Discrete optimal control: second order optimality conditions
| 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; 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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