Three singularities in control problems (Q2745856)
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scientific article; zbMATH DE number 1655342
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Three singularities in control problems |
scientific article; zbMATH DE number 1655342 |
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17 October 2002
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singular perturbation
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singular systems
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linear-quadratic optimal feedback design
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0.90178823
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0.8941741
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0.8903082
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0.8903082
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Three singularities in control problems (English)
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The linear-quadratic optimal feedback design for singular singularly-perturbed systems (SSPS) is considered. There are several sources of singularities.NEWLINENEWLINENEWLINEThe first one is connected with small parameters in the coefficients of the derivatives in the differential equations.NEWLINENEWLINENEWLINEThe second singularity shows up if the reduced DAE system has index \(>1\).NEWLINENEWLINENEWLINEAnd the last singularity is due to singularity of the weighting matrix in the performance criterion. The Tikhonov-Levinson theory, the standard time-scale modeling and the Riccati equation approach to the control problem do not apply for the SSPS. Therefore in the case of the design of a linear-quadratic optimal control, the related difficulties have to be considered. The interactions between singularities are studied and the different approaches to the optimal control design are explained.
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