Second order sufficiency criteria for a discrete optimal control problem

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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; discrete linear Hamiltonian system; discrete quadratic functional; accessory problem; optimality conditions; conjugate interval; discrete Riccati equation; normality
Description In this work we derive second order necessary and sufficient optimality conditions for a discrete optimal control problem with one variable and one fixed endpoints, and with equality control constraints. In particular, the positivity of the second variation, which is a discrete quadratic functional with appropriate boundary conditions, is characterized in terms of the nonexistence of intervals conjugate to 0, the existence of a certain conjoined basis of the associated linear Hamiltonian difference system, or the existence of a symmetric solution to the implicit and explicit Riccati matrix equations. Some results require a certain minimal normality assumption, and are derived using the sensitivity analysis technique.
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