Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.

Special issue on system identification and estimation

It is our great pleasure and honor to organize this special issue“System Identification and Estimation”.System identification has been a surprisingly lively and resilient area of research in the control community for many years.It grew out of statisticians’interest in time series analysis beginning in the 1940s and became a“regular control topic”in the 1960s,as indicated by thefirst IFAC Symposium on System Identification held in Prague,Czech Republic,in 1967.Sixty years later,it is still an important area of research in thefield of control.It is relevant to ask why the interest in system identification has remained so intense.One answer might be that more and more applications in engineering require mathematical models and the combined use of system identification and physical modeling is the basic way to obtain reliable models.This special issue is focusing on the latest development,trends,and novel methods for system identification and estimation and these contributions will give interesting and inspiring insights into the current status of the area.

SIGNAL ESTIMATION WITH BINARY-VALUED SENSORS

This paper introduces several algorithms for signal estimation using binary-valued outputsensing.The main idea is derived from the empirical measure approach for quantized identification,which has been shown to be convergent and asymptotically efficient when the unknown parametersare constants.Signal estimation under binary-valued observations must take into consideration oftime varying variables.Typical empirical measure based algorithms are modified with exponentialweighting and threshold adaptation to accommodate time-varying natures of the signals.Without anyinformation on signal generators,the authors establish estimation algorithms,interaction between noisereduction by averaging and signal tracking,convergence rates,and asymptotic efficiency.A thresholdadaptation algorithm is introduced.Its convergence and convergence rates are analyzed by using theODE method for stochastic approximation problems.

Multipliers on weighted Hardy spaces over locally compact Vilenkin groups

A weighted Hpω(G) multiplier theorem on the multiplier operator T associated with a function m∈ L∞ (Γ) is shown and the atomic decomposition of functions fin Hp*(G) is obtained, where G is a Vilenkin group, r its dual, 0 【 p≤1 and ω is a weight on G which is more general than that proposed by C. W. Onneweer et al.

Variable selection in identification of a high dimensional nonlinear non-parametric system

The problem of variable selection in system identification of a high dimensional nonlinear non-parametric system is described. The inherent difficulty, the curse of dimensionality, is introduced. Then its connections to various topics and research areas are briefly discussed, including order determination, pattern recognition, data mining, machine learning, statistical regression and manifold embedding. Finally, some results of variable selection in system identification in the recent literature are presented.