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Discussion on: "Unified Approach to the Problem of Full Decoupling via Output Feedback"

EUROPEAN JOURNAL OF CONTROL 2010年第4期16卷 326-328页

作者： Kotta, Uelle Mullari, Tanel Tallinn Univ Technol Inst Cybernet Tallinn EE-12618 Tallinn Estonia

The article under discussion studies the unmeasurable disturbance decoupling problem (DDP) via the dynamic output feedback from a unified viewpoint for continuous-and discrete-time nonlinear control systems as well as for discrete event systems. This is a challenging problem, not having today a complete solution, that is the necessary and sufficient solvability conditions together with the constructive algorithm to compute the feedback law. In [1] the intrinsic coordinate-free necessary solvability conditions were obtained in terms of the maximal conditioned invariant subspace and the smallest controlled invariant subspace. The article under discussion provides the sufficient algorithm-based solvability conditions. Unfortunately it does not provide the explicit algorithm for problem solution; the steps of the algorithm are scattered implicitly in the different parts of the article, partly presented in the unified manner, partly treated separately for the continuous and discrete cases.

关键词： computability Debates DECOUPLING Subspace Output feedback discrete event systems constructive algorithm explicit algorithm

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Minimally parametric form of the equations of motion of aircraft

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INTERNATIONAL APPLIED MECHANICS 1995年第10期31卷 852-858页

作者： Legenkii, VI

The analysis of an example illustrates the high "resolution" of group analysis of the system (1), (2); only three of the nine symmetry operators found can be determined by means of the -theorem. With the aid of the above-determined symmetry operators it can be confirmed that two essential parameters can be formed out of the eight parameters of the system (1), (2): the thrust—weight ratio (P) and the lift—drag ratio (k). The application of group methods leads to constructive algorithms for seeking the required transformations, which the investigator can use to find the substitutions needed for any problem at hand.

关键词： Aircraft Operon critical parameter Symmetry Parametric OPERATORS Equations of motion symmetry operator Researchers Operators constructive algorithm Automatic incident detection

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Inverse problem for the differential pencil on an arbitrary graph with partial information given on the coefficients

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ANALYSIS AND MATHEMATICAL PHYSICS 2019年第3期9卷 1393-1409页

作者： Bondarenko, Natalia P. Samara Natl Res Univ Dept Appl Math & Phys Moskovskoye Shosse 34 Samara 443086 Russia Saratov NG Chernyshevskii State Univ Dept Mech & Math Astrakhanskaya 83 Saratov 410012 Russia

In this paper, a partial inverse problem for the quadratic Sturm-Liouville pencil on a geometrical graph of arbitrary structure is studied. We suppose that the coefficients of differential expressions are known a priori on all the graph edges except one, and recover the coefficients on the remaining edge, using a part of the spectrum. The results of the paper are uniqueness theorems and a constructive algorithm for solving the partial inverse problem.

关键词： Partial inverse problem Quadratic Sturm-Liouville pencil Quantum graph Uniqueness theorem constructive algorithm Riesz basis

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Improved constructive learning algorithms for fuzzy inference system identification

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2007年第4期2卷 322-331页

作者： Alimi, Sonia Chtourou, Mohamed Natl Sch Engineers Sfax Dept Elect Engn BP W Sfax 3038 Tunisia

This paper presents an improved constructive learning algorithm for fuzzy inference system identification. An incremental training procedure that starts with a single pattern and a single-fuzzy rule has been used: if after several attempts, the fuzzy model cannot reduce the error within the specified tolerance;it grows by adding a new fuzzy rule. In order to overcome the over-training problem and to ameliorate the performance of the previous algorithm, two techniques of reduction have been introduced. In the first one, the growing of the fuzzy rules is conditioned by the generalisation error. In the second approach, a technique based on the similarity measures has been applied. The presented approaches have been applied for two examples to show the identification performance.

关键词： constructive algorithm fuzzy rule reduction generalisation similarity measures fuzzy inference system FIS

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Solution asymptotics at large times for the non-linear Schrodinger equation

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IZVESTIYA MATHEMATICS 1997年第4期61卷 757-794页

作者： Naumkin, PI Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Chair Gen Math Moscow 117234 Russia

We consider a spatially uniform asymptotic representation at large times of the solution to the Cauchy problem for the non-linear Schrodinger equation. If the non-linear term decreases in time faster than the linear terms, then the asymptotics are quasi-linear. Of particular interest is the case in which the non-linearity decreases in time at the same rate as or even more slowly than the linear terms and thus has a stronger effect on the solution asymptotics at large times. In this paper we employ an appropriate change of variables to reduce this case to the quasi-linear one. Namely, we derive an integral equation with rapidly decreasing non-linearity for the new unknown function, which can be solved by the method of successive approximations. Thus, we have a constructive algorithm for calculating the asymptotics of the solution to the Cauchy problem for the non-linear Schrodinger equation from the initial data.

关键词： Solution nonlinear equations constructive algorithm RAW DATA asymptotic Schrodinger equation nonlinearity Cauchy problem

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Training a sigmoidal node is hard

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NEURAL COMPUTATION 1999年第5期11卷 1249-1260页

作者： Hush, DR Univ Calif Los Alamos Natl Lab Los Alamos NM 87545 USA

This article proves that the task of computing near-optimal weights for sigmoidal nodes under the L-1 regression norm is NP-Hard. For the special case where the sigmoid is piecewise linear, we prove a slightly stronger result: that computing the optimal weights is NP-Hard. These results parallel that for the one-node pattern recognition problem-that determining the optimal weights for a threshold logic node is also intractable. Our results have important consequences for constructive algorithms that build a regression model one node at a time. It suggests that although such methods are (in principle) capable of producing efficient size representations (Barron, 1993;Jones, 1992), finding such representations may be computationally intractable. These results holds only in the deterministic sense;that is, they do not exclude the possibility that such representations may be found efficiently with high probability. In fact it motivates the use of heuristic or randomized algorithms for this problem.

关键词： Line of nodes constructivity Optimal constructive algorithm Sigmoid Colon

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Simultaneous Stabilization: Universal Controller Synthesis

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AUTOMATION AND REMOTE CONTROL 2011年第9期72卷 1852-1863页

作者： Korovin, S. K. Fursov, A. S. Moscow MV Lomonosov State Univ Moscow Russia

We consider the simultaneous stabilization problem for linear time-invariant stationary objects of arbitrary order. For such objects, we formulate numerically verifiable necessary and sufficient simultaneous stabilization conditions and show a constructive algorithm for the construction of a stabilizing controller with minimal restrictions on the structure and parameters of the stabilized objects. We give a general scheme of studying simultaneous stabilizability of a family of objects and analyze in detail a numerical algorithm for finding a stabilizing controller with applied interval analysis. To solve the problem, we use an approach based on the study of affine transformations of controller parameter spaces into the spaces of coefficients of denominators of closed-loop objects.

关键词： Concurrency Controllers algorithm CONSTRUCTION constructive algorithm

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Study transit network design for Rivera of Uruguay

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JOURNAL OF INTERDISCIPLINARY MATHEMATICS 2017年第8期20卷 1655-1659页

作者： Chao, Henry Cent Police Univ Dept Traff Sci Taoyuan Taiwan

We offer a complete examination for the paper of Mauttone and Urquhart that was published in Computers & Operations Research, Vol. 36, No. 8, 2440-2449 (2009), for a route set construction algorithm for the transit network design problem of the city Rivera, Uruguay. We point out several questionable results in Mauttone and Urquhart (2009) and then we provide possible revisions for those dubious findings that will help researchers develop better transportation plan in the future.

关键词： Transit network design problem constructive algorithm

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Constructing Node-Independent Spanning Trees in Augmented Cubes

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FUNDAMENTA INFORMATICAE 2020年第2期176卷 103-128页

作者： Cheng, Baolei Fan, Jianxi Lyu, Qiang Lin, Cheng-Kuan Li, Xiaoyan Chen, Guo Soochow Univ Sch Comp Sci & Technol Suzhou 215006 Peoples R China Fuzhou Univ Coll Math & Comp Sci Fuzhou 350116 Peoples R China

For a network, edge/node-independent spanning trees (ISTs) can not only tolerate faulty edges/nodes, but also be used to distribute secure messages. As important node-symmetric variants of the hypercubes, the augmented cubes have received much attention from researchers. The n-dimensional augmented cube AQ(n) is both (2n - 1)-edge-connected and (2n - 1)-nodeconnected (n not equal 3), thus the well-known edge conjecture and node conjecture of ISTs are both interesting questions in AQ(n). So far, the edge conjecture on augmented cubes was proved to be true. However, the node conjecture on AQ(n) is still open. In this paper, we further study the construction principle of the node-ISTs by using the double neighbors of every node in the higher dimension. We prove the existence of 2k - 1 node-ISTs rooted at node 0 in AQ(n)(vertical bar 00...0}/n-k (n >= k >= 4) by proposing an ingenious way of construction and propose a corresponding O(N logN) time algorithm, where N = 2(k) is the number of nodes in AQ(n)(vertical bar 00...0}/n-k.

关键词： Augmented cubes node-independent spanning trees constructive algorithm secure message distribution

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Distributed algorithms for the Lovasz Local Lemma and Graph Coloring 14

Distributed Algorithms for the Lovasz Local Lemma and Graph ...

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ACM Symposium on Principles of Distributed Computing (PODC)

作者： Chung, Kai-Min Pettie, Seth Su, Hsin-Hao Acad Sinica Taipei Taiwan Univ Michigan Ann Arbor MI 48109 USA

ISBN: (纸本)9781450329446

The Lovasz Local Lemma (LLL), introduced by Erd}os and Lovasz in 1975, is a powerful tool of the probabilistic method that allows one to prove that a set of n \bad" events do not happen with non-zero probability, provided that the events have limited dependence. However, the LLL itself does not suggest how to find a point avoiding all bad events. Since the work of Beck (1991) there has been a sustained effort to find a constructive proof (i.e. an algorithm) for the LLL or weaker versions of it. In a major breakthrough Moser and Tardos (2010) showed that a point avoiding all bad events can be found efficiently. They also proposed a distributed/parallel version of their algorithm that requires O (log2 n) rounds of communication in a distributed network. In this paper we provide two new distributed algorithms for the LLL that improve on both the efficiency and simplicity of the Moser-Tardos algorithm. For clarity we express our results in terms of the symmetric LLL though both algorithms deal with the asymmetric version as well. Let p bound the probability of any bad event and d be the maximum degree in the dependency graph of the bad events. When epd2 < 1 we give a truly simple LLL algorithm running in O(log 1=epd2 n) rounds. Under the tighter condition ep(d + 1) < 1, we give a slightly slower algorithm running in O(log2 d . log 1=ep(d+1) n) rounds. Furthermore, we give an algorithm that runs in sublogarithmic rounds under the condition p . f (d) < 1, where f (d) is an exponential function of d. Although the conditions of the LLL are locally verifiable, we prove that any distributed LLL algorithm requires Omega(log* n) rounds. In many graph coloring problems the existence of a valid coloring is established by one or more applications of the LLL. Using our LLL algorithms, we give logarithmic-time distributed algorithms for frugal coloring, defective coloring, coloring girth-4 (triangle-free) and girth-5 graphs, edge coloring, and list coloring.

关键词： Lovasz Local Lemma distributed graph coloring constructive algorithm probabilistic method locality

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