Determination of the non-trivial integrability conditions of implicit systems of differential equations and applications to optimal control (Q2783524)
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scientific article; zbMATH DE number 1730491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Determination of the non-trivial integrability conditions of implicit systems of differential equations and applications to optimal control |
scientific article; zbMATH DE number 1730491 |
Statements
17 April 2002
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maximum principle
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implicit differential equations
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jets
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Gröbner bases
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optimal control
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0.9295095
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0.92286503
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0.91268724
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0.91091204
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0.9105845
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Determination of the non-trivial integrability conditions of implicit systems of differential equations and applications to optimal control (English)
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This dissertation treats optimal control problems for implicit ordinary differential systems with mixed state and control constraints. A definition of complete system is offered based on jets. This leads to an algebraic theory which allows the author to use Gröbner bases in order to construct the completion of a system. Relations to the differential index are discussed. The contents are: Optimal control processes, Complete systems, Equivalent systems, Algorithmic determination of a complete system, Minimum principle for an implicit optimal control problem.
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