2003 Fiscal Year Final Research Report Summary
Study on the construction of control theory by the notion of invariance and the development of its introductory course
| Project/Area Number |
13650479
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Control engineering
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| Research Institution | Hokkaido University |
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Principal Investigator |
SHIMA Masasuke Hokkaido Univ., Graduate School of Eng., Prof., 大学院・工学研究科, 教授 (10029457)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOMICHI Masahiro Miyazaki Univ., Faculty of Eng., Asso.Prof., 工学部, 助教授 (30274773)
KAWAMURA Takeshi Kitami Inst.of Tech., Dep.of Electrical and Electronic Eng., Asso.Prof., 電気電子工学科, 助教授 (80234128)
ISURUGI Yoshihisa Hokkaido Univ., Graduate School of Eng., Asso.Prof., 大学院・工学研究科, 助教授 (00109480)
YAMASHITA Yuu Nara Inst.of Science and Tech., Graduate School of Inf.Sciences, Asso.Prof., 情報科学研究科, 助教授 (90210426)
ENOMOTO Ryuji Toba National College of Maritime Tech., Control and Information Tech Dept., Asso.Prof., 制御情報工学科, 助教授 (90203645)
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| Project Period (FY) |
2001 – 2003
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| Keywords | invariance / robust stability / monotonicity / Lie algebra / constrained system / singular optimal control / canonical equation / variational expression |
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| Research Abstract |
Firstly, the role of invariance in the control theory is studied [1]Invariance with respect to the variation of parameters : Using Frazer-Duncan theorem and monotonicity conditions, we derived a necessary and sufficient condition for the stability of linear systems without regard to the variation of interval parameters, and presented a monotonization method for the system which is not monotone. [2]Feedback design considering structures of Lie algebra : Feedback stabilization and improvement of tracking properties ties are studied for the under actuated mechanical systems such as axi-symmetric underactuated aircraft and PVTOL aircraft [3]Invriant formulation of design theory using invariance condition : Modem trends of studies of analytical dynamics with constraints are surveyed with focus to Poisson geometry, Lie algebroid and applications to control theory [4]Invariance optimality and Lie algebra : The existence region of optimal singular trajectories is classified by the dimensions of accessibility algebra, state space and input space A condition of optimality of Bang-bang control, conditions for the existence of optimal singular controllers and an approximation method of time optimal control are presented. Secondly, considering the shove results, we looked for the possibility of unified theory [5]Structure of control theory and development of an introductory course : Using the canonical equations and variations of inputs and initial conditions, we derived a variational expression of performance criterion or output and found that the expression is very convenient to survey the whole structure of control theory and has the possibility of constructing an introductory course to control theory. This is the main objective of this study attained in the last stage, though the whole contents are not prepared yet.
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