1998 Fiscal Year Final Research Report Summary
Research on analysis and synthesis method of nonlinear control systems based on gain scheduling theory
| Project/Area Number |
09650490
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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 |
計測・制御工学
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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) |
1997 – 1998
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| Keywords | gain scheduling / nonlinear control / L^2 gain / LMI / hidden loop problem |
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| Research Abstract |
To establish the solution method and the design algorithm for nonlinear control problems, we investigated stability analysis and synthesis problems, control problems with L^2 gain performance and robust control problems. First, using an extended quadratic Lyapunov function which reflects a special structure of model, we proposed design methods of state feedback control and output feedback control. Through simulation studies in real system models, we showed efficiencies of the proposed method. As for the solution method of parameter-dependent linear matrix inequalities which appear in the proposed method, we also proposed a new solution method via finite-dimensional linear matrix inequalities, which borrows an idea of solution method of linear matrix inequalities in gain scheduling algorithms. Next, focusing on a special type of nonlinear systems which have kth-degree polynomial type of nonlinearlity, we developed a new analysis method of L^2 gain of nonlinear systems based on reachable sets and fin ite-dimensional linear matrix inequalities. The main point of our approach to nonlinear control problems is to consider full state or a part of state of nonlinear systems as a scheduling parameter and to apply analysis and synthesis methods for linear systems to the linear systems with scheduling parameter. In this approach, one problem which arises is how to estimate a priori the range of scheduling parameter and/or the range of the variation of scheduling parameter. We succeeded also in developing an solution method for this problem.
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