2016/10/11 by Tong Zhou, Zhou, Tong
Computer Science · Engineering · Mathematics · #Cybersecurity and Information Systems #Distributed Control Multi-Agent Systems #Stability and Control of Uncertain Systems #math.DS #math.OC
paper · pdf · doi:10.48550/arxiv.1610.03143
7 Pages
arxiv created 2016/10/11 · arxiv updated 2016/10/12
A new proof is given for the mathematical equivalence among three k-sparse controllability problems of a networked system, which plays key roles in Olshevsky,2014, in the establishment of the NP-hardness of the associated minimal controllability problems (MCP). Compared with the available ones, a completely deterministic approach is adopted. Moreover, only primary algebraic operations are utilized in all the derivations. These results enhance the available conclusions about the NP-hardness of a MCP, and can also be directly applied to the computational complexity analysis for a minimal observability problem. In addition, the results of Olshevsky,2014, have also been extended to situations in which there are also some other restrictions, such as bounded element magnitude, etc., on the system input matrix.