Discrete optimal control: second order optimality conditions

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Authors

HILSCHER Roman ZEIDAN Vera

Year of publication 2002
Type Article in Periodical
Magazine / Source Journal of Difference Equations and Applications
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords discrete maximum principle; linear Hamiltonian difference system; discrete quadratic functional; accessory problem; optimality conditions; conjugate interval; Riccati difference equation
Description In this paper we present a survey and refinement of our recent results in the discrete optimal control theory. For a general nonlinear discrete optimal control problem (P), second order necessary and sufficient optimality conditions are derived via the nonnegativity and positivity of the discrete quadratic functional I corresponding to its second variation. Thus, we fill the gap in the discrete-time theory by connecting the discrete control problems with the theory of conjugate intervals, Hamiltonian systems, and Riccati equations.
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