一种新的多输入非线性控制系统高阶逼近线性化的计算方法

通常,即使对于一个可逼近反馈线性化的非线性系统,求得一 个所需的坐标变换和反馈仍然是困难的,原因在于需要求解一组偏微分 方程. 在本文中, 为了求得逼近反馈线性化所需的非线性反馈及坐标变 换, 我们首先引入了一个扩展的坐标空间, 针对一类线性可控的多输入非 线性系统,推导了系统新的矩阵表达式。基于这些准备,我们提出了一种 新的有效的构造化算法,它降低了计算所需的运算量。最后通过一个例 子我们介绍了本方法的应用.     

A general approach to input-output pseudolinearization fornonlinear systems

A nonlinear system is said to be input-output pseudolinearized if its family of linearizations about constant operating points has input-output behavior that is independent of the particular operating point. The problem of constructing static state feedback laws that achieve input-output pseudolinearization for a general class of nonlinear systems is considered. A generalization of the well-known structure algorithm to the case of parameterized families of linear systems plays an important role     

求解强非线性动力系统响应的一种新方法

将同伦理论和参数变换技术相结合提出了一种可适用于求解强非线性动力系统响应的新方法．即PE-HAM方法(基于参数展开的同伦分析技术)．其主要思想是通过构造合适的同伦映射,将一非线性动力系统的求解问题,转化为一线性微分方程组的求解问题,然后借助于参数展开技术消除长期项,进而得到系统的解析近似解．为了检验所提方法的有效性,研究了具有精确周期的保守Duffing系统的响应,求出了其解析的近似解表达式．在与精确周期的比较中,可以得出：在非线性强度。很大,甚至在α→∞时,近似解的周期与原系统精确周期的误差也只有2．17％．数值模拟结果说明了新方法的有效性．     

A parallel algorithm for approximate regularity

Spatial regularity amidst a seemingly chaotic image is often meaningful. Many papers in computational geometry are concerned with detecting some type of regularity via exact solutions to problems in geometric pattern recognition. However, real-world applications often have data that is approximate, and may rely on calculations that are approximate. Thus, it is useful to develop solutions that have an error tolerance.

A solution has recently been presented by Robins et al. [Inform. Process. Lett. 69 (1999) 189–195] to the problem of finding all maximal subsets of an input set in the Euclidean plane that are approximately equally-spaced and approximately collinear. This is a problem that arises in computer vision, military applications, and other areas. The algorithm of Robins et al. is different in several important respects from the optimal algorithm given by Kahng and Robins [Patter Recognition Lett. 12 (1991) 757–764] for the exact version of the problem. The algorithm of Robins et al. seems inherently sequential and runs in O(n^5/2) time, where n is the size of the input set. In this paper, we give parallel solutions to this problem.     

A new method for constructing sliding surfaces of linear time-invariant systems

A new method for constructing the sliding surfaces is developed by using the pole-assignment method; unlike the usual cases, the pole-assignment method is applied to the overall closed-loop system and not the system in the sliding mode. Most importantly, the design procedure is simple since the sliding surfaces can be determined in an explicit form. Also, three significant properties listed in a theorem are proved and demonstrated by a numerical example.     

A new parallel algorithm for constructing Voronoi tessellations from distributed input data

We present a new parallel algorithm for generating consistent Voronoi diagrams from distributed input data for the purposes of simulation and visualization. The algorithm functions by building upon any serial Voronoi tessellation algorithm. The output of such a serial tessellator is used to determine the connectivity of the distributed domains without any assumptions about how points are distributed across those domains, and then in turn to build the portion of the global tessellation local to each domain using information from that domains neighbors. The result is a generalized methodology for adding distributed capabilities to serial tessellation packages. Results from several two-dimensional tests are presented, including strong and weak scaling of its current implementation.     

A new algorithm for integration of dynamic systems

A high precision unconditionally stable algorithm for computation of linear dynamic structural systems is described. It shares the advantageous property (typical for lower order algorithms) of the amplification matrix preserving a banded form due to discretization in space. Hence in contrast to the known high precision algorithms employing full matrices, less computer space and fewer operations are needed. The new algorithm is free of artificial damping in the undamped case as well as of artificial oscillation in the postcritical damping region. Local truncation error analysis is made and rate of convergence is proved. Applications to problems allowing comparison with existing results are presented. Excellent agreement with exact solutions is achieved and engineering accuracy is attained with relatively few time steps.     

A sublinear algorithm for approximate keyword searching

Given a relatively short query stringW of lengthP, a long subject stringA of lengthN, and a thresholdD, theapproximate keyword search problem is to find all substrings ofA that align withW with not more than D insertions, deletions, and mismatches. In typical applications, such as searching a DNA sequence database, the size of the databaseA is much larger than that of the queryW, e.g.,N is on the order of millions or billions andP is a hundred to a thousand. In this paper we present an algorithm that given a precomputedindex of the databaseA, finds rare matches in time that issublinear inN, i.e.,N ^c for somec<1. The sequenceA must be overa. finite alphabet . More precisely, our algorithm requires 0(DN ^pow() logN) expected-time where =D/P is the maximum number of differences as a percentage of query length, and pow() is an increasing and concave function that is 0 when =0. Thus the algorithm is superior to current O(DN) algorithms when is small enough to guarantee that pow() < 1. As seen in the paper, this is true for a wide range of , e.g., . up to 33% for DNA sequences (¦¦=4) and 56% for proteins sequences (¦¦=20). In preliminary practical experiments, the approach gives a 50-to 500-fold improvement over previous algorithms for prolems of interest in molecular biology.This work was supported in part by the National Institutes of Health under Grant R01 LM04960-01 and the Aspen Center for Physics.     

A New Representation and Algorithm for Constructing Convex Hulls in Higher Dim ensional Spaces

This paper presents a new and simple scheme to describe the convex hull in R^d,which only uses three kinds of the faces of the convex hull.i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop and efficient new algorithm for constructing the convex hull of a finite set of points incrementally.This algorithm employs much less storage and time than that of the previously-existing approaches.The analysis of the runniing time as well as the storage for the new algorithm is also theoretically made.The algorithm is optimal in the worst case for even d.     

An algorithm for constructing Darboux transformations of type I for third-order hyperbolic operators of two variables

Darboux transformations of type I are invertible Darboux transformations with explicit short formulas for inverse transformations. These transformations are invariant with respect to gauge transformations, and, for gauge transformations acting on third-order hyperbolic operators of two variables, a general-form system of generating differential invariants is known. In the paper, first-order Darboux transformations of type I for this class of operators are considered. The corresponding operator orbits are directed graphs with at most three edges originating from each vertex. In the paper, an algorithm for constructing such orbits is suggested. We have derived criteria for existence of first-order Darboux transformations of type I in terms of the generating invariants, formulas for transforming invariants, and the so-called “triangle rule” property of orbits. The corresponding implementation in the LPDO package is described. The orbits are constructed in two different forms, one of which outputs the graph in the format of the well-known built-in Maple package Graph Theory.     

生化系统稳态优化的一种新算法

针对一类生化系统的稳态优化问题, 在已有间接优化方法(IOM)的线性优化问题中引入一个反映S–系统解和原模型解一致性的等式约束, 应用Lagrangian乘子法将修正后的非线性优化问题转化为一个等价的线性优化问题, 提出了一种改进的稳态优化新算法. 该优化算法不仅可以收敛到正确的系统最优解, 而且可用现有的线性规划算法去计算. 最后将算法应用于几个生化系统的稳态优化中, 结果表明, 本文提出的优化算法是有效的.     

A new dynamic voting algorithm for distributed database systems

We consider the problem of keeping a distributed database system that has been partitioned because of site or communication link failures partially operable while ensuring data consistency. A dynamic-voting-consistency algorithm is proposed, and its correctness is demonstrated. The proposed algorithm results in improved efficiency in executing read requests by not requiring a read quorum. This algorithm is effective in environments where the majority of user requests are “read” types of requests. Furthermore, the proposed algorithm results in efficient recovery by avoiding updating those data objects that are still current. Under the proposed algorithm, the majority partition would be available even if changes in the network topology take place at a higher rate than the update rate, as long as only simple partitioning takes place     

Parallel algorithm for constructing k-valued fault-tolerant diagnostic tests in intelligent systems

A parallel algorithm for constructing k-valued fault-tolerant diagnostic tests is described. This algorithm combines two algorithms, viz. a parallel algorithm for constructing an irredundant implication matrix designed to distinguish objects from different patterns and a parallel algorithm for constructing irredundant h-fold column coverings. The IMSLOG intelligent instrumental software (IIS), on the basis of which we construct intelligent systems for various disciplines is described. A sufficient condition for constructing diagnostic tests tolerant to the given number of measurement (entry) errors of values of characteristic features of the object under investigation is applied to ensure fault-tolerance. Suggestions for further research are given.     

A subquadratic algorithm for approximate limited expression matching

In this paper we present an efficient subquadratic-time algorithm for matching strings and limited expressions in large texts. Limited expressions are a subset of regular expressions that appear often in practice. The generalization from simple strings to limited expressions has a negligible affect on the speed of our algorithm, yet allows much more flexibility. Our algorithm is similar in spirit to that of Masek and Paterson [MP], but it is much faster in practice. Our experiments show a factor of four to five speedup against the algorithms of Sellers [Se] and Ukkonen [Uk1] independent of the sizes of the input strings. Experiments also reveal our algorithm to be faster, in most cases, than a recent improvement by Chang and Lampe [CL2], especially for small alphabet sizes for which it is two to three times faster.The research of U. Manber was supported in part by a Presidential Young Investigator Award DCR-8451397, with matching funds from AT&T, and by NSF Grant CCR-9001619. G. Myers research was supported in part by NIH Grant LM04960, NSF Grant CCR-9001619, and the Aspen Center for Physics.     

A parallel algorithm for constructing a labeled tree

A tree T is labeled when the n vertices are distinguished from one another by names such as v₁, v₂…v_n . Two labeled trees are considered to be distinct if they have different vertex labels even though they might be isomorphic. According to Cayley's tree formula, there are n^n-2 labeled trees on n vertices. Prufer used a simple way to prove this formula and demonstrated that there exists a mapping between a labeled tree and a number sequence. From his proof, we can find a naive sequential algorithm which transfers a labeled tree to a number sequence and vice versa. However, it is hard to parallelize. In this paper, we shall propose an O(log n) time parallel algorithm for constructing a labeled tree by using O(n) processors and O(n log n) space on the EREW PRAM computational model     

A faster divide-and-conquer algorithm for constructing delaunay triangulations

An easily implemented modification to the divide-and-conquer algorithm for computing the Delaunay triangulation ofn sites in the plane is presented. The change reduces its (n logn) expected running time toO(n log logn) for a large class of distributions that includes the uniform distribution in the unit square. Experimental evidence presented demonstrates that the modified algorithm performs very well forn2¹⁶, the range of the experiments. It is conjectured that the average number of edges it creates—a good measure of its efficiency—is no more than twice optimal forn less than seven trillion. The improvement is shown to extend to the computation of the Delaunay triangulation in theL _p metric for 1<p.This research was supported by National Science Foundation Grants DCR-8352081 and DCR-8416190.     

A faster divide-and-conquer algorithm for constructing delaunay triangulations

An easily implemented modification to the divide-and-conquer algorithm for computing the Delaunay triangulation ofn sites in the plane is presented. The change reduces its Θ(n logn) expected running time toO(n log logn) for a large class of distributions that includes the uniform distribution in the unit square. Experimental evidence presented demonstrates that the modified algorithm performs very well forn≤2¹⁶, the range of the experiments. It is conjectured that the average number of edges it creates—a good measure of its efficiency—is no more than twice optimal forn less than seven trillion. The improvement is shown to extend to the computation of the Delaunay triangulation in theL _p metric for 1<p≤∞.     

类Lyapunov非线性系统降维观测器设计

对一般形式的非线性系统,引入了Lyapunov稳定意义下观测器存在性的概念,讨论了降维观测器的存在性.指出若相对于一特别形式的Lyapunov函数在Lyapunov稳定意义下存在全维观测器,则还存在降维观测器,并给出了降维观测器之设计方法.为说明该方法的指导意义,用该方法相对于Lipschitz非线性系统给出了降维观测器设计,并对该设计相对于一具体模型进行了仿真分析,仿真结果表明了该设计方法的正确性及实用性.