Convergence analysis of the implicit Euler-discretization and sufficient conditions for optimal control problems subject to index-one differential-algebraic equations

DOI10.1007/s11228-018-0471-xzbMath1419.49007OpenAlexW2793524867MaRDI QIDQ2316063

Björn Martens, Matthias Gerdts

Publication date: 26 July 2019

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-018-0471-x

zbMATH Keywords

convergence analysisoptimal controldifferential-algebraic equationsecond order sufficient conditionsRiccati-equationEuler-discretizationLegendre-Clebsch

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Existence theories for optimal control problems involving ordinary differential equations (49J15) Numerical methods for differential-algebraic equations (65L80) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (4)

Error estimates for Runge-Kutta schemes of optimal control problems with index 1 DAEs ⋮ Error Analysis for the Implicit Euler Discretization of Linear-Quadratic Control Problems with Higher Index DAEs and Bang–Bang Solutions ⋮ Convergence Analysis for Approximations of Optimal Control Problems Subject to Higher Index Differential-Algebraic Equations and Mixed Control-State Constraints ⋮ Convergence Analysis for Approximations of Optimal Control Problems Subject to Higher Index Differential-Algebraic Equations and Pure State Constraints

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation
• Optimal control of ODEs and DAEs.
• First and second order sufficient conditions for optimal control and the calculus of variations
• Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
• Second-order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hilbert spaces
• Runge-Kutta methods in optimal control and the transformed adjoint system
• Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions
• Second-order sufficient conditions for state-constrained optimal control problems
• Optimality, stability, and convergence in nonlinear control
• Second-order sufficient conditions for control problems with mixed control-state constraints
• Mathematical Systems Theory I
• Lipschitz Continuity for Constrained Processes
• First and second order sufficient optimality conditions in mathematical programming and optimal control
• Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems
• First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
• On the Time-Discretization of Control Systems
• Error bounds for euler approximation of a state and control constrained optimal control problem¹

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