Publication details

First order conditions for generalized variational problems over time scales

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Year of publication 2011
Type Article in Periodical
Magazine / Source Computers & Mathematics with Applications
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Time scale; Optimal control problem; Weak Pontryagin principle; First order optimality conditions; Weak local minimum; Calculus of variations problem; Euler-Lagrange equation; Transversality condition; Natural boundary condition; Isoperimetric problem
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Description In this paper we derive the weak Pontryagin principle for generalized optimal control problems over time scales. Three types of problems are considered, namely (i) the problems involving the values of the state endpoints in the Lagrangian and the dynamics, (ii) the problems with an integral of the state in the Lagrangian and the dynamics, and (iii) the isoperimetric problems. As special cases we obtain the first order optimality conditions for the corresponding calculus of variations problems, which have been of a recent interest in the literature. Our method is based on transforming the generalized optimal control or calculus of variations problem into a traditional optimal control problem on time scales, to which the known weak Pontryagin principle can be applied.
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