Second order sufficiency criteria for a discrete optimal control problem
| Authors | |
|---|---|
| Year of publication | 2002 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Difference Equations and Applications |
| MU Faculty or unit | |
| 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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