Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control

Abstract

This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the same time, the structures of a sliding mode surface and a sliding mode controller are also constructed. A sufficient criterion is presented to ensure the robust synchronization of FOCS according to the stability theory of the fractional calculus and sliding mode control technique. In addition, the result can be applied to identical or non-identical chaotic systems with fractional-order. In the end, we build two practical examples to illustrate the feasibility of our theoretical results.

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

“…In recent times, differential equation and fractional differential equation models have found their applications in a variety of fields including biology [1][2][3][4][5][6], physics [7][8][9][10], engineering [11][12][13][14], mathematics [15][16][17][18], information technology, and so on [19][20][21][22][23][24][25][26][27]. They are also one of the most rudimentary tools for neural networks.…”

Adaptive Output Synchronization of General Complex Dynamical Network with Time-Varying Delays

“…Ever since small-world and scale-free features were discovered in many real-world networks (see [1,2] and the references therein) synchronization in complex dynamical network has attracted much attention for its potential application in [3][4][5][6][7][8][9][10][11][12][13]. It is motivated by a broad area of potential applications: Networks of robots, formations of flying and underwater vehicles, control of industrial, electrical, communication, and production networks, etc.…”

“…It is well known that under some extremely strict conditions, complex dynamical network models can achieve synchronization, especially for chaotic synchronization. In the past decades, many control methods have been proposed for chaotic synchronization, see [11,18,19] and the references therein. Min et al [18] studied the synchronization of three different chaotic systems by using the theory of discontinuous dynamical systems.…”

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

“…[1][2][3][4] However, it has a thousand years of history, as a branch of research about the human brain, because human brain contains a billion numbers of neurons and each neuron contains more than two thousand synapsis. Nowadays, the dynamics of neural networks have been widespread applications from diverse and numerous fields of automatic control, 5 combinatorial optimization, 6 image and signal processing, 7 and so on. Cohen-Grossberg, 8 Hopfield, 9 and Tank and Hopfield 10 demonstrated recurrently connected neural networks, which are allowed to optimize problem solving technique, and they play a key role in hardware implementations of dynamic neural networks.…”