| Project/Area Number |
11650448
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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 | KOBE UNIVERSITY |
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Principal Investigator |
OHTA Yuzo Kobe University Faculty of Engineering Professor, 工学部, 教授 (80111772)
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| Co-Investigator(Kenkyū-buntansha) |
MASUBUCHI Izumi Kobe University Faculty of Engineering Research Associate, 工学部, 助手 (90283150)
藤崎 泰正 神戸大学, 工学部, 助教授 (30238555)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Computational geometry / Operations on sets / Robust control / Nonlinear Control / Switched systems / Polygon interval arithmetic / Piecewise linear Lvapunov functions / Linear matrix inequalities |
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| Research Abstract |
The main results obtained through the research are summarized as follows.
1. Development of CAD system for robust controllers design of linear systems.
We developed a CAD system for robust controllers design of linear systems using value sets. For systems which has completely decomposable transfer functions and/or characteristic equations, the method using polygon interval arithmetic is very useful to compute value sets. We proposed and implemented a method computing value sets of multi-polynomial functions, which need not be completely decomposable.
2. Generation of piecewise linear Lyapunov functions.
We proposed a new class of piecewise linear Lyapunov functions (PWLLFs) and derived stability results. A candidate of PWLLF has parameters corresponding to hyperplanes intersecting stability region. The set of stability conditions are formulated as Linear Programming Problem (LP) in terms of parameters inserted by the hyperplanes. If the computed optimal value is negative, we construct a PWLLF using the solution. When the optimal value of the LP is nonnegative, we modify the PWLLF candidate by adding appropriate hyperplanes to introduce more freedom in the LP formulation and arrive at the desired result. The optimal value of the resulting new LP is always less than or equal to that of the old LP.We also proposed a scheme to generate hyperplanes such that the optimal value of the new LPs is less than that of the old LP.Moreover, a fast method to compute the optimal solutoion of the new LP.
3. Data structure for Euclidean cell complex.
We proposed and implemented data structure for Euclidean cell complex. We used this data structure in programs for generation of PWLLFs and will be used for controller design using PWLLFs.
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