Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations
For optimal control problems subject to index-one differential-algebraic equations in semi-explicit form we discuss second order sufficient conditions in form of a coercivity condition taking into account the two-norm discrepancy. Furthermore we introduce a related Riccati-type and Legendre-Clebsch...
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| Published in | Set-valued and variational analysis Vol. 27; no. 2; pp. 405 - 431 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
15.06.2019
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1877-0533 1877-0541 |
| DOI | 10.1007/s11228-018-0471-x |
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| Abstract | For optimal control problems subject to index-one differential-algebraic equations in semi-explicit form we discuss second order sufficient conditions in form of a coercivity condition taking into account the two-norm discrepancy. Furthermore we introduce a related Riccati-type and Legendre-Clebsch condition which are sufficient for the validity of the coercivity condition. Using the implicit Euler-discretization we approximate the optimal control problem and analyze the convergence of solutions of the local minimum principle for the discretized optimal control problem by applying the general convergence framework of Stetter, which requires the discretization method to be continuous, consistent, and stable. |
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| AbstractList | For optimal control problems subject to index-one differential-algebraic equations in semi-explicit form we discuss second order sufficient conditions in form of a coercivity condition taking into account the two-norm discrepancy. Furthermore we introduce a related Riccati-type and Legendre-Clebsch condition which are sufficient for the validity of the coercivity condition. Using the implicit Euler-discretization we approximate the optimal control problem and analyze the convergence of solutions of the local minimum principle for the discretized optimal control problem by applying the general convergence framework of Stetter, which requires the discretization method to be continuous, consistent, and stable. |
| Author | Martens, Björn Gerdts, Matthias |
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| Keywords | Riccati-equation Optimal control Euler-discretization Second order sufficient conditions 65L80 65L20 Differential-algebraic equation 49K15 49J15 Convergence analysis Legendre-Clebsch |
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| SubjectTerms | Algebra Analysis Coercivity Control theory Convergence Differential equations Discretization Economic models Indexing Mathematical analysis Mathematics Mathematics and Statistics Optimal control Optimization |
| Title | Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations |
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