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• W1980532011 abstract "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." @default.
• W1980532011 created "2016-06-24" @default.
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• W1980532011 date "2009-05-01" @default.
• W1980532011 modified "2023-10-16" @default.
• W1980532011 title "Weak maximum principle and accessory problem for control problems on time scales" @default.
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• W1980532011 doi "https://doi.org/10.1016/j.na.2008.04.025" @default.
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