Weak maximum principle and accessory problem for control problems on time scales
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Nonlinear Analysis |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1016/j.na.2008.04.025 |
| Field | General mathematics |
| Keywords | Time scale; Optimal control problem; Controllability; Normality; Weak maximum principle; Dubois-Reymond Lemma; First variation; Second variation; Feasible family |
| Description | In this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state-endpoints equality constraints. Using the first variation, a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the Dubois-Reymond Lemma to the optimal control setting and time scales. A second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions. The control problem is studied under a controllability assumption, and with or without the shift in the state variable. These two forms of the problem are shown to be equivalent. |
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