Discrete optimal control: The accessory problem and necessary optimality conditions

DOI10.1006/jmaa.1999.6679zbMath0987.49016OpenAlexW2017804236MaRDI QIDQ1974236

Vera Zeidan, Roman Šimon Hilscher

Publication date: 24 October 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6679

zbMATH Keywords

discrete maximum principlenecessary conditions for optimalitydiscrete Hamiltonian systemdiscrete optimal controlJacobi systemdiscrete quadratic functionalaccessory problemconjugate interval

Mathematics Subject Classification ID

Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (10)

Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey ⋮ Differential stability of discrete optimal control problems with possibly nondifferentiable costs ⋮ Calculus of variations on time scales: Weak local piecewise \(C_{\text{rd}}^{1}\) solutions with variable endpoints. ⋮ Weak maximum principle and accessory problem for control problems on time scales ⋮ Coupled Intervals in the Discrete Optimal Control ⋮ Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions ⋮ Optimal control of a discrete-time plant-herbivore/pest model with bistability in fluctuating environments ⋮ Coupled intervals in the discrete calculus of variations: necessity and sufficiency ⋮ Discrete Optimal Control: Second Order Optimality Conditions ⋮ Second Order Sufficiency Criteria for a Discrete Optimal Control Problem

Cites Work

• Equivalence of discrete Euler equations and discrete Hamiltonian systems
• A discrete interpretation of Reid's roundabout theorem for generalized differential systems
• Disconjugacy and transformations for symplectic systems
• Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
• Necessary Conditions for Optimal Control Problems: Conjugate Points
• Sufficiency Criteria via Focal Points and via Coupled Points
• Positivity of Block Tridiagonal Matrices
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