Riccati equations for abnormal time scale quadratic functionals

DOI10.1016/j.jde.2007.10.012zbMath1355.49031OpenAlexW1996616034MaRDI QIDQ2480292

Roman Šimon Hilscher, Vera Zeidan

Publication date: 31 March 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.10.012

zbMATH Keywords

controllabilitynormalitypositivityRiccati equationquadratic functionaltime scalenonnegativityconjoined basis

Mathematics Subject Classification ID

Linear-quadratic optimal control problems (49N10) Additive difference equations (39A10) Dynamic equations on time scales or measure chains (34N05)

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Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter ⋮ Rayleigh principle for linear Hamiltonian systems without controllability ⋮ Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases ⋮ The minimum plane path for movable end-points and the nonsimultaneous variations ⋮ Nabla time scale symplectic systems and related quadratic functionals ⋮ Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties ⋮ Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions ⋮ Symmetric three-term recurrence equations and their symplectic structure ⋮ Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems ⋮ Sturmian theory for linear Hamiltonian systems without controllability ⋮ Riccati equations for linear Hamiltonian systems without controllability condition ⋮ Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems ⋮ Weyl-Titchmarsh theory for time scale symplectic systems on half line ⋮ Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter ⋮ Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions ⋮ Local minimality properties of circular motions in \(1/r^\alpha\) potentials and of the figure-eight solution of the 3-body problem ⋮ Picone type identities and definiteness of quadratic functionals on time scales

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