Estimation of communication-delays through adaptive synchronization of chaos

This paper deals with adaptive synchronization of chaos in the presence of time-varying communication-delays. We consider two bidirectionally coupled systems that seek to synchronize through a signal that each system sends to the other one and is transmitted with an unknown time-varying delay. We show that an appropriate adaptive strategy can be devised that is successful in dynamically identifying the time-varying delay and in synchronizing the two systems. The performance of our strategy with respect to the choice of the initial conditions and the presence of noise in the communication channels is tested by using numerical simulations. Another advantage of our approach is that in addition to estimating the communication-delay, the adaptive strategy could be used to simultaneously identify other parameters, such as e.g., the unknown time-varying amplitude of the received signal.Comment: Accepted for publication in Chaos, Solitons & Fractal

Dynamic Server Allocation over Time Varying Channels with Switchover Delay

We consider a dynamic server allocation problem over parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot the server decides either to stay with the current queue or switch to another queue based on the current connectivity and the queue length information. Switchover delay occurs in many telecommunications applications and is a new modeling component of this problem that has not been previously addressed. We show that the simultaneous presence of randomly varying connectivity and switchover delay changes the system stability region and the structure of optimal policies. In the first part of the paper, we consider a system of two parallel queues, and develop a novel approach to explicitly characterize the stability region of the system using state-action frequencies which are stationary solutions to a Markov Decision Process (MDP) formulation. We then develop a frame-based dynamic control (FBDC) policy, based on the state-action frequencies, and show that it is throughput-optimal asymptotically in the frame length. The FBDC policy is applicable to a broad class of network control systems and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple Myopic policies that provably achieve more than 90% of the stability region. In the second part of the paper, we extend our results to systems with an arbitrary but finite number of queues.Comment: 38 Pages, 18 figures. arXiv admin note: substantial text overlap with arXiv:1008.234

Impact of time-variant turbulence behavior on prediction for adaptive optics systems

For high contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to measure the incoming disturbance and then apply the correction. By predicting the behavior of the atmospheric disturbance over the time delay we can in principle achieve a better AO performance. Atmospheric turbulence parameters which determine the wavefront phase fluctuations have time-varying behavior. We present a stochastic model for wind speed and model time-variant atmospheric turbulence effects using varying wind speed. We test a low-order, data-driven predictor, the linear minimum mean square error predictor, for a near-infrared AO system under varying conditions. Our results show varying wind can have a significant impact on the performance of wavefront prediction, preventing it from reaching optimal performance. The impact depends on the strength of the wind fluctuations with the greatest loss in expected performance being for high wind speeds.Comment: 10 pages, 8 figures; Accepted to JOSA A March 201

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grants BB/C506264/1 and 100/EGM17735, an International Joint Project sponsored by the Royal Society of the U.K., the Research Grants Council of Hong Kong under Grant HKU 7031/06P, the National Natural Science Foundation of China under Grant 60804028, and the Alexander von Humboldt Foundation of Germany

Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying