Stability analysis of an aperiodic sampled-data control system is considered for application to network and embedded control. The stability condition is described in a linear matrix inequality to be satisfied for all ...
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ISBN:
(纸本)9781424438723
Stability analysis of an aperiodic sampled-data control system is considered for application to network and embedded control. The stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals. Although this condition is numerically intractable, a tractable sufficient condition can be constructed with the mean value theorem. Special attention is paid to tightness of the sufficient condition for less conservative stability analysis. A region-dividing technique for reduction of conservatism and generalization to stabilization are also discussed. Examples show the efficacy of the approach.
The track-to-track association problem is to determine the pairing of sensor-level tracks that correspond to the same true target from which the sensor-level tracks originated. This problem is crucial for multisensor ...
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ISBN:
(纸本)9780982443804
The track-to-track association problem is to determine the pairing of sensor-level tracks that correspond to the same true target from which the sensor-level tracks originated. This problem is crucial for multisensor data fusion and is complicated by the presence of individual sensor biases, random errors, false tracks, and missed tracks. A popular approach to performing track-to-track association between two sensor systems is to jointly optimize the a posteriori relative bias estimate between the sensors and the likelihood of track-to-track association. Algorithms that solve this problem typically generate the K best bias-association hypotheses and corresponding bias-association likelihoods. In this paper, we extend the above approach in two ways. First, we derive a closed-form expression for computing "pure" track-to-track association likelihoods, as opposed to bias-association likelihoods which are weighted by a unique relative bias estimate. Second, we present an alternative formulation of the track-to-track association problem in which we optimize solely with respect to association likelihoods. These results facilitate what is commonly known as system-level track ambiguity management.
This paper proposes an identification method for linear systems with roughly quantized outputs. Measurement data sampled from low resolution sensors have large quantization errors, which deteriorate the identification...
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ISBN:
(纸本)9781424427932
This paper proposes an identification method for linear systems with roughly quantized outputs. Measurement data sampled from low resolution sensors have large quantization errors, which deteriorate the identification accuracy. While the identification problem is formulated into quadratic programming with uncertainty, a proposed method provides an approximate optimal solution via semidefinite programming. Numerical examples demonstrate that we can estimate both plant parameters and true outputs in practical time and show the effectiveness of the proposed method.
One of the strongest techniques available for showing lower bounds on bounded-error communication complexity is the logarithm of the approximation rank of the communication matrix-the minimum rank of a matrix which is...
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ISBN:
(纸本)9780769537177
One of the strongest techniques available for showing lower bounds on bounded-error communication complexity is the logarithm of the approximation rank of the communication matrix-the minimum rank of a matrix which is close to the communication matrix in l(infinity) norm. Krause showed that the logarithm of approximation rank is a lower bound in the randomized case, and later Buhrman and de Wolf showed it could also be used for quantum communication complexity. As a lower bound technique, approximation rank has two main drawbacks: it is difficult to compute, and it is not known to lower bound the model of quantum communication complexity with entanglement. Linial and Shraibman recently introduced a quantity, called gamma(alpha)(2), to quantum communication complexity, showing that it can be used to lower bound communication in the model with shared entanglement. Here alpha is a measure of approximation which is related to the allowable error probability of the protocol. This quantity can be written as a semidefinite program and gives bounds at least as large as many techniques in the literature, although it is smaller than the corresponding alpha-approximation rank, rk(alpha). We show that in fact log gamma(alpha)(2)(A) and log rk(alpha)(A) agree up to small factors. As corollaries we obtain a constant factor polynomial time approximation algorithm to the logarithm of approximation rank, and that the logarithm of approximation rank is a lower bound for quantum communication complexity with entanglement.
With the work of Khot and Vishnoi [18] as a starting point, we obtain integrality gaps for certain strong SDP relaxations of UNIQUE GAMES. Specifically, we exhibit a UNIQUE GAMES gap instance for the basic semidefinit...
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ISBN:
(纸本)9780769538501
With the work of Khot and Vishnoi [18] as a starting point, we obtain integrality gaps for certain strong SDP relaxations of UNIQUE GAMES. Specifically, we exhibit a UNIQUE GAMES gap instance for the basic semidefinite program strengthened by all valid linear inequalities on the inner products of up to exp(Omega(log log n)(1/4)) vectors. For a stronger relaxation obtained from the basic semidefinite program by R rounds of Sherali-Adams lift-and-project, we prove a UNIQUE GAMES integrality gap for R = Omega(log log n)(1/4). By composing these SDP gaps with UGC-hardness reductions, the above results imply corresponding integrality gaps for every problem for which a UGC-based hardness is known. Consequently, this work implies that including any valid constraints on up to exp(Omega(log log n)(1/4)) vectors to natural semidefinite program, does not improve the approximation ratio for any problem in the following classes: constraint satisfaction problems, ordering constraint satisfaction problems and metric labeling problems over constant-size metrics. We obtain similar SDP integrality gaps for BALANCED SEPARATOR, building on [11]. We also exhibit, for explicit constants gamma;delta > 0, an n-point negative-type metric which requires distortion Omega(log log n)(gamma) to embed into l(1), although all its subsets of size exp(Omega(log log n)(delta)) embed isometrically into l(1).
We consider the problem of evaluating the probability of error of binary communication systems in the presence of additive noise and intersymbol interferences whose statistics are inexactly known due to the estimation...
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We consider the problem of evaluating the probability of error of binary communication systems in the presence of additive noise and intersymbol interferences whose statistics are inexactly known due to the estimation errors of the channel coefficients. We present a new method using semidefinite programming to evaluate tight bounds on the error probability based on the upper and lower bounds on the moments of those interferences. Numerical results are provided and compared with a previously published technique.
Existing global optimization techniques for nonconvex quadratic programming (QP) branch by recursively partitioning the convex feasible set and thus generate an infinite number of branch-and-bound nodes. An open quest...
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Existing global optimization techniques for nonconvex quadratic programming (QP) branch by recursively partitioning the convex feasible set and thus generate an infinite number of branch-and-bound nodes. An open question of theoretical interest is how to develop a finite branch-and-bound algorithm for nonconvex QP. One idea, which guarantees a finite number of branching decisions, is to enforce the first-order Karush-Kuhn-Tucker (KKT) conditions through branching. In addition, such an approach naturally yields linear programming (LP) relaxations at each node. However, the LP relaxations are unbounded, a fact that precludes their use. In this paper, we propose and study semidefinite programming relaxations, which are bounded and hence suitable for use with finite KKT-branching. Computational results demonstrate the practical effectiveness of the method, with a particular highlight being that only a small number of nodes are required.
For a given schedule of a round-robin tournament and a matrix of distances between homes of teams, an optimal home-away assignment problem is to find a home-away assignment that minimizes the total traveling distance....
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ISBN:
(纸本)3540262245
For a given schedule of a round-robin tournament and a matrix of distances between homes of teams, an optimal home-away assignment problem is to find a home-away assignment that minimizes the total traveling distance. We propose a technique to transform the problem to MIN RES CUT. We apply Goemans and Williamson's 0.878-approximation algorithm for MAX RES CUT, which is based on a positive semidefinite programming relaxation, to the obtained MIN RES CUT instances. Computational experiments show that our approach quickly generates solutions of good approximation ratios.
Abstract Analysis and safety considerations of chemical and biological processes frequently require an outer approximation of the set of all feasible steady-states. Nonlinearities, uncertain parameters, and discrete v...
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Abstract Analysis and safety considerations of chemical and biological processes frequently require an outer approximation of the set of all feasible steady-states. Nonlinearities, uncertain parameters, and discrete variables complicate the calculation of guaranteed outer bounds. In this paper, the problem of outer-approximating the region of feasible steady-states, for processes described by uncertain nonlinear differential algebraic equations including discrete variables and discrete changes in the dynamics, is adressed. The calculation of the outer bounding sets is based on a relaxed version of the corresponding feasibility problem. It uses the Lagrange dual problem to obtain certificates for regions in state space not containing steady-states. These infeasibility certificates can be computed efficiently by solving a semidefinite program, rendering the calculation of the outer bounding set computationally feasible. The derived method guarantees globally valid outer bounds for the steady-states of nonlinear processes described by differential equations. It allows to consider discrete variables, as well as switching system dynamics. The method is exemplified by the analysis of a simple chemical reactor showing parametric uncertainties and large variability due to the appearance of bifurcations characterising the ignition and extinction of a reaction.
We reduce the approximation factor for the vertex cover to 2 - Theta(1/root log n) (instead of the previous 2 - Theta lnlnn/2lnn obtained by Bar-Yehuda and Even [1985] and Monien and Speckenmeyer [1985]). The improvem...
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We reduce the approximation factor for the vertex cover to 2 - Theta(1/root log n) (instead of the previous 2 - Theta lnlnn/2lnn obtained by Bar-Yehuda and Even [1985] and Monien and Speckenmeyer [1985]). The improvement of the vanishing factor comes as an application of the recent results of Arora et al. [2004] that improved the approximation factor of the sparsest cut and balanced cut problems. In particular, we use the existence of two big and well-separated sets of nodes in the solution of the semidefinite relaxation for balanced cut, proven by Arora et al. [2004]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big well-separated sets in the sense of Arora et al. [2004] translates into the existence of a big independent set.
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