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主 催：計測自動制御学会中部支部
日 時：平成17年3月16日(水) 11時00分〜12時00分
場 所：名古屋大学工学部
2号館 222講義室
講師：
Venkataramanan
Balakrishnan 教授
School of Electrical and Computer Engineering
Purdue University
概要：
Several important problems in systems and control theory can be reformulated
as semidefinite programming (SDP) problems, i.e., minimization of a linear
objective subject to Linear Matrix Inequality (LMI) constraints.
From convex optimization duality theory, conditions for infeasibility of the
LMIs as well as dual optimization problems can be formulated. These can in
turn be re-interpreted in control or system theoretic terms, often yielding
new results or new proofs for existing results from control theory.
We present such connections for a few problems associated with linear
time-invariant systems. We then turn to computational issues.
The reduction of a control problem to an SDP problem often requires a large
number of auxiliary variables, so that the resulting SDP problem can be very
large, even though the underlying control problem is not particularly
large-scale. This limits the problem sizes that can be handled by
general-purpose SDP solvers, and hence the applicability of SDP in practical
engineering problems. This is true for example with SDP problems where the
underlying LMIs have a special form that is typically encountered with the
application of the Kalman-Yakubovich-Popov (KYP) Lemma.
We discuss efficient implementations of primal-dual interior-point methods
for SDP problems with KYP LMIs, and show how orders-of-magnitude savings
in computation can be realized when problem structure is exploited using
straightforward linear algebra techniques.
連絡先：
名古屋大学大学院工学研究科
機械理工学専攻
藤本健治
Tel/Fax: 052-789-3854
