Abstract
In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.
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Dedicated to Lothar von Wolfersdorf on the occasion of his 60th birthday
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Goebel, M., Raitums, U. Constrained control of a nonlinear two point boundary value problem, I. J Glob Optim 4, 367–395 (1994). https://doi.org/10.1007/BF01099264
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DOI: https://doi.org/10.1007/BF01099264