Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Exponential Cluster Synchronization of Neural Networks with Proportional Delays

Exponential cluster synchronization of neural networks with proportional delays is studied in this paper. Unlike previous constant delay or bounded time delay, we consider the time-varying proportional delay is unbounded, less conservative, and more widely applied. Furthermore, we designed a novel adaptive controller based on Lyapunov function and inequality technique to achieve exponential cluster synchronization for neural networks and by using a unique way of equivalent system we proved the main conclusions. Finally, an example is given to illustrate the effectiveness of our proposed method

A robust packet scheduling algorithm for proportional delay differentiation services

Abstract — Proportional delay differentiation (PDD) model is an important approach for relative differentiated services provisioning on the Internet. It aims to maintain pre-specified packet queueing-delay ratios between different classes of traffic at each hop. Existing PDD packet scheduling algorithms are able to achieve the goal in long time-scales when the system is highly utilized. This paper presents a new PDD scheduling algorithm, called Little’s average delay (LAD), based on a proof of Little’s Law. It monitors the arrival rate and the cumulative delays of the packets from each traffic class, and schedules the packets according to their transient queueing properties so as to achieve the desired class delay ratios in both short and long time-scales. Simulation results show that, in comparison with other PDD scheduling algorithms, LAD can provide no worse level of service quality in long time-scales and more accurate and robust control over the delay ratio in short time-scales. In particular, LAD outperforms its main competitors significantly when the desired delay ratio is large. I