計数工学科 システム情報談話会

投稿日:2007/05/05投稿者:小野順貴
東京大学工学部計数工学科 システム情報談話会

日時:2006年5月22日(火) 11:00--12:30

場所:東京大学工学部6号館 3階セミナー室A (本郷キャンパス)
   (アクセス)

講師:Brian D. O. Anderson 教授 
     (Research School of Information  Sciences and Engineering, 
      Australian National University) 

題目:Solution of a distributed formation stabilization problem

概要:
This talk deals with a formation stabilization problem. 
The formations  considered comprise a collection of point agents 
in the plane. One agent is the leader of the formation, another 
agent termed the first follower is required to maintain a nominated 
distance from the leader, and the remaining agents of the formation 
are required to maintain two nominated distances from two other agents, 
which may include the leader or the first follower. Motions of the 
formation consistent with maintaining all these distances then 
correspond to translation or rotation of the formation as a whole. 

Decentralized control laws are needed to restore distance values when 
they are perturbed away from their nominal. We explain how to formulate 
the control problem, and present it in the following linear algebra 
terms: Given a real square matrix A, when is there a real diagonal 
matrix Lambda such that Lambda x A has all its eigenvalues with negative 
real part, and how may such a matrix be constructed? A sufficient 
condition (which in a sense is not ‘far’ from a necessary condition) 
is obtained, involving the principal minors of A, and it is fulfilled 
in the application problem. Some associated open problems are also exposed. 


連絡先:  原 辰次    (shinji_hara@ipc.i.u-tokyo.ac.jp)
         小島千昭   (chiaki_kojima@ipc.i.u-tokyo.ac.jp)