2000 Fiscal Year Final Research Report Summary
Studies on Analysis and Synthesis of Control Systems Based on Infinite-Dimensional Linear Matrix Inequalities
| Project/Area Number |
11650456
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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 | Waseda University |
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Principal Investigator |
UCHIDA Kenko Waseda University, School of Science and Engineering. Professor, 理工学部, 教授 (80063808)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Analysis of controlled system / Controller synthesis / Infinite-dimensional LMI / Hidden-loop problem / Gain scheduling / Linear time-delay system / Uncertain parameter / L2 gain |
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| Research Abstract |
In this research we established a unified methodology of analysis and control synthesis for linear systems with uncertain parameters, uncertain but measurable parameters (scheduling parameters), and spatially distributed parameters. The proposed algorithm is based on infinite-dimensional linear matrix inequalities which are sufficient conditions not only for analysis of prescribed performances, e.g. stability and input-output L2 gain but also for solvability of control synthesis which realizes prescribed performances. The Linear system with scheduling parameters, which is a special case of the systems we consider, can describe a class of nonlinear systems by taking some internal variables as scheduling parameters, but this description leads generally to a hard problem in analysis and control synthesis, called the "hidden-loop problem". The proposed algorithm succeeds in overcoming the hidden-loop problem by introducing the linear matrix inequality that characterizes a reachable set of state. As linear systems with spatially distributed parameters, in particular, we discuss linear time-delay systems, and propose an algorithm based on the particular type of infinite-dimensional linear matrix inequalities that depend on the time-delay parameter. We also proposed a reduction method of the infinite-dimensional linear matrix inequality to a finite-dimensional matrix inequality. The main point of the reduction method is to construct a convex polyhedron in parameter space, and is an extension of the idea that the present researcher used previously in the problem of gain scheduling. Efficacy of the proposed algorithm was demonstrated through numerical simulations and experiments.
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Research Products
(12 results)
