L0 norm constraint based external control source allocation for the minimum cost control of directed networks. (May 2018)

• Record Type: Journal Article
• Authors: Deng, Lei; Li, Guoqi; Pei, Jing; Huang, Jiangshuai
• Is Part Of: ISA transactions. Volume 76(2018)
• Page Start: 88
• Page End: 96
• Publication Date: 2018-05
• Subjects: Minimum cost control -- Directed networks -- L0 norm -- Probabilistic projection -- Key nodes selection; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2018.03.009
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: Locating a pre-given number of key nodes that are connected to external control sources so as to minimize the cost of controlling a directed network x ̇ ( t ) = A x ( t ) + B u ( t ), known as the minimum cost control problem, is of critical importance. Considering a network consisting of N nodes with M external control sources, the state of art techniques employ iterative searching to determine the input matrix B that characterizes how nodes are connected to external control sources, in a matrix space R N × M . The nodes having M largest values of a defined importance index are selected as key nodes. However, such techniques may suffer from large performance penalty in some networks due to the diversity of real-life networks. To address this outstanding issue, we propose an iterative method, termed " L 0 -norm constraint based projected gradient method" (LPGM). We probabilistically search the input matrix in each iteration by restricting its L 0 norm as a fixed value M, which implies that each control source is always only connected to a single key node during the whole searching process. Simulation results show that the solution always efficiently approaches a suboptimal key node set in a few iterations. These results provide a new point of view regarding the key nodes selection in the minimum cost control of directed networks. Highlights: Formulating a minimum-cost control problem on how to allocate control sources onto key nodes for one-to-one connection. An iterative method termed L0-norm constraint based projected gradient method (LPGM), is proposed to solve the problem. Probabilistic projection is applied for switching between a full matrix space and the one under L0-norm constraint. LPGM is physically plausible and shall pave the way for its applications in practical large scale complex networks.