One-step extension approach to optimal Hankel-norm approximationand H∞-optimization problems

A methodology is presented for Hankel approximation and H ^∞-optimization problems that is based on a new formulation of a one-step extension problem which is solved by the Sarason interpolation theorem. The parameterization of all optimal Hankel approximants for multivariable systems is given in terms of the eigenvalue decomposition of an Hermitian matrix composed directly from the coefficients of a given transfer function matrix φ. Rather than starting with the state-space realization of φ, the authors use polynomial coefficients of φ as input data. In terms of these data, a natural basis is given for the finite dimensional Sarason model space and all computations involve only manipulations with finite matrices     

Balanced realization of Pade approximants of e-sT

An algorithm to calculate the balanced realization of all-pass Pade approximants of e^-sT is presented. The algorithm makes use of a regular C-type continued fraction expansion of e^-sT and a properly scaled recurrence formula is used to generate the coefficients of the Pade denominator polynomial. A truncation property of the balanced realization is discussed     

L^{1}-optimal compensators for continuous-time systems

Previous work has been concerned with minimizing thel^{1}-norm of an error pulse response for discrete-time SISO [1] and MIMO [2] systems. In this paper we study the problem of minimizing the L¹-norm of the error impulse response for SISO continuous-time systems. This problem is quite different from the discrete-time problem in that irrational solutions are obtained even when the problem data are rational. Two methods are suggested for the solution of the continuous-time problem; an exact method which leads to a finite-dimensional nonlinear programming problem, and an approximate method which leads to a linear programming problem.     

Methods of solving a polynomial equation for anH∞ optimal control problem for a single-inputsingle-output discrete-time system

A polynomial equation for the H_∞ optimal control problem is reduced to a nonlinear algebraic equation. Two methods are proposed for solving the algebraic equation. One method uses the singularity of a linear algebraic equation as the optimality index. The other gives an approximate solution by solving an eigenvalue problem. A numerical example is presented     

Recovering missing pixels for Landsat ETM + SLC-off imagery using HJ-1A /1B as auxiliary data

To improve the usability of Enhanced Thematic Mapper Plus (ETM+) scan line corrector (SLC)-off data, this article proposes using HJ-1A/1B imagery as auxiliary (i.e. reference) data to recover the SLC-off ETM+ data. The least-median-of-squares (LMedS) method is newly proposed to recover missing pixels of Landsat 7 by removing the variant or abnormal digital number values. In particular, for the visible and near-infrared bands, using HJ-1A/1B for recovery has three clear advantages: the same spatial resolution, similar spectral resolution, and approximate temporal resolution. The experiments show that all of the reference-recovery methods are better than the non-reference-recovery method. The results of using of auxiliary data in reference-recovery methods, from best to worst, are Landsat 8, HJ-1A/1B, and Landsat 7. However, for recovering missing pixels, HJ-1A/1B is superior to the ETM+ auxiliary data due to the shorter time interval in Landsat 7 (a few hours). Hence, HJ-1A/1B should be considered a useful auxiliary data to recover ETM+ SLC-off imagery data.     

H∞ optimal control as a weightedWiener-Hopf problem

It is shown that H_∞ optimization is equivalent to weighted H₂ optimization in the sense that the solution of the latter problem also solves the former. The weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state-space realization. The authors do not suggest transforming H_∞ optimization problems to H₂ optimization problems as a computational approach. Rather, their results reveal an interesting connection between H_∞ and H₂ optimization problems which is expected to offer additional insight. For example, H₂ optimal controllers are known to have an optimal observer-full state feedback structure. The result obtained shows that the minimum entropy solution of H_∞ optimal control problems can be obtained as an H₂ optimal solution. Therefore, it can be expected that the corresponding H_∞ optimal controller has an optimal observer-full state feedback structure     

Minimum ℓ1, ℓ2, and ℓ∞ Norm Approximate Solutions to an Overdetermined System of Linear Equations

Cadzow, J. A., Minimum ℓ₁, ℓ₂, and ℓ_∞ Norm Approximate Solutions to an Overdetermined System of Linear Equations, Digital Signal Processing12 (2002) 524–560Many practical problems encountered in digital signal processing and other quantitative oriented disciplines entail finding a best approximate solution to an overdetermined system of linear equations. Invariably, the least squares error approximate solution (i.e., minimum ℓ₂ norm) is chosen for this task due primarily to the existence of a convenient closed expression for its determination. It should be noted, however, that in many applications a minimum ℓ₁ or ℓ_∞ norm approximate solution is preferable. For example, in cases where the data being analyzed contain a few data outliers a minimum ℓ₁ approximate solution is preferable since it tends to ignore bad data points. In other applications one may wish to determine an approximate solution whose largest error magnitude is the smallest possible (i.e., a minimum ℓ_∞ norm approximate solution). Unfortunately, there do not exist convenient closed form expressions for either the minimum ℓ₁ or the minimum ℓ_∞ norm approximate solution and one must resort to nonlinear programming methods for their determination. Effective algorithms for determining these two solutions are herein presented (see Cadzow, J. A., Data Analysis and Signal Processing: Theory and Applications).     

Characteristic equation and stable states of flipflops

Stable states of flipflops can be determined from algebraic solutions of a characteristic equation. A short discussion of the four CS-flipflops leads to the Earle latch. There are two Earle latch realizations—one is an approximate realization with metastable states and the other is an exact realization with no metastable states. Realization is by delay-free gates and logical delayors. The generality enables application to the ST-flipflops widely used as an element of data shift registers.     

0/1背包问题

本文对“0/1背包问题”采用贪婪算法、动态规划、回溯法、分枝限界四种不同方法进行求解和算法分析,并通过各种算法的实现,研究了0/1背包问题的实质。     

0/1背包问题

本文对“0／1背包问题”采用贪婪算法、动态规划、回溯法、分枝限界四种不同方法进行求解和算法分析．并通过各种算法的实现．研究了0／1背包问题的实质。     

l1 optimal robust controller for SISO plant undercoprime factor perturbations

The problem of synthesis of l₁ optimal robust controller for SISO plant under coprime factor perturbations and bounded external disturbance is considered. A geometric interpretation of l₁ optimal robust controller, standard l₁ optimal controller, and two other optimal robust controllers is presented. The existence of l₁ optimal robust linear controller is proved and an algorithm for approximate solution of the problem is proposed. The algorithm is reduced to approximate solution of finite family of standard l₁ optimization problems     

Novel ammonia-sensing phenomena in sol–gel derived Ba0.5Sr0.5TiO3 thin films

In this paper, ammonia-sensing behavior of barium strontium titanate (BST) thin films have been reported for the first time. Thin films of BST deposited by sol–gel spin coating technique have been found to show an increase in resistance when exposed to ammonia gas. The sensitivity variation was from 20 to 60%, with lowest detection limit of about 160 ppm. The films were prepared with different pre-sintering temperatures and thickness and effect of these parameters on the ammonia-sensing have been studied. The optimum temperature for operation was found to be close to 270 °C. The ammonia-sensing studies were also performed for other gases like ethanol, NO₂ and CO; but the sensitivity in these cases was negligibly smaller than that in case of ammonia.     

Approximate characterisation of nonstationary discrete time G/G/1 systems

Discrete time models are often important in performance analysis, particularly at the microscopic level. This paper presents formulas for the approximate characterisation of nonstationary behaviour in discrete time G/G/1 queues. A pair of recursion formulas gives, approximately, the probability of delay and the mean delay for the n th arrival in such queues.The formulas are simple to program and economical to compute. In some circumstances they give exact, rather than approximate, results. They are particularly useful in studying the response of a system to a sudden overload.     

基于BER的ASN．1编解码原理与设计实现

本文介绍了ASN．1和BER基本编码规则，分析了7号信令协议栈的TCAP层消息结构和ASN．1之间的关系，详细介绍了应用于信令中继系统中的ASN．1编解码模块的设计和实现。     

An approximate transient analysis of the M(t)/M/1 queue

An approach, based on recent work by Stern [56], is described for obtaining the approximate transient behavior of both the M/M/1 and M(t)/M/1 queues, where the notation M(t) indicates an exponential arrival process with time-varying parameter λ(t). The basic technique employs an M/M/1K approximation to the M/M/1 queue to obtain a spectral representation of the time-dependent behavior for which the eigen values and eigenvectors are real.Following a general survey of transient analysis which has already been accomplished, Stern's M/M/1/K approximation technique is examined to determine how best to select a value for K which will yield both accurate and computationally efficient results. It is then shown how the approximation technique can be extended to analyze the M(t)/M/1 queue where we assume that the M(t) arrival process can be approximated by a discretely time-varying Poisson process.An approximate expression for the departure process of the M/M/1 queue is also proposed which implies that, for an M(t)/M/1 queue whose arrival process is discretely time-varying, the departure process can be approximated as discretely time-varying too (albeit with a different time-varying parameter).In all cases, the techniques and approximations are examined by comparison with exact analytic results, simulation or alternative discrete-time approaches.     

基于贪婪策略的0/1背包问题算法研究

对求解0/1背包问题的贪婪策略进行了详细的讨论.在分析价值密度贪婪算法缺陷的基础上,提出了重做贪婪选择的改进算法,并从理论和实验两个方面证明了其求解质量的提高.本文还详细分析了k阶优化算法,并证明了其近似比为k/(k 1),最后编程模拟了该算法的实现过程,并对结果进行了分析.     

On the dual of a mixed H 2/l 1 optimisation problem

The general discrete-time Single-Input Single-Output (SISO) mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.     

Adaptive structuring of binary search trees using conditionalrotations

Consider a set A={A₁,A₂ ,. . ., A_n} of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S=[s₁,s₂ ,. . ., s_N] and are to be arranged lexicographically using a binary search tree (BST). If S is known a priori, it is well known that an optimal BST may be constructed using A and S. The case when S is not known a priori is considered. A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme, the restructuring is performed only if it decreases the weighted path length (WPL) of the overall resultant tree. An optimized version of the latter method, which requires only one extra integer field per record has, is presented. Initial simulation results comparing this algorithm with various other static and dynamic schemes indicates that this scheme asymptotically produces trees which are an order of magnitude closer to the optimal one than those produced by many of the other BST schemes reported in the literature     

A method for calculating successive approximate solutions for a class of block banded M/G/1 type Markovian models

This paper presents an efficient equilibrium solution algorithm for a class of infinite block banded M/G/1 type Markov chains. By re-blocking the states, these are a class of the so-called quasi-birth-and-death (QBD) type chains. The proposed algorithm is not based on an iterative approach, so that the exact solution can be computed in a known finite number of steps. The key point on which the algorithm is based is the identification of a linear dependence among variables. This dependence is expressed in terms of a companion matrix. The equilibrium solution of the Markov chain is obtained operating on this matrix.

An attractive feature of the algorithm is that it allows the computation of a succession of approximate solutions with growing accuracy, until the exact solution is obtained in a finite number of steps. The class of block-banded M/G/1 type Markov chains we consider requires that the lower diagonal block is invertible and that the chain is ergodic. However, many models arising from telecommunication systems satisfy this restriction. Results for a case study show that the proposed algorithm is efficient and quite accurate, even when providing approximate solutions.