2002 Fiscal Year Final Research Report Summary
Analysis and Design of Control Systems Utilizing Data Structure and Algorithms
| Project/Area Number |
13650487
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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 Hiroshima University, Graduate School of Engineering, Associate Professor, 大学院・工学研究科, 助教授 (90283150)
FUJISAKI Yasumasa Kbbe Universily, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30238555)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Computer Geometry / Piecewise Linear Lyapunov Function / Bilinear optimization Problem / Polytope Lyapunov Function / Switched Systems / Nonlinear Control / Robust Control / Bump-less Control |
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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 have 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 Ly apunov functions.
We proposed a new class of piecewise linear Lyapunov functions (PLLFs) and derived stability results. A candidate of PLLF 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
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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, we propose a fast method to compute the optimal solution 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 PLLFs and will be used for controller design using PLLFs
4. Solution method of bilinear optimization problems.
The main issue in designing controllers using PLLFs is to solve bilinear optimization problems, which is non-convex problems, and, hence, it is not so easy to solve. But we believe that the problem rather easy to solve that bilinear matrix inequality problems. We proposed a method using Zoutendijk method. We implement this method, but further research is needed to improve convergence of the method. Less
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