A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements

In this paper, the H∞ output-feedback control problem is investigated for a class of two-dimensional (2-D) nonlinear systems with time-varying delays under imperfect measurements. Randomly occurring nonlinearities (RONs) are introduced in the system to account for probabilistic nonlinear disturbances typically caused by networked environments and governed by a sequence of random variables obeying the Bernoulli distribution. The imperfect measurement outputs are subject to both data missing and randomly occurring sensor saturations (ROSSs), which are put forward to characterize the network-induced phenomena such as probabilistic communication failures and limited capacity of the communication devices. The aim of this paper is to design an output-feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H∞ performance index is satisfied. Sufficient conditions are presented by resorting to intensive stochastic analysis and matrix inequality techniques, which not only guarantee the existence of the desired controllers for all possible time-delays, RONs, missing measurements and ROSSs but also lead to the explicit expressions of such controllers. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61174136, 61134009 and 61329301, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the “333 Project” Foundation of Jiangsu Province, the Programme for New Century Excellent Talents in University under Grant NCET-12-0117, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Exponential dichotomy and stability of neutral type equations

AbstractA linear functional differential equation of neutral type with unbounded delay Lx(dds)Dx+Bx=0, where D and B are linear bounded retarded operators with exponentially fading memory, is considered. It is shown that if operator L is interpreted as operator from the space C into the special space C−1 of distributions, then its invertibility is equivalent to the presence of exponential dichotomy of the solutions of this equation. As applications, we prove the theorems on stability and instability in the first approximation for neutral functional differential equations of a general form

Sharp Bounds in Stochastic Network Calculus

The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper it is uncovered that for bursty arrival processes (specifically Markov-Modulated On-Off (MMOO)), whose amenability to \textit{per-flow} analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately indeed be very loose (e.g., by several orders of magnitude off). In response to this uncovered weakness of SNC, the (Standard) per-flow bounds are herein improved by deriving a general sample-path bound, using martingale based techniques, which accommodates FIFO, SP, EDF, and GPS scheduling. The obtained (Martingale) bounds gain an exponential decay factor of ${\mathcal{O}}(e^{-\alpha n})$ in the number of flows $n$. Moreover, numerical comparisons against simulations show that the Martingale bounds are remarkably accurate for FIFO, SP, and EDF scheduling; for GPS scheduling, although the Martingale bounds substantially improve the Standard bounds, they are numerically loose, demanding for improvements in the core SNC analysis of GPS

A Review of Some Subtleties of Practical Relevance

This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The framework prsented in this paper makes it possible to provide simpler formulation and strengthen, generalize, or provide alternative interpretation of the existing results