Second Order Sufficiency Criteria for a Discrete Optimal Control Problem

DOI10.1080/10236190290027684zbMath1010.49020OpenAlexW2027327044MaRDI QIDQ3148759

Vera Zeidan, Roman Šimon Hilscher

Publication date: 14 October 2002

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190290027684

zbMATH Keywords

conjugacysecond variationoptimality conditionaccessory problemaccessory systemoptimal control... discrete system

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Discrete-time control/observation systems (93C55) Linear-quadratic optimal control problems (49N10) Additive difference equations (39A10) Discrete version of topics in analysis (39A12) Optimality conditions (49K99)

Related Items (24)

Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals ⋮ On the no-gap second-order optimality conditions for a discrete optimal control problem with mixed constraints ⋮ Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints ⋮ Optimality Conditions in Discrete Optimal Control Problems with State Constraints ⋮ Geometric optimization and \(D^ P\)-completeness ⋮ Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey ⋮ Second-order sufficient optimality conditions for an optimal control problem with mixed constraints ⋮ Differential stability of discrete optimal control problems with possibly nondifferentiable costs ⋮ Second-order optimality conditions in a discrete optimal control problem ⋮ Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. ⋮ Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity ⋮ Optimality conditions for discrete calculus of variations problems ⋮ Optimality conditions for discrete optimal control problems with equality and inequality type of constraints ⋮ Sensitivity analysis for discrete optimal control problems ⋮ Optimality conditions for discrete optimal control problems ⋮ Weak maximum principle and accessory problem for control problems on time scales ⋮ Second-order necessary optimality conditions for an optimal control problem ⋮ Second-order necessary optimality conditions for a discrete optimal control problem ⋮ Coupled Intervals in the Discrete Optimal Control ⋮ Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions ⋮ 2-Regularity and 2-Normality Conditions in Discrete Optimal Control Problems ⋮ Coupled intervals in the discrete calculus of variations: necessity and sufficiency ⋮ Second-order necessary optimality conditions for a discrete optimal control problem ⋮ Second-order necessary optimality conditions for an optimal control problem with nonlinear state equations

Cites Work

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• On the sufficiency of the linear maximum principle for discrete-time control problems
• The \((n,n)\)-disconjugacy of a \(2n\)-th order linear difference equation
• Disconjugacy and transformations for symplectic systems
• Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
• Discrete optimal control: The accessory problem and necessary optimality conditions
• A Conjugate Points Theory for a Nonlinear Programming Problem
• The discrete-time maximum principle : a survey and some new results
• Solution point differentiability without strict complementarity in nonlinear programming
• Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity
• Riccati Matrix Difference Equations and Disconjugacy of Discrete Linear Systems
• Sufficiency Criteria via Focal Points and via Coupled Points
• Sensitivity analysis for nonlinear programming using penalty methods
• Reid roundabout theorem for symplectic dynamic systems on time scales

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