Network Design for Controllability Metrics

被引:8
作者
Becker, Cassiano O. [1 ]
Pequito, Sergio [2 ]
Pappas, George J. [1 ]
Preciado, Victor M. [1 ]
机构
[1] Univ Penn, Dept Elect & Syst Engn, Philadelphia, PA 19104 USA
[2] Rensselaer Polytech Inst, Dept Ind & Syst Engn, Troy, NY 12180 USA
来源
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS | 2020年 / 7卷 / 03期
基金
美国国家科学基金会;
关键词
Bilinear matrix equality; controllability Gramian; convex optimization; network design; networked dynamics; STRUCTURAL CONTROLLABILITY; DYNAMICAL NETWORKS; OBSERVABILITY; ALLOCATION; SYSTEMS;
D O I
10.1109/TCNS.2020.2978118
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this article, we consider the problem of tuning the edge weights of a networked system described by linear time-invariant dynamics. We assume that the topology of the underlying network is fixed, and that the set of feasible edge weights is a given polytope. In this setting, we first consider a feasibility problem consisting of tuning the edge weights such that certain controllability properties are satisfied. The particular controllability properties under consideration are 1) a lower bound on the smallest eigenvalue of the controllability Gramian and 2) an upper bound on the trace of the Gramian inverse. In both cases, the edge-tuning problem can be stated as a feasibility problem involving bilinear matrix equalities, which we approach using a sequence of convex relaxations. Furthermore, we also address a design problem consisting of finding edge weights able to satisfy the aforementioned controllability constraints while seeking to minimize a cost function of the edge weights, which we assume to be convex. Finally, we verify our results with numerical simulations over a number of random network realizations, as well as with an IEEE 14-bus power system topology.
引用
收藏
页码:1404 / 1415
页数:12
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