2014 Fiscal Year Final Research Report
Commutative Algebraic Algorithms for Analysis and Control of Nonlinear Systems
| Project/Area Number |
24656263
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Control engineering
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| Research Institution | Kyoto University (2013-2014)
Osaka University (2012) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 非線形システム / 制御理論 / 可換環論 / 代数幾何 / システム解析 / 最適制御 |
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| Outline of Final Research Achievements |
Theory of analysis and control for nonlinear systems has been developed by applying commutative algebra and algebraic geometry mainly to discrete-time polynomial systems and rational systems. New sufficient conditions have been obtained for reachability and stability, and new solution methods have been obtained for finite-horizon optimal control problems. The implicit function representation of an optimal state feedback control is derived by recursive elimination of variables in the stationary conditions for an optimal control problem. Moreover, new results have also been obtained about algebraic construction of canonical forms and feedback controllers of nonlinear systems. In particular, a complete parameterization of static output feedback controllers has been obtained for a model matching problem. These results are expected to open new directions of research in nonlinear control theory.
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| Free Research Field |
制御工学
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