共查询到20条相似文献,搜索用时 31 毫秒
1.
《Automatica》1987,23(4):535-540
In this paper, the problem of simultaneous stabilization in the case where each plant has a different domain of stability associated with it is studied. Specifically, it is supposed that one is given plants P0, P1,…, Pr together with domains of stability D0,…, Dr, and the objective is to find a common controller C such that the poles of the closed-loop transfer matrix H(Pi, C) are all inside the corresponding domain of stability Di, for i = 0,…, r. This formulation of the simultaneous stabilization problem generalizes earlier problem formulations wherein it was assumed that all the domains of stability were the same, and is believed to be a more realistic formulation of the problem of preserving system stability in the event of sensor or actuator failure. In the paper, necessary and sufficient conditions for the existence of a common controller are derived, in the case where one of the domains (say D0) is a subset of the rest. The case of two plants P0, P1 with D0 a subset of D1 is studied in great detail, and the following result is established: the two plants can be simultaneously stabilized in the above generalized sense if and only if they can be simultaneously stabilized with respect to the larger of the two regions. More precisely there exists a controller C such that the poles of H(Pi, C) lie inside Di for i = 0, 1 if and only if there exists a controller such that the poles of bothH(P0, C) and of H(P1, C) lie inside the larger region D1. 相似文献
2.
Telikepalli Kavitha 《Theory of Computing Systems》2014,55(1):229-249
We consider the problem of maintaining information about the rank of a matrix M under changes to its entries. For an n×n matrix M, we show an amortized upper bound of O(n ω?1) arithmetic operations per change for this problem, where ω<2.373 is the exponent for matrix multiplication, under the assumption that there is a lookahead of up to Θ(n) locations. That is, we know up to the next Θ(n) locations (i 1,j 1),(i 2,j 2),…?, whose entries are going to change, in advance; however we do not know the new entries in these locations in advance. We get the new entries in these locations in a dynamic manner. The dynamic matrix rank problem was first studied by Frandsen and Frandsen who showed an upper bound of O(n 1.575) and a lower bound of Ω(n) for this problem and later Sankowski showed an upper bound of O(n 1.495) for this problem when allowing randomization and a small probability of error. These algorithms do not assume any lookahead. For the dynamic matrix rank problem with lookahead, Sankowski and Mucha showed a randomized algorithm (with a small probability of error) that is more efficient than these algorithms. 相似文献
3.
《CVGIP: Graphical Models and Image Processing》1994,56(3):231-246
Given a polygonal curve P =[p1, p2, . . . , pn], the polygonal approximation problem considered calls for determining a new curve P′ = [p′1, p′2, . . . , p′m] such that (i) m is significantly smaller than n, (ii) the vertices of P′ are an ordered subset of the vertices of P, and (iii) any line segment [p′A, p′A + 1 of P′ that substitutes a chain [pB, . . . , pC] in P is such that for all i where B ≤ i ≤ C, the approximation error of pi with respect to [p′A, p′A + 1], according to some specified criterion and metric, is less than a predetermined error tolerance. Using the parallel-strip error criterion, we study the following problems for a curve P in Rd, where d = 2, 3: (i) minimize m for a given error tolerance and (ii) given m, find the curve P′ that has the minimum approximation error over all curves that have at most m vertices. These problems are called the min-# and min-ϵ problems, respectively. For R2 and with any one of the L1, L2, or L∞ distance metrics, we give algorithms to solve the min-# problem in O(n2) time and the min-ϵ problem in O(n2 log n) time, improving the best known algorithms to date by a factor of log n. When P is a polygonal curve in R3 that is strictly monotone with respect to one of the three axes, we show that if the L1 and L∞ metrics are used then the min-# problem can be solved in O(n2) time and the min-ϵ problem can be solved in O(n3) time. If distances are computed using the L2 metric then the min-# and min-ϵ problems can be solved in O(n3) and O(n3 log n) time, respectively. All of our algorithms exhibit O(n2) space complexity. Finally, we show that if it is not essential to minimize m, simple modifications of our algorithms afford a reduction by a factor of n for both time and space. 相似文献
4.
Stable polyhedra in parameter space 总被引:1,自引:0,他引:1
A typical uncertainty structure of a characteristic polynomial is P(s)=A(s)Q(s)+B(s) with A(s) and B(s) fixed and Q(s) uncertain. In robust controller design Q(s) may be a controller numerator or denominator polynomial; an example is the PID controller with Q(s)=KI+KPs+KDs2. In robustness analysis Q(s) may describe a plant uncertainty. For fixed imaginary part of Q(jω), it is shown that Hurwitz stability boundaries in the parameter space of the even part of Q(jω) are hyperplanes and the stability regions are convex polyhedra. A dual result holds for fixed real part of Q(jω). Also σ-stability with the real parts of all roots of P(s) smaller than σ is treated.Under the above conditions, the roots of P(s) can cross the imaginary axis only at a finite number of discrete “singular” frequencies. Each singular frequency generates a hyperplane as stability boundary. An application is robust controller design by simultaneous stabilization of several representatives of A(s) and B(s) by a PID controller. Geometrically, the intersection of convex polygons must be calculated and represented tomographically for a grid on KP. 相似文献
5.
《Environmental Modelling & Software》2003,18(3):243-251
The scale-invariant behavior of air pollutant concentration (APC) time structure was investigated by applying the box counting method to APC time series. One-year series of hourly average APC observations, including O3, CO, SO2, NO, NO2, and PM10 which were obtained from urban, traffic, and national park air monitoring station at Taipei (Taiwan), were transferred into a useful compact form through this method, namely, the box-dimension (DB)-threshold (Th) and critical scale (CS)-threshold (Th) plots. The validity of this approach was supported with the result that the practical implications of DB-Th (or CS-Th) plots could be interpreted in terms of traditional statistical parameters. Since the dependences of both DB and CS on the Th values were closely related to the variation of APC in time, they were used to characterize the temporal distribution of APC. The analysis confirmed the existence of scale invariance in those investigated APC time series. Moreover, the DB (CS) was shown to be a decreasing (increasing) function of the threshold level, implying multifractal characteristics, i.e. the weak and intense regions scale differently. Some practical applications based on the box counting method were also discussed. 相似文献
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7.
The set of permutations of ??n??={1,??,n} in one-line notation is ??(n). The shorthand encoding of a 1?a n ????(n) is a 1?a n?1. A shorthand universal cycle for permutations (SP-cycle) is a circular string of length n! whose substrings of length n?1 are the shorthand encodings of ??(n). When an SP-cycle is decoded, the order of ??(n) is a Gray code in which successive permutations differ by the prefix-rotation ?? i =(1 2 ? i) for i??{n?1,n}. Thus, SP-cycles can be represented by n! bits. We investigate SP-cycles with maximum and minimum ??weight?? (number of ?? n?1s in the Gray code). An SP-cycle n a n b?n z is ??periodic?? if its ??sub-permutations?? a,b,??,z equal ??(n?1). We prove that periodic min-weight SP-cycles correspond to spanning trees of the (n?1)-permutohedron. We provide two constructions: B(n) and C(n). In B(n) the spanning trees use ??half-hunts?? from bell-ringing, and in C(n) the sub-permutations use cool-lex order by Williams (SODA, 987?C996, 2009). Algorithmic results are: (1)?memoryless decoding of B(n) and C(n), (2)?O((n?1)!)-time generation of B(n) and C(n) using sub-permutations, (3)?loopless generation of B(n)??s binary representation n bits at a time, and (4)?O(n+??(n))-time ranking of B(n)??s permutations where ??(n) is the cost of computing a permutation??s inversion vector. Results (1)?C(4) improve on those for the previous SP-cycle construction D(n) by Ruskey and Williams (ACM Trans. Algorithms 6(3):Art.?45, 2010), which we characterize here using ??recycling??. 相似文献
8.
Barnaby Martin 《Information Processing Letters》2011,111(20):999-1003
Building on a result of Larose and Tesson for constraint satisfaction problems (CSPs), we uncover a dichotomy for the quantified constraint satisfaction problem QCSP(B), where B is a finite structure that is a core. Specifically, such problems are either in ALogtime or are L-hard. This involves demonstrating that if CSP(B) is first-order expressible, and B is a core, then QCSP(B) is in ALogtime.We show that the class of B such that CSP(B) is first-order expressible (indeed trivial) is a microcosm for all QCSPs. Specifically, for any B there exists a C — generally not a core — such that CSP(C) is trivial, yet QCSP(B) and QCSP(C) are equivalent under logspace reductions. 相似文献
9.
On the problem of general structural assignments of linear systems through sensor/actuator selection
A systematic method is developed for determining an output matrix C for a given matrix pair (A,B) such that the resulting linear system characterized by the matrix triple (A,B,C) has the pre-specified system structural properties, such as the finite and infinite zero structure and the invertibility structures. Since the matrix C describes the locations of the sensors, the procedure of choosing C is often referred to as sensor selection. The method developed in this paper for sensor selection can be applied to the dual problem of actuator selection, where, for a given matrix pair (A,C), a matrix B is to be determined such that the resulting matrix triple (A,B,C) has the pre-specified structural properties. 相似文献
10.
Judyta Wegrzyn Adam Samborski Louisa Reissig Piotr M. Korczyk Slawomir Blonski Piotr Garstecki 《Microfluidics and nanofluidics》2013,14(1-2):235-245
We demonstrate a strategy for construction of high-throughput microfluidic systems generating gradations of chemistry in micro-droplets. The productivity of the systems that we propose is limited only by the maximum rate of the droplet formation, and does not need to be limited by the rate of mixing. Multilayer polycarbonate chips transform two miscible input streams A and B into N streams of droplets, containing mixtures [A] i , [B] i . Exemplary devices generate linear ([B] i ∝ i) and logarithmic gradations (ln[B] i ∝ i). We also analyze the use of the same strategy for the generation of concentration gradation in the streams of droplets comprising mixtures of liquids of different viscosities. The devices preserve the required distribution of compositions, while allowing the volume of the droplets to be tuned over almost two orders of magnitude (i.e. between 3 and 80 nL). 相似文献
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12.
《Journal of Systems and Software》2004,73(1):3-14
Optimal broadcasting schemes for interconnection networks (INs) are most essential for the efficient interprocess communication amongst parallel computers. In this paper two novel broadcasting schemes are proposed for hypercube computers with bursty background traffic and a single-port mode of message passing communication. The schemes utilize a maximum entropy (ME) based queue-by-queue decomposition algorithm for arbitrary queueing network models (QNMs) [D.D. Kouvatsos, I. Awan, Perform. Eval. 51 (2003) 191] and are based on binomial trees and graph theoretic concepts. It is shown that the overall cost of the one-to-all broadcasting scheme is given by max{ω1,ω2,…,ω2n/2}, where ωi, i=1,2,…,2n/2 is the total weight at each leaf node of the binomial tree and n is the degree of the hypercube. Moreover, the upper bound of the total cost of the neighbourhood broadcasting scheme is determined by ∑i=1Fmax{ωi}, where F is an upper bound of the number of steps and is equal to 1.33⌈log2(n−1)⌉+1. Evidence based on empirical studies indicates the suitability of the schemes for achieving optimal broadcasting costs. 相似文献
13.
In a cascaded plant with n sensing points, n independent feedback loops are available to achieve quantitative sensitivity specifications. The optimum design is defined as that which achieves this with minimum net effect, of the n sensor noise sources, at the plant input. A design procedure is presented wherein one works backwards step by step from the system output, designing each loop function Li almost as if the remaining loops (Li+j, j>0) are perfect. Even in large plant ignorance problems, only the outer loop Li may be large over some frequency range. In general |Li|max < 1, i ≠ 1 and |Li+1|max < |Li|max. Each Li has only one distinct frequency range say at ωc, i requiring trade-off between Li and Li+1. Only in this range is significant design effort required. However, ωc, i+1 >ωc, i so the primary price paid is in the steadily increasing “bandwidth” of each loop. The design procedure is highly transparent with strong universalistic features, permitting the use of universal design curves. 相似文献
14.
Given a nonnegative real (m, n) matrixA and positive vectorsu, v, then the biproportional constrained matrix problem is to find a nonnegative (m, n) matrixB such thatB=diag (x) A diag (y) holds for some vectorsx ∈ ? m andy ∈ ? n and the row (column) sums ofB equalu i (v j )i=1,...,m(j=1,..., n). A solution procedure (called the RAS-method) was proposed by Bacharach [1] to solve this problem. The main disadvantage of this algorithm is, that round-off errors slow down the convergence. Here we present a modified RAS-method which together with several other improvements overcomes this disadvantage. 相似文献
15.
《Computers & Mathematics with Applications》2005,49(7-8):1279-1284
In this paper, a fully parallel method for finding some or all finite eigenvalues of a real symmetric matrix pencil (A, B) is presented, where A is a symmetric tridiagonal matrix and B is a diagonal matrix with b1 > 0 and bi ≥ 0, i = 2,3,…,n. The method is based on the homotopy continuation with rank 2 perturbation. It is shown that there are exactly m disjoint, smooth homotopy paths connecting the trivial eigenvalues to the desired eigenvalues, where m is the number of finite eigenvalues of (A, B). It is also shown that the homotopy curves are monotonic and easy to follow. 相似文献
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17.
For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V(G), then the eccentric connectivity index of G, ξC(G), is defined as, ∑vi∈V(G)diei, where di is the degree of a vertex vi and ei is its eccentricity. In this report we compare the eccentric connectivity index (ξC) and the Zagreb indices (M1 and M2) for chemical trees. Moreover, we compare the eccentric connectivity index (ξC) and the first Zagreb index (M1) for molecular graphs. 相似文献
18.
The Ziegler–Nichols process dynamics characterization is based on the estimation of the ultimate gain ku and ultimate frequency ωu. The angle φ of the tangent to the Nyquist curve at the frequency ωu is introduced, as an additional parameter in the frequency domain. The essential dynamic characteristics of the process can be captured by using the tangent rule, proposed here as an extension of the Ziegler–Nichols approach. The validity of the tangent rule is confirmed by using the PID controller optimization on a test batch consisting of stable, integrating and unstable processes, including dead-time. Parameters ku, ωu and φ can be determined from the sustained oscillations, using the phase-locked loop identifier module. 相似文献
19.
Maw-Shang Chang 《Theoretical computer science》2011,412(23):2496-2502
Let G be a class of graphs. A graph G has G-width k if there are k independent sets N1,…,Nk in G such that G can be embedded into a graph H∈G such that for every edge e in H which is not an edge in G, there exists an i such that both endvertices of e are in Ni. For the class B of block graphs we show that graphs with B-width at most 4 are perfect. We also show that B-width is NP-complete and show that it is fixed-parameter tractable. For the class C of complete graphs, similar results are also obtained. 相似文献
20.
We consider the following circle placement problem: given a set of pointsp i ,i=1,2, ...,n, each of weightw i , in the plane, and a fixed disk of radiusr, find a location to place the disk such that the total weight of the points covered by the disk is maximized. The problem is equivalent to the so-called maximum weighted clique problem for circle intersection graphs. That is, given a setS ofn circles,D i ,i=1,2, ...,n, of the same radiusr, each of weightw i , find a subset ofS whose common intersection is nonempty and whose total weight is maximum. AnO (n 2) algorithm is presented for the maximum clique problem. The algorithm is better than a previously known algorithm which is based on sorting and runs inO (n 2 logn) time. 相似文献