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Problem of Optimum Control Connected with Environmental Problems

The problem of optimization of time of passing through area is considered by an object which behavior is described by a linear differential system with delay. Necessary conditions of optimality in the form of the maximum principle of Pontryagin are obtained. It is based on the reduction of an initial task to the general problem of mathematical programming and use of the rule of multipliers of Lagrange on any linear spaces. Differential properties of the selected criterion of quality are investigated.