Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control
| Authors | |
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| Year of publication | 2004 |
| Type | Article in Periodical |
| Magazine / Source | Mathematische Nachrichten |
| MU Faculty or unit | |
| 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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