Asymptotic methods in the theory of optimum correction for systems with slowly varying parameters

This paper deals with the problem of optimum control for the case where the constraints are linear differential equations and the functional is of quadratic type. It is assumed that the matrix of these simultaneous equations dependsslowly on the time. The paper describes a method which permits to construct effectively asymptotic solutions of such a problem when the matrix of the characteristic equation which corresponds to Pontryagin's set of equations does not have any simple elementary divisors.Portions of this research were presented at the Colloquium on Advanced Problems and Methods for Space Flight Optimization, Liège, Belgium, 1967.