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...
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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.
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...
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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.
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 prio...
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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.
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 ...
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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.
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 t...
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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.
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 stronge...
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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.
After Hironaka's monumental work, where an existential proof of resolution ofsingularities was given (cf. [11]), several alternative proofs have appeared. Some of them aresimplified non-constructive versions (cf. ...
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After Hironaka's monumental work, where an existential proof of resolution ofsingularities was given (cf. [11]), several alternative proofs have appeared. Some of them aresimplified non-constructive versions (cf. [1,2,6]), while others are constructive algorithms ofresolution of singularities (cf. [3,12,13,8,9,10]). The latter versions provide proofs ofdesingularization within Hironaka's line of development.
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 stabiliza...
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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.
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 transi...
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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.
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 augmente...
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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.
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