Multiscale Q-learning with linear function approximation

We present in this article a two-timescale variant of Q-learning with linear function approximation. Both Q-values and policies are assumed to be parameterized with the policy parameter updated on a faster timescale as compared to the Q-value parameter. This timescale separation is seen to result in significantly improved numerical performance of the proposed algorithm over Q-learning. We show that the proposed algorithm converges almost surely to a closed connected internally chain transitive invariant set of an associated differential inclusion.     

On approximation of infinite-dimensional quantum channels

We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the χ-capacity as a function of a channel, strong additivity of the χ-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.     

On the Hankel-norm approximation of linear stochastic systems

We derive ordering and interlocking properties for the singular values of the block-Hankel matrices corresponding to different spectral factors of a given spectral density matrix. The results are then applied to Hankel-norm approximation of SISO stochastic systems. In particular we show that the minimum phase model may be approximated in Hankel norm by systems of a certain prescribed dimension with better accuracy than any other model with the same output process. We also provide upper bounds on the gain in accuracy obtained by choosing the minimum phase model over some other model.     

基于修正函数线性拟合的Turbo码译码算法

新一代移动通信系统LTE/LTE-A具有高吞吐率的突出特点和需求,但高速译码也对误码率和延时等提出了更高的要求。现有的Turbo码译码算法中,Log-MAP算法译码性能较好,但算法复杂度高,时延大;而Max-Log-MAP算法虽然具有较低的复杂度,但译码性能较差。为此,提出一种基于修正函数线性拟合的Turbo译码算法,该算法针对不同刻度区间采用不同的拟合参数。实验仿真表明,该算法与现有算法比较,能够达到Log-MAP算法的译码性能,且避免了Log-MAP的大量运算,从而在保证较好译码性能的基础上,有效地降低了译码延时,并且便于硬件实现。     

改进的超越函数分段线性逼近方法

针对超越函数计算中所采用的分段线性逼近算法存在的无法提前确定精度及部分区间资源浪费的问题,提出一种改进的分段线性逼近超越函数算法。该算法由预定义的逼近区间端点计算出用于逼近的线性函数,根据被逼近函数的凹凸性对所计算线性函数进行调整,在此基础上计算出预定义逼近区间内调整后函数与被逼近函数之间的最大误差;按照所需精度的要求,自动调整逼近区间,通过该过程的迭代,获得了较少分段次数。算法结果在Matlab上进行仿真,仿真结果表明,所提算法的分段数相比等分法减少了60%。所提算法在保证精度的前提下,降低了查找表（LUT）的资源消耗。     

On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems

This paper focuses on 'mixed' delay-independent/delay-dependent asymptotic stability problems of a class of linear systems described by delay-differential equations involving several constant but unknown delays. We give some sufficient conditions for characterizing unbounded stability regions in the delays parameter space. The proposed approach makes use of some appropriate Liapunov-Krasovskii functionals, and the results obtained are expressed in terms of matrix inequalities. We also discuss several ways to construct such analytic functionals. These results allow us to recover (or to improve) as limit cases previous delay-independent or/and delay-dependent conditions from the control literature.     

A tree-structured adaptive network for function approximation inhigh-dimensional spaces

Nonlinear function approximation is often solved by finding a set of coefficients for a finite number of fixed nonlinear basis functions. However, if the input data are drawn from a high-dimensional space, the number of required basis functions grows exponentially with dimension, leading many to suggest the use of adaptive nonlinear basis functions whose parameters can be determined by iterative methods. The author proposes a technique based on the idea that for most of the data, only a few dimensions of the input may be necessary to compute the desired output function. Additional input dimensions are incorporated only where needed. The learning procedure grows a tree whose structure depends upon the input data and the function to be approximated. This technique has a fast learning algorithm with no local minima once the network shape is fixed, and it can be used to reduce the number of required measurements in situations where there is a cost associated with sensing. Three examples are given: controlling the dynamics of a simulated planar two-joint robot arm, predicting the dynamics of the chaotic Mackey-Glass equation, and predicting pixel values in real images from pixel values above and to the left.     

On linear system reduction by impulse energy approximation

Linear system reduction by impulse response energy approximation is analyzed and limitations are discussed. To show that in general the claims made for the procedure are not true, a numerical example is included.     

On the quasi-balanceable class of linear quantum stochastic systems

This paper is concerned with the characterization of the quasi-balanceable class of linear quantum stochastic systems (i.e., systems that can be approximated via the recently proposed quasi-balanced truncation method). It has previously been shown that the quasi-balanceable class of systems includes the class of completely passive systems. In this work, we refine the previously established characterization of quasi-balanceable systems and show that the class of quasi-balanceable systems is strictly larger than the class of completely passive systems. We derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Exploiting this result, we prove that all linear quantum stochastic systems with a pure Gaussian steady state (active systems included) are all quasi-balanceable, and establish a new complete parameterization for this important class of systems. Examples are provided to illustrate our results.     

基于分支函数线性逼近的测试数据自动生成算法

软件测试是保证软件可靠性的一个重要手段.面向路径测试是软件测试中一种重要方法.提出了一种分支函数线性逼近的测试数据自动生成算法.结合赵瑞莲给出的谓词切片算法和程序DUC表达方式以及本文提出的算法,给出了一个基于程序执行的路径测试及测试数据自动生成新算法.由于算法采用DUC表达式,不仅可以从源端判断子路径是否可行,而且有效地降低了不可行路径对算法性能的影响.另外,与现有文献中单纯利用分支函数极小化方法的算法相比,新算法由于有机结合了分支函数线性逼近和极小化方法的长处,因此减少了测试用例的数量,提高了测试效率.     

具有广义线性隶属函数的典型模糊系统的通用逼近性*

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数,推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构,证明了典型模糊系统是单调、递减的有界连续函数;在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数,最后仿真实例证明了本设计的有效性。     

On null controllability of linear systems in Banach spaces

Our aim here is to give characterizations for the null controllability of linear systems in general Banach spaces. The starting point of this paper is the work of Pengnian Chen and Huashu Qin (Systems Control Lett. 45 (2002) 155), which solves the problem of exact controllability. In fact, the results of (Systems Control Lett. 45 (2002) 155) say that, in case of setting in general Banach spaces, there are the same characterizations of exact controllability as in the case of reflexive Banach spaces. An open problem raised in (Systems Control Lett. 45 (2002) 155) is the validity of a similar result for null controllability. We give here a positive answer to this problem. However, it seems to us that the technique of (Systems Control Lett. 45 (2002) 155) does not work for null controllability, and, consequently, our approach is completely different.     

Low frequency approximation for a class of linear quantum systems using cascade cavity realization

This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. This approximation method builds on a previous result for cascade realization and gives good approximations at low frequencies.     

Pawlak近似空间中软集的软上（下）近似

在Pawlak近似空间上首次引入了等效软集的软上下近似的概念,研究了软上下近似的交、并、补代数运算的若干性质。结果令人满意。     

Some theorems on linear positive operators and functionals and their applications

In this paper, we prove two theorems concerning linear positive operators and functionals in a very general sense. We show how these results can be used to derive new results in a wide range of applications from approximation theory, to the numerical treatment of differential equations and to the numerical analysis connected with signals and images.     

基于FPGA的电子鼻中Sigmoid函数分区间线性逼近实现

对表驱动线性逼近方法实现的sigmoid函数进行分析,在Matlab中对其仿真,得到误差曲线。该误差曲线在不同区间内误差相差较大,由此提出分区间线性逼近法实现sigmoid函数。不同区间采用不同的插值间隔,以尽量减少ROM资源的使用。经Matlab仿真,得到改进后的误差曲线,其最大误差未增大。最后在Quartus II中建立工程,调用Modlesim进行RTL仿真,证明该方法可行。     

On the approximation rate of hierarchical mixtures-of-experts for generalized linear models.

We investigate a class of hierarchical mixtures-of-experts (HME) models where generalized linear models with nonlinear mean functions of the form psi (alpha + xT beta) are mixed. Here psi (.) is the inverse link function. It is shown that mixtures of such mean functions can approximate a class of smooth functions of the form psi (h(x)), where h(.) epsilon W2;K infinity (a Sobolev class over [0, 1]s), as the number of experts m in the network increases. An upper bound of the approximation rate is given as O(m-2/s) in Lp norm. This rate can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor x.     

On optimal approximation of high-order linear systems by low-order models

An engineering solution to the problem of approximating a high-order linear system by a low-order model is suggested, which consists in formulating a quadratic error functional as a basic tool for the construction of a physically transparent and practically meaningful approximation criterion. For various different modes of operation analytical expressions for the evaluation of the functional as well as the gradients with respect to the unknown model parameters are given, which allows known gradient techniques to be applied for finding the optimal model parameters. In addition a representation for a general multivariate model, using only the minimal number of unknown parameters, is given.     

On the order reduction of linear function observers

This note analyzes a new algorithm presented in [1] for designing a linear function observer with a minimum number of arbitrary poles. It shows that the maximum order of the observer of [1] isnu + ... + nu_{p} - pforp leq qandn - qforp geq q, instead ofp(nu_{1} - 1)as suggested in [1], wherenu{i}, i = 1top, are the descending ordered observability indexes of system (A, C) andn,p, andqare the order of the system, the number of the functions, and the number of the system outputs, respectively. This note also shows the significance of this result. For presentational purposes, only a special case of [1] is considered here. However, the technical properties as proved in this note are general.