional que es adecuada para los sistemas de orden fraccional considerados. Se ha demostrado que una vez que las trayectorias del estado del sistema alcancen la superficie de deslizamiento propuesta, convergerán al origen dentro de un tiempo finito dado. En segundo lugar, en términos de la superficie deslizante terminal no singular establecida, que combina el control difuso y los esquemas de control de modo deslizante, se introduce una ley de control de modo deslizante difusa única novedosa y robusta que puede forzar las trayectorias del sistema de error dinámico de circuito cerrado para alcanzar el deslizamiento superficie durante un tiempo finito. Finalmente, utilizando el teorema de estabilidad fraccional de Lyapunov, se demuestra la estabilidad del método propuesto. El método propuesto se implementa para la sincronización de dos sistemas caóticos Genesio-Tesi de orden fraccional con parámetros inciertos y perturbaciones externas para verificar la efectividad del controlador de modo de deslizamiento difuso terminal no-singular de orden fraccional propuesto.The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.• National Natural Science Foundation of China. Becas U1604146, U1404610, 61473115, 61203047 • Science and Technology Research Project in Henan Province. 152102210273, 162102410024 • Foundation for the University Technological Innovative Talents of Henan Province. Beca 18HASTIT019peerReviewe

Adaptive Hybrid Projective Synchronization Of Hyper-chaotic Systems

In this paper, we design a procedure to investigate the hybrid projective synchronization (HPS) technique among two identical hyper-chaotic systems. An adaptive control method (ACM) is pro- posed which is based on Lyapunov stability theory (LST). The considered technique globally determines the asymptotical stability and establishes identification of parameter simultaneously via HPS approach. Additionally, numerical simulations are carried out for visualizing the effectiveness and feasibility of discussed scheme by using MATLAB

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance

The multistage homotopy perturbation method for solving chaotic and hyperchaotic Lu system

The multistage homotopy-perturbation method (MHPM) is applied to the nonlinear chaotic and hyperchaotic Lü systems. MHPM is a technique adapted from the standard homotopy-perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the technique applied in this work, the results are compared with a fourth-order Runge-Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems