اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGramian-Based Model Reduction of Directed Networks
74
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and observability Gramians are proposed for semistable systems, and their solutions are characterized by Lyapunov-like equations. Then, we introduce a concept of vertex clusterability to guarantee the boundedness of the approximation error and use the newly proposed Gramians to facilitate the evaluation of the dissimilarity of each pair of vertices. An clustering algorithm is thereto provided to generate an appropriate graph clustering, whose characteristic matrix is employed as the projections in the Petrov-Galerkin reduction framework. The obtained reduced-order system preserves the weakly connected directed network structure, and the approximation error is computed by the pseudo Gramians. Finally, the efficiency of the proposed approach is illustrated by numerical examples.
قيم البحث
اقرأ أيضاً
The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the CME have
been proposed. In this work we focus on one such model, the Linear Noise Approximation. Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced order LNA converges to the full order model in the mean square sense. Using this as motivation we derive a network structure preserving reduction algorithm based on structured projections. We present convex optimisation algorithms that describe how such projections can be computed and we discuss when structured solutions exits. We also show that for a certain class of systems, structured projections can be found using basic linear algebra and no optimisation is necessary. The algorithms are then applied to a linearised stochastic LNA model of the yeast glycolysis pathway.
In this paper, we consider the problem of model order reduction of stochastic biochemical networks. In particular, we reduce the order of (the number of equations in) the Linear Noise Approximation of the Chemical Master Equation, which is often used
to describe biochemical networks. In contrast to other biochemical network reduction methods, the presented one is projection-based. Projection-based methods are powerful tools, but the cost of their use is the loss of physical interpretation of the nodes in the network. In order alleviate this drawback, we employ structured projectors, which means that some nodes in the network will keep their physical interpretation. For many models in engineering, finding structured projectors is not always feasible; however, in the context of biochemical networks it is much more likely as the networks are often (almost) monotonic. To summarise, the method can serve as a trade-off between approximation quality and physical interpretation, which is illustrated on numerical examples.
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these properties should b
e preserved by model reduction procedures, although traditional projection based approaches struggle to do this. We propose a projection based model reduction algorithm which uses generalised block diagonal Gramians to preserve structure and positivity. Two algorithms are presented, one provides more accurate reduced order models, the second provides easier to simulate reduced order models. The results are illustrated through numerical examples.
In this paper, we compare four measures of the empirical observability gramian, including the determinant, the trace, the minimum eigenvalue, and the condition number, which can be used to quantify the observability of system states and to obtain the
optimal PMU placement for power system dynamic state estimation. An adaptive optimal PMU placement method is proposed by automatically choosing proper measures as the objective function. It is shown that when the number of PMUs is small and thus the observability is very weak, the minimum eigenvalue and the condition number are better measures of the observability and are preferred to be chosen as the objective function. The effectiveness of the proposed method is validated by performing dynamic state estimation on an Northeast Power Coordinating Council (NPCC) 48-machine 140-bus system with the square-root unscented Kalman filter.
In this paper we examine a symmetric tensor decomposition problem, the Gramian decomposition, posed as a rank minimization problem. We study the relaxation of the problem and consider cases when the relaxed solution is a solution to the original prob
lem. In some instances of tensor rank and order, we prove generically that the solution to the relaxation will be optimal in the original. In other cases, we present interesting examples and approaches that demonstrate the intricacy of this problem.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
