We present a voting system that is based on an iterative method that assigns a reputation to n + m items, a objects and m raters, applying sonic filter to the votes. Each racer evaluates a Subset of objects leading to...
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ISBN:
(纸本)9783642028939
We present a voting system that is based on an iterative method that assigns a reputation to n + m items, a objects and m raters, applying sonic filter to the votes. Each racer evaluates a Subset of objects leading to an n x in rating matrix with a given sparsity pattern. From this rating matrix a formula is defined for the reputation of raters and objects. We propose a natural and intuitive nonlinear formula and also provide an iterative algorithm that linearly converges to the unique vector oh reputations and this for any rating matrix. In contrast to classical outliers detection, no evaluation is discarded in this method but cash one is taken into account with different weights for the reputations of the objects. The complexity of one iteration step is linear in the number of evaluations, making our algorithm efficient for large data set.
The finite horizon Linear-Quadratic (LQ) optimal control problem with nonnegative state constraints (denoted by LQ(+)) is studied for positive linear systems in discrete time. Necessary and sufficient optimality condi...
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ISBN:
(纸本)9783642028939
The finite horizon Linear-Quadratic (LQ) optimal control problem with nonnegative state constraints (denoted by LQ(+)) is studied for positive linear systems in discrete time. Necessary and sufficient optimality conditions arc obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ+ problem by means of a corresponding Hamiltonian system. In addition, necessary and sufficient conditions arc reported for the LQ(+)-optimal control to he given by the standard LQ-optimal state feedback law. Sufficient conditions are also reported for the positivity of the LQ-optimal closed-loop system. In particular, such conditions arc Obtained for the problem of minimal energy control with penalization of the final state. Moreover a positivity criterion for the LQ-optimal closed-loop system is derived for positive systems with a positively invertible (dynamics) generator
This paper considers the servomechanism problem for MIMO positive LTI systems. In particular, the servomechanism problem of nonnegative constant reference signals for stable MIMO positive LTI systems with unmeasurable...
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ISBN:
(纸本)9783642028939
This paper considers the servomechanism problem for MIMO positive LTI systems. In particular, the servomechanism problem of nonnegative constant reference signals for stable MIMO positive LTI systems with unmeasurable Unknown constant nonnegative disturbances under strictly nonnegative control inputs is solved using a clamping LQ regulator.
The eigenvalues of a matrix polynomial can be determined classically by solving a generalized eigenproblem for a linearized matrix pencil, for instance by writing the matrix polynomial in companion form. We introduce ...
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ISBN:
(纸本)9783642028939
The eigenvalues of a matrix polynomial can be determined classically by solving a generalized eigenproblem for a linearized matrix pencil, for instance by writing the matrix polynomial in companion form. We introduce a general scaling technique, based on tropical algebra, which applies in particular to this companion form. This scaling, which is inspired by all earlier work of Akian, Bapat, and Gaubert, relics oil the computation of "tropical roots". We give explicit hounds, in a typical case, indicating that these roots provide accurate estimates of the order of magnitude of the different eigenvalues, and we show by experiments that this scaling improves the accuracy (measured by normwise backward error) of the computations, particularly in situations in which the data have various orders of magnitude. In the case of quadratic polynomial matrices, we recover in this way a scaling due to Fail, Lin, and Van Dooren, which coincides with the tropical scaling when the two tropical roots are equal. If not the eigenvalues generally split in two groups, and the tropical method leads to making one specific scaling for each of the groups.
Identifiability is a fundamental prerequisite for model identification. Differential algebra tools have been applied to Study identifiability of dynamic systems described by nonlinear polynomial equations. In a previo...
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ISBN:
(纸本)9783642028939
Identifiability is a fundamental prerequisite for model identification. Differential algebra tools have been applied to Study identifiability of dynamic systems described by nonlinear polynomial equations. In a previous paper a differential algebra method for testing identifiability for locally and globally non accessible systems has been proposed. In this paper we describe a strategy to simplify the above differential algebra method to test identifiability of systems which are non accessible from everywhere. In particular we make the method more efficient and thus of snore general applicability. A strategy for testing identifiability also of nonlinear models described by non polynomial equations is proposed.
In the paper, the k-switching reachability set R-k of a continuous-tune positive switched system is introduced, and a necessary and sufficient condition for the chain of this sets {R-k,k is an element of N} to stop in...
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ISBN:
(纸本)9783642028939
In the paper, the k-switching reachability set R-k of a continuous-tune positive switched system is introduced, and a necessary and sufficient condition for the chain of this sets {R-k,k is an element of N} to stop increasing after some finite index k is given. It is shown that, for special classes of (multiple-input) positive switched systems, reachability always ensures that R-n = R-+(n), n being the system dimension.
We give a survey of delectability, observability and reconstructability concepts for positive systems and sketch some applications to the analysis of stochastic equations.
ISBN:
(纸本)9783642028939
We give a survey of delectability, observability and reconstructability concepts for positive systems and sketch some applications to the analysis of stochastic equations.
In [Jain, Tynan, Linear Algebra and its Applications 379, 381-394, 2004], the authors shown that a nonnegative square matrix A satisfies that AA(#) >= O, being A(#) the group inverse of A, if and only if A is permu...
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ISBN:
(纸本)9783642028939
In [Jain, Tynan, Linear Algebra and its Applications 379, 381-394, 2004], the authors shown that a nonnegative square matrix A satisfies that AA(#) >= O, being A(#) the group inverse of A, if and only if A is permutationally similar to a matrix with a special Structure. In this paper, a similar Structure for this kind of matrices, slightly simplified, is presented, where the restriction of the nonnegativity of the matrix A is omitted. In addition, this result to characterize the {k}-group involutory matrices is applied.
A nonsingular real matrix A is said to be inverse-positive if all the elements of its inverse are nonnegative. This class of matrices contains the M-matrices, from which inherit some of their properties and applicatio...
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ISBN:
(纸本)9783642028939
A nonsingular real matrix A is said to be inverse-positive if all the elements of its inverse are nonnegative. This class of matrices contains the M-matrices, from which inherit some of their properties and applications, especially in Economy. In this work we analyze the inverse-positive concept for a particular type of pattern: the checkerboard pattern. In addition, we study the Hadamard product of certain classes of inverse-positive matrices whose entries have a particular sign pattern.
The problem of synthesizing stabilizing state-feedback controllers is solved when the closed-loop system is required to remain positive, for the class of 2-D linear systems described by the Fornasini-Marchesini second...
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ISBN:
(纸本)9783642028939
The problem of synthesizing stabilizing state-feedback controllers is solved when the closed-loop system is required to remain positive, for the class of 2-D linear systems described by the Fornasini-Marchesini second model. First, a constructive necessary and sufficient condition expressed as a Linear Programming problem is provided for stabilization of these systems when the states must be nonnegative (assuming that the boundary conditions are nonnegative). It is shown how it is simple to include additional constraints (such as positive controls). Moreover, this result is also extended to include uncertainty in the model, making possible to synthesize robust state-feedback controllers, solving Linear Programming problems. Some numerical examples are included to illustrate the proposed approach for different design problems.
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