Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

DOI10.1007/s40314-013-0057-zzbMath1306.49008OpenAlexW2147223786MaRDI QIDQ2514047

Iguer Luis Domini dos Santos, Geraldo Nunes Silva

Publication date: 30 January 2015

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-013-0057-z

zbMATH Keywords

optimal controltime scalesFilippov's measurable selection theorem

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Existence theories for optimal control problems involving ordinary differential equations (49J15) Dynamical systems in control (37N35) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (6)

On Hölder calmness and Hölder well-posedness for optimal control problems ⋮ A distributed optimization algorithm over Markov switching topology under adversarial attack ⋮ Interval consensus of variable quantity multi-agent systems under complex topology ⋮ Discontinuous dynamic equations on time scales ⋮ Filippov-Pliss lemma for dynamical inclusions on a time scale ⋮ On qualitative and quantitative results for solutions to first-order dynamic equations on time scales

Cites Work

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• A unified theory of maximum principle for continuous and discrete time optimal control problems
• Positive periodic solutions and optimal control for a distributed biological model of two interacting species
• Transversality conditions for infinite horizon variational problems on time scales
• Coexistence and optimal control problems for a degenerate predator-prey model
• Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems
• Systems of first order inclusions on time scales
• Hamilton-Jacobi-Bellman equations on time scales
• The existence of optimal controls
• Necessary conditions of optimality for a class of optimal control problems on time scales
• Avoidance control on time scales
• Weak maximum principle and accessory problem for control problems on time scales
• Necessary conditions for a class of optimal control problems on time scales
• On existence of optimal control governed by a class of the first-order linear dynamic systems on time scales
• Differential inclusions and optimal control
• Convex analysis and measurable multifunctions
• Calculus of variations on time scales: Weak local piecewise \(C_{\text{rd}}^{1}\) solutions with variable endpoints.
• Dynamic equations on time scales: A survey
• On open-loop and feedback attainability of a closed set for nonlinear control systems
• First order dynamic inclusions on time scales
• Absolute continuity and existence of solutions to dynamic inclusions in time scales
• First order conditions for generalized variational problems over time scales
• Existence of solutions for second-order dynamic inclusions
• Existence results for dynamic inclusions on time scales with nonlocal initial conditions
• Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives
• First and second order linear dynamic equations on time scales
• Existence results for impulsive dynamic inclusions on time scales
• Nonlinear dynamic systems and optimal control problems on time scales
• On Certain Questions in the Theory of Optimal Control
• Criterions for absolute continuity on time scales

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