書誌事項
- タイトル別名
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- Design of Nonlinear Optimal Regulators Using a Riemannian Metric Quadratic Performance
抄録
Differential geometric approach is useful for solving a special class of nonlinear control problems. The purpose of this paper is to present a linearization method of nonlinear systems by the Riemannian geometric approach, and to apply the linearization mapping to the design of nonlinear systems.<br>A geomeric model can be derived by replacing the orthogonal straight coordinate frame on the state space with a suitable curvilinear frame. Such a Riemannian geometric model has been proposed by the authors after the derivation of the geodesic curve on the gravitational gauge field in Einstein's principle of general relativity.<br>In this paper an attention is placed on a problem to decrease the dimension of the Riemannian space of the model by a proper choice of the construction of the space, which leads to decrease the computation time remarkably. For the design of control systems, a new quadratic-form performance index is introduced using Riemannian metric tensors. A nonlinear optimal regulator is constructed which is homeomorphic to the corresponding linear optimal regulator. A method to derive a curvilinear coordinates frame fitted to the nonlinear system is proposed by solving a partial differential equation with respect to the homeomorphism. A computational algorithm is proposed and numerical examples are shown.
収録刊行物
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- 計測自動制御学会論文集
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計測自動制御学会論文集 33 (6), 461-468, 1997
公益社団法人 計測自動制御学会
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詳細情報 詳細情報について
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- CRID
- 1390282679476471040
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- NII論文ID
- 130003791231
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- ISSN
- 18838189
- 04534654
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- データソース種別
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- JaLC
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- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可