On First Order Necessary Conditions for Variational and Optimal Control Problems

摘要

A general variational problem is considered which contains most control problems as special cases. Included are differential constraints as well as isoparametric and finite inequalities on both state and control vairables. The method of M. R. Hestenes for proving first order necessary conditions is used to obtain similar conditions under weaker hypothesis, principally requiring Lebeque integrability of all functions with respect to time. It is then shown these results can be easily extended to include the problem with inequality constraints on the space variables independent of control variables. (Author)