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）
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
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)