The idea of representation of discontinuous solutions for optimal control problem with the aid of singular time transformation appeared first in original works of V. F. Krotov (1960-1961), where the discontinuous solutions of classic variational problem were represented with the aid of the curve length parametrization. It led to the different topology with only point-wise convergence except the discontinuity points and to the different based on the Helley theorem compactness condition for the set of admissible curves. The key point of this approach was the extention of classic integral criterion to the class of discontionus functions with preserving its continuity in the original topology, which was important for variational analysis. However, even if the results related to semicontinuity of the integral functionals were known (Tihomirov1968), they were hardly applicable to variational analysis, since they do not give the approach to construction of more or less wide class of variations admissible for discontinuous solutions. First universal description of discontinuous solution appeared in (Gurman1972) where the jumps of phase variables were described with the aid of time change. This was the first step to the development of impulse control systems with the aid of nonlinear differential equations with measures. However, for variational analysis of such systems it was important to have the property of stability or robustness with respect to variations of the impulse controls. These conditions in the form of {\it Frobenius conditions} were obtained later in (Miller 1997). They appeared to be the foundation of the method of discontinous time transformation (Miller 1982)and opened the way to the derivation of necessary and sufficient optimality conditions. The general theory of the optimization problems with ordinary and impulsive controls has been developed on the basis of this approach (Miller, Rubinovich 2003).
