Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

The main objective of this paper is to simplify the implementation of continuous and discontinuous 3-D space vector pulsewidth modulations (SVPWMs). This paper analyzes the relationships, whether in or coordinates, between three-phase voltages and the following elements: the tetrahedron in which the reference vector resides, three adjacent active switching vectors (or three switching states), and their duration times. Based on the analysis, the calculation of the turn-on time of each switch in the actual implementation is simplified, and discontinuous PWM (DPWM) methods in three-leg inverters can be extended to four-leg inverters without the phase angle. In addition, two more DPWM methods that are peculiar to 3-D SVPWM are presented. This simplified algorithm does not use irrational operations or look-up tables, and it alleviates the computation burden of the processor. The simulation and experimental results are provided to validate the effectiveness of the proposed algorithm.

Analysis and Simplification of Three-Dimensional Space Vector PWM for Three-Phase Four-Leg Inverters

In the fractional calculus, one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory. Fractional Logistic map and fractional Lorenz maps of Riemann–Liouville type are proposed in this paper. The general chaotic behaviors are investigated in comparison with the Caputo one. Chaos synchronization is designed according to the stability results. The numerical results show the method’s effectiveness and fractional chaotic map’s potential role for secure communication.

Chaos synchronization of fractional chaotic maps based on the stability condition

Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller

This paper investigates the chaos control of a class of fractional-order chaotic systems via sliding mode. First, the sliding mode control law is derived to make the states of the fractional-order chaotic systems asymptotically stable. Second, the designed control scheme guarantees asymptotical stability of the uncertain fractional-order chaotic systems in the presence of an external disturbance. Finally, simulation results are given to demonstrate the effectiveness of the proposed sliding mode control method.

Control of a class of fractional-order chaotic systems via sliding mode

Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks

This paper brings attention to the chaotic antisynchronization and synchronization for a novel class of chaotic systems with different structure and dimensions by using a new sliding mode control strategy. This approach needs only n−1 controllers, where n is the number of the salve system dimensions. And our method uses proportional integral (PI) surface and saturation function to simplify the task of assigning the performance of the closed-loop error system in sliding motion. Furthermore, the sufficient conditions are derived, and representative examples are proposed as well. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the proposed control scheme, which are in agreement with theoretical analysis.

Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme

This paper proposes a novel distributed multi-agent finite-time control strategy with time delays for the state of charge balancing and voltage restoration in a dc microgrid with distributed battery energy storage systems. The delays can be different and theoretically unbounded for each battery system. Feedback linearization method is applied to convert the state of charge balancing and voltage restoration problems to double-integrator and single-integrator systems with input time delays, respectively. Then, the Artstein transformation is applied to reduce the time delayed systems to delay-free systems. Based on the reduced models, the finite-time control is modified to achieve the state of charge balancing and voltage restoration. Only the state of charge and its derivative and voltage information are required to be transmitted over a sparse communication network to generate the control signals. The finite-time Lyapunov method ensures accurate convergence and finite-time stability. The proposed secondary control strategy can be integrated with conventional primary droop control. The proposed control strategy is resilient to communication link failures and features plug-and-play capability. The performance is verified with an RTDS Technologies real-time digital simulator, using switching converter models and nonlinear lead-acid battery models.

Distributed Finite-Time Multiagent Control for DC Microgrids With Time Delays

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.

Runfan Zhang

Papers

Control of a class of fractional-order chaotic systems via sliding mode

Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks

Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme

Distributed Finite-Time Multiagent Control for DC Microgrids With Time Delays

Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control.