Rational ℒ1 suboptimal compensators forcontinuous-time systems

The persistent disturbance rejection problem (ℒ¹ optimal control) for continuous time-systems leads to nonrational compensators, even for single input/single output systems. As noted in Dahleh and Pearson (1987), the difficulty of physically implementing these controllers suggests that the most significant application of the continuous time ℒ¹ theory is to furnish achievable performance bounds for rational controllers. In this paper the authors use the theory of positively invariant sets to provide a design procedure, based upon the use of the discrete Euler approximating system, for suboptimal rational ℒ¹ controllers with a guaranteed cost. The main results of the paper show that (i) the ℒ ¹ norm of a continuous-time system is bounded above by the l ¹ norm of an auxiliary discrete-time system obtained by using the transformation z=1+rs and (ii) the proposed rational compensators yield ℒ¹ cost arbitrarily close to the optimum, even in cases where the design procedure proposed in the above mentioned paper fails due to the existence of plant zeros on the stability boundary     

Rejection of persistent ℒ∞-boundeddisturbances for nonlinear systems

A nonlinear ℒ¹-control problem, which deals with the rejection of persistent bounded disturbances for nonlinear systems, is investigated. The concept of invariance plays an important role in the ℒ¹-performance analysis and synthesis. The main idea is to construct an invariant subset in the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to the subset. The relation between the ℒ¹-control of a continuous-time system and the l¹ -control of its Euler approximated discrete-time system is established     

On the type of a polynomial f, when f(0)f−f(0)f is a monomial

A polynomial is said to be of type (p₁, p₂, p₃) relative to a directed line in the complex plane if, counting multiplicities, it has p₁ zeros to the left of, p₂ zeros on, and p₃ zeros to the right of the line. In this paper we determine explicitly the types of all polynomials belonging to a very restricted (but infinite) family of polynomials. A polynomial ƒ belongs to this family if and only if its coefficients are such that the polynomial ƒ^*(0)ƒ(z)−ƒ(0) ƒ^*(z) is a monomial; here ƒ^* denotes the reflection of ƒ in the directed line.

A special case of the present result appeared in an earlier publication.     

C6H6和SO3相互作用的理论研究（英文）

采用B3LYP和MP2方法在6-31G*、6-31+G*和6-311+G**基组下对C6H6…SO3复合物体系的4种可能结构进行自由优化,得3种。在考虑基组重叠误差校正基础上,得结合能,并用自然键轨道分析方法讨论其相互作用。结果表明,用B3LYP/6-31G*计算3种复合物的结合能分别为-17.75, -18.33, -18.80 kJ/mol,且C6H6和SO3结合时电子从苯环向SO3转移,形成电荷转移复合物,它们之间的作用包含π-p作用方式。     

Spatially referenced methods of processing raster and vector data

The authors consider a general method of constructing addressing and arithmetic systems for two-dimensional image data using the hierarchy of ‘molecular’ tilings based on an original isohedral ‘atomic’ tiling. (Each molecular title at level k is formed from a constant number of tiles at level k−1; this is termed the ‘aperture’ property of the hierarchy.) In addition they present 11 objective criteria (which are of significance in cartographic image processing), by which these hierarchies and tilings may be described and compared.

Of the 11 topologically distinct types of isohedral tiling, three ([3⁶], [4⁴] and [6³]) are composed of regular polygons, and two of these ([3⁶] and[4⁴]) satisfy the condition that all tiles have the same ‘orientation’. In general, although each level in a hierarchy is topologically equivalent, the tiles may differ in shape at different levels and only [6³], [4⁴], [4.8²] and [4.6.12] are capable of giving rise to hierarchies in which the tiles at all levels are the same shape. The possible apertures of hierarchies obeying this condition are n² (for any n > 1)in the cases of [6³] and [4⁴]; n² or 2n² in the case of [4.8²]; and n² or 3n² in the case of [4.6.12].

In contrast the only tiling exhibiting the uniform ‘adjacency’ criterion is[3⁶]. However, hierarchies based on this atomic tiling generate molecular tiles with different shapes at every level. If these disadvantages are accepted, hierarchies based on first-level molecular tiles referred to as the 4-shape, 4′-shape, 7-shape and 9-shape are generated. Of these the 4-shape and the 9-shape appear to satisfy many of the cartographically desirable properties in addition to having an atomic tiling which exhibits uniform adjacency.

In recent years the generalized balanced ternary addressing system has been developed to exploit the image processing power of the 7-shape. The authors have generalized and extended this system as ‘tesseral addressing and arithmetic’, showing how it can be used to render a 4-shape into a spatially correct linear quadtree.     

Rational suboptimal continuous-time controller design

We obtain rational suboptimal continuous-time solutions to some optimal control problems specified via time domain performance criteria. These include ℒ₁ and ℒ_∞ norms and peak overshoot. The approach uses linear semi-infinite programming to compute weights for a given finite set of rational basis functions and makes the best possible use of the basis. The closed-loop transfer functions obtained satisfy appropriate interpolation constraints for internal stability and the formulation allows additional linear constraints to be incorporated     

Analysis of Parallel Algorithms for Matrix Chain Product and Matrix Powers on Distributed Memory Systems

Given N matrices A₁, A_2,...,A_N of size NtimesN, the matrix chain product problem is to compute A₁timesA₂times...timesA_N. Given an NtimesN matrix A, the matrix powers problem is to calculate the first N powers of A, that is, A, A², A³,..., A^N. We solve the two problems on distributed memory systems (DMSs) with p processors that can support one-to-one communications in T(p) time. Assume that the fastest sequential matrix multiplication algorithm has time complexity O(N^alpha), where the currently best value of a is less than 2.3755. Let p be arbitrarily chosen in the range 1lesplesN^alpha+1/(log N)². We show that the two problems can be solved by a DMS with p processors in T_chain(N,p)=O((N^alpha+1/p)+T(p))((N^2(2+1/alpha/p^2/alpha)(log+p/N)^1-2/alpha+log+((p log N)/N^alpha)) and T_power (N,p)=O(N^alpha+1/p+T(p)((N^2(1+1/alpha)/p^2/alpha)(log+p/2 log N)^1-2/alpha+(log N)²))) times, respectively, where the function log+ is defined as follows: log+ x=log x if xges1 and log+ x=1 if 0相似文献   

Embedding of complete binary trees into meshes with row-columnrouting

This paper considers the problem of embedding complete binary trees into meshes using the row-column routing and obtained the following results: a complete binary tree with 2^p-1 nodes can be embedded (1) with link congestion one into a ⁹/₈√(2^p)×⁹/ ₈√(2^p) mesh when p is even and a √( ⁹/₈2^p)×√(⁹/ ₈2^p) mesh when p is odd, and (2) with link congestion two into a √(2^p)×√(2^p) mesh when p is even, and a √(2^p-1)×√(2^p-1) mesh when p is odd     

Weighted estimation and tracking for branching processes withimmigration

For branching processes with immigration, we propose an approach which allows us to consistently estimate the means m, λ, and the variances σ², b² of the offspring and immigration distributions, respectively. Generally, statistical results for branching processes are established under the well-known trichotomy m<1, m=1, and m>1. For example, no parameters of the immigration distribution can be consistently estimated if m>1. The purpose of the paper is to obtain, through the introduction of a suitable adaptive control, strongly consistent estimators for all the parameters m, λ, σ², and b² without any restriction on the range of m. Central limit theorems and laws of iterated logarithm are also provided     

An efficient parallel recognition algorithm forbipartite-permutation graphs

We present a parallel recognition algorithm for bipartite-permutation graphs. The algorithm can be executed in O(log n) time on the CRCW PRAM if O(n³/log n) processors are used, or O(log² n) time on the CREW PRAM if O(n³/log² n) processors are used. Chen and Yesha (1993) have presented another CRCW PRAM algorithm that takes O(log²n) time if O(n ³) processors are used. Compared with Chen and Yesha's algorithm, our algorithm requires either less time and fewer processors on the same machine model, or fewer processors on a weaker machine model. Our algorithm can also be applied to determine if two bipartite-permutation graphs are isomorphic     

Java heap protection for debugging native methods

Java virtual machine (JVM) crashes are often due to an invalid memory reference to the JVM heap. Before the bug that caused the invalid reference can be fixed, its location must be identified. It can be in either the JVM implementation or the native library written in C invoked from Java applications. To help system engineers identify the location, we implemented a feature using page protection that prevents threads executing native methods from referring to the JVM heap. This feature protects the JVM heap during native method execution; if the heap is referred to invalidly, it interrupts the execution by generating a page-fault exception. It then reports the location where the exception was generated. The runtime overhead for using this feature depends on the frequency of native method calls because the protection is switched on each time a native method is called. We evaluated the runtime overhead by running the SPECjvm98, SPECjbb2000, VolanoMark, and JFCMark benchmark suites on a PC with two Intel Xeon^® 1.6 GHz processors. The performance loss was less than 2% for the benchmark items that do not call native methods so frequently (10⁴ times per second) and 5%–20% for the benchmark items that do (10⁴–10⁵ times per second). The worst performance loss was 54%, which was recorded for a benchmark item that calls native methods 2.0×10⁶ times per second.     

Application of the independent molecule model to elucidate the dynamics of structure I methane hydrate

Raman spectroscopy has exhibited the C–H stretch (A₁ mode) frequency ν₁ of hydrated methanes at 2915 cm⁻¹ for the 5¹² cage and 2905 cm⁻¹ for the 5¹²6² cage. These values are lower than the frequency of 2916.5 cm⁻¹ in gaseous methane. In this paper, we theoretically examine the Raman spectra observed in methane hydrate by normal mode analysis using the independent molecule model. By a breakdown of the symmetry, the four frequencies in modes A₁, E, T₂ and T₂ observed in gaseous methane are separated into nine frequencies in the hydrate. It is necessary to consider the anharmonic potential energy within methane and hydrogen bonding between methane hydrogen and water oxygen in order to get a result in qualitative agreement with experiment. The frequency in the 5¹²6² cage is shifted downward in comparison to the one in 5¹², and the frequencies in the both cages are also shifted downward compared with the frequencies in gas. Calculations are also reported for the isotopic methane (CD₄, ¹³CH₄) hydrates.     

Quartic discriminants and tensor invariants

Discusses the calculation of discriminants of polynomials. The discriminant is a function of the coefficients that indicates if the polynomial has any double roots. The discriminant Δ₄ of a homogeneous quartic f(x,w) = Ax⁴+4Bx³w+6Cx² w²+4Dxw³+Ew⁴ = 0 is Δ₄ = 27(I₃)²-(I₂)³, where I₂ = AE-4BD+3C² and I₃ = ACE-AD ²-B²E+2BCD-C³ (this is the Hilbert representation). The author shows how to write the discriminant as a tensor diagram. The discriminant of a polynomial is an example of an invariant quantity. Tensor diagrams are particularly useful to express invariant quantities. Adding a dimension moves us from the world of (1D) homogeneous polynomials to 2D homogeneous (2DH) geometry (curves in the projective plane). It is shown that a relationship exists between the possible root structures of a 4th-order polynomial and the possible degeneracies of a 3rd-order curve     

Robust stabilization of uncertain linear systems: quadraticstabilizability and H∞ control theory

The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H^∞ optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations between these robust stabilization problems and H^∞ control theory are explored. It is also shown that in a number of cases, if a robust stabilization problem can be solved via Lyapunov methods, then it can be also be solved via H ^∞ control theory-based methods     

Robust nonlinear H∞-output feedback control

This paper investigates the problem of robust H_∞-output feedback control for nonlinear systems with time-varying parameter uncertainty satisfying some integral functional constraints. We address the problem of designing a compensator such that the L₂-gain of the mapping from the exogenous input noise to the penalty output is minimized or guaranteed to be less than or equal to a prescribed value. We establish the interconnection between the robust nonlinear H_∞-control problem and the nonlinear H _∞-control problem, Based on this connection, a sufficient condition for the existence of a solution to the robust nonlinear H_∞-output feedback control problem is derived in terms of a “scaled” Hamilton-Jacobi inequality     

Fabrication of ultrathin p++ silicon microstructuresusing ion implantation and boron etch-stop

This paper discusses the fabrication of submicron p⁺⁺ silicon microstructures for a number of MEMS applications using boron ion implantation, rapid thermal annealing, and boron etch-stop. To form these thin structures, the silicon is implanted with boron at an energy of 40 keV and doses of 5×10¹⁵ cm^-2 and 7×10¹⁵ cm^-2, which produce a peak concentration of more than 10²⁰ cm^-3, sufficient for achieving an effective etch-stop in ethylene diamine pyrocathecol. The thickness of the p⁺⁺ layer varies from 0.2 to 0.3 μm depending on the annealing time and temperature. SUPREM simulation has been used to determine optimum implantation and annealing conditions. A number of microstructures, including thin silicon diaphragms as large as 2 mm on a side and 0.2 μm thick, hot wire anemometers with a temperature coefficient of resistance of ~1600 ppm/°C, and piezoresistive sound detectors, have been fabricated with high reproducibility, uniformity, and yield     

Frequency-weighted ℒ∞ norm and optimal Hankelnorm model reduction

A new relative error model reduction method is proposed using frequency-weighted balanced realization, and explicit ℒ_∞ norm error bounds are also derived for the relative error and multiplicative error. The method only needs to solve two Lyapunov equations. It is further shown that this method is equivalent to the balanced stochastic truncation if the plant is square and minimum phase. This paper also gives a complete solution to the frequency-weighted Hankel norm approximation with antistable weighting. These results are then applied to ℒ_∞ norm model reduction, and several numerically effective algorithms are proposed. It is shown through many numerical examples that these algorithms work very well and in many cases produce almost optimal solutions     

一类非线性离散时间系统的神经网络解耦策略

考虑用神经网络作为补偿器,对一类非线性系统进行输入输出解耦.给出了这类系 统的可解耦的充要条件,并证明在该条件下系统可解耦成线性系统且极点可任意配置.基于 此,给出了这类系统的一个神经网络解耦方法.     

On the complexity of purely complex μ computation and relatedproblems in multidimensional systems

In this paper, the following robust control problems are shown to be NP-hard: given a purely complex uncertainty structure Δ, determine if: 1) μ_Δ(M)<1, for a given rational matrix M; 2) ∥M(·)∥_μ<1, for a given rational transfer matrix M(s); and 3) inf(Q∈H^∞)∥F(T,Q)∥_μ<1, for a given linear fractional transformation F(T,Q) with rational coefficients. In other words, purely complex μ computation, analysis, and synthesis problems are NP-hard. It is also shown that checking stability and computing the H^∞ norm of a multidimensional system, are NP-hard problems. Therefore, it is rather unlikely to find nonconservative polynomial time algorithms for solving the problems in complete generality