A fractional state space realization method with block pulse basis

In this paper, a new analytic method for the fractional state space modeling of non-integer systems is presented. The tool of orthogonal functions and particularly the block pulse basis is used jointly with their generalized operational matrices in order to establish the state space representation which is not always obvious in the fractional framework. The commensurate case which is the simplest one is firstly handled. Then, the same development is generalized to the non-commensurate case defining so a nonlinear criterion to be minimized. Examples and simulations are presented to show the usefulness of the technique.     

Initial conditions and initialization of linear fractional differential equations

Mastery of the initial conditions of fractional order systems remains an open problem, in spite of a great number of contributions. This paper proposes a solution dedicated to linear fractional differential equations (FDEs), which is based on an equivalence principle between the original system and an exactly equivalent infinite dimensional ordinary differential equation (ODE). This equivalence principle is derived from the fractional integration operator concept and the frequency distributed state space model of this operator. Thanks to this principle, the FDE initial conditions problem is converted into a conventional ODE initialization problem, however with an infinite dimensional state vector. Practical FDE initialization is performed using an observer based technique applied to the equivalent ODE; a numerical example demonstrates the efficiency of this approach.     

两类压缩态光场的特性比较

本文指出光场压缩态|α,z〉A=S(z)D(α)|0〉和|α,z〉B=D(α)S(z)|0〉不完全等价,它们实质上是本文命名的压缩子(Squeezon)湮灭算符b=SaS~+的两个本征态,具有完全相同的压缩特性,但本征值不同,光子统计分布和光子统计特性有显著差异,所含的能量状况亦很不相同。     

A novel truncated approximation based algorithm for state estimation of discrete-time Markov jump linear systems

In this paper, state estimation problem for discrete-time Markov jump linear systems is considered. First, three equalities are proposed. Next, they are applied to the state estimation problem of considered systems so that a novel suboptimal algorithm in the sense of minimum mean-square error estimate is obtained where the computation and storage load of the suboptimal algorithm is not ever-increasing with the length of the noise observation sequence. The proposed algorithm and the suboptimal adaptive algorithm proposed in [1] are all based on a truncated approximation strategy. However, compared with the algorithm of [1], the proposed algorithm requires much less approximations. Computer simulations are carried out to evaluate the performance of the proposed algorithm.     

Experimental study of fractional order proportional derivative controller synthesis for fractional order systems

In recent years, studies on real systems have revealed inherent fractional order dynamic behavior, and fractional order systems have attracted more and more attentions. It is intuitively true that these fractional order models require the corresponding fractional order controllers to achieve desired performance. In this paper, an experimental study of the fractional order proportional and derivative (FO-PD) controller systematic design is presented, to validate the control performance for the fractional order systems with generalized fractional capacitor membrane model. The performance of the designed FO-PD controller is compared with both the integer order and fractional order controllers which are designed based on the approximate integer order system. This comparison results are presented both in the simulation and the hardware-in-the-loop experiment.     

Steady state and transient state behaviours analyses of TCP connections considering interactions between TCP connections and network

The Internet uses a window‐based congestion control mechanism in transmission control protocol (TCP). In the literature, there have been a great number of analytical studies on TCP. Most of those studies have focused on the statistical behaviour of TCP by assuming a constant packet loss probability in the network. However, the packet loss probability, in reality, changes according to the packet transmission rates from TCP connections. Conversely, the window size of a TCP connection is dependent on the packet loss probability in the network. In this paper, we explicitly model the interaction between the congestion control mechanism of TCP and the network as a feedback system. By using this model, we analyse the steady state and the transient state behaviours of TCP. We derive the throughput and the packet loss probability of TCP, and the number of packets queued in the bottleneck router. We then analyse the transient state behaviour using a control theoretic approach, showing the influence of the number of TCP connections and the propagation delay on the transient state behaviour of TCP. Copyright © 2005 John Wiley & Sons, Ltd.