Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control

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Authors

HILSCHER Roman ZEIDAN Vera

Year of publication 2004
Type Article in Periodical
Magazine / Source Mathematische Nachrichten
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Discrete quadratic functional; Nonnegativity; Positivity; Linear Hamiltonian difference system; Conjugate interval; Conjoined basis; Riccati difference equation; Discrete Jacobi condition
Description In this paper we provide a characterization of the nonnegativity of a discrete quadratic functional I with fixed right endpoint in the optimal control setting. This characterization is closely related to the kernel condition earlier introduced by M.Bohner as a part of a focal points definition for conjoined bases of the associated linear Hamiltonian difference system. When this kernel condition is satisfied only up to a certain critical index m, the traditional conditions, which are the focal points, conjugate intervals, implicit Riccati equation, and partial quadratic functionals, must be replaced by a new condition. This new condition is determined to be the nonnegativity of a block tridiagonal matrix, representing the remainder of I after the index m, on a suitable subspace.
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