TY - JOUR
T1 - Analysis of robust performance with multiple objectives
AU - Ito, Hiroshi
AU - Ohmori, Hiromitsu
AU - Sano, Akira
PY - 1995/5/22
Y1 - 1995/5/22
N2 - Performance robustness with multiple objectives of linear control systems having structured norm-bounded uncertainty is considered. In order to deal with any two objective functions Ψ1 and Ψ2 associated with a single feedback control system, the combined criterion Ψ[Ψ1 ψ2]Ψ {slanted equal to or less-than}S 1 is often used. The paper, however, considers Ψ ψ1 Ψ ≤ 1 and Ψ W, 11 ≤ 1 directly. It is shown that it is possible to assess robust performance of two objectives by a single μ test if repeated nonscalar blocks are adequately introduced in the structure of μ. In other words, a performance robustness problem with multiple objectives is proved to be equivalent to a stability robustness problem with extra repeated uncertainty blocks. This equivalence theorem is applicable to various system and norm setups including sampled-data systems.
AB - Performance robustness with multiple objectives of linear control systems having structured norm-bounded uncertainty is considered. In order to deal with any two objective functions Ψ1 and Ψ2 associated with a single feedback control system, the combined criterion Ψ[Ψ1 ψ2]Ψ {slanted equal to or less-than}S 1 is often used. The paper, however, considers Ψ ψ1 Ψ ≤ 1 and Ψ W, 11 ≤ 1 directly. It is shown that it is possible to assess robust performance of two objectives by a single μ test if repeated nonscalar blocks are adequately introduced in the structure of μ. In other words, a performance robustness problem with multiple objectives is proved to be equivalent to a stability robustness problem with extra repeated uncertainty blocks. This equivalence theorem is applicable to various system and norm setups including sampled-data systems.
KW - Linear feedback systems
KW - Multi-objective control
KW - Robust performance
KW - Robust stability
KW - Structured singular value
KW - Structured uncertainty
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U2 - 10.1016/0167-6911(94)00067-6
DO - 10.1016/0167-6911(94)00067-6
M3 - Article
AN - SCOPUS:0029307531
SN - 0167-6911
VL - 25
SP - 141
EP - 149
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 2
ER -