Complex Dynamical Network Control for Trajectory Tracking Using Delayed Recurrent Neural Networks

Abstract

In this paper, the problem of trajectory tracking is studied. Based on the V-stability and Lyapunov theory, a control law that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a complex dynamical network is obtained. To illustrate the analytic results, we present a tracking simulation of a dynamical network with each node being just one Lorenz’s dynamical system and three identical Chen’s dynamical systems.

FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

“…is is essential for the design of a globally and asymptotically stabilizing control law for time-delay systems [20]. In this work, the following Lyapunov-Krasovskii functional is proposed as in [19,32]:…”

“…In [18], the pinning synchronization in an array of coupled delayed neural networks with both constant and delayed couplings is presented, showing that the network can be pinned to a homogenous state by applying adaptive feedback control. It is worth noting that the Lyapunov-Krasovskii approach has been demonstrated to be an efficient method to deal with the global asymptotic stability of a recurrent neural network with time delay [19,20]. In [21], the stability of linear continuous-time systems with time delay by employing new Lyapunov-Krasovskii functionals is presented.…”

Fractional Complex Dynamical Systems for Trajectory Tracking using Fractional Neural Network

“…, N . Therefore, the tracking problem can be restated as a global asymptotic stabilization problem for the system (10).…”

“…Its behavior can be difficult to control and the dynamics of its nodes require a precise analysis, see for example [4]. In the classical case, one can track the nodes of the network by using Lyapunov theory and neural networks as in [10].…”

Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control

“…Controlling and synchronizing chaotic dynamical systems has recently attracted a great deal of attention within the engineering society, in which different techniques have been proposed. For instance, linear state space feedback, Lyapunov-Krasovskii function methods [1], adaptive control [2]. Using the inverse optimal control approach, a control law [3], which allows reproducing chaos on a Dynamical Neural Network, was discussed in [4].…”