Generalized solutions of nonlinear optimization problems with impulse controls. I: Existence of solutions (Q1287316)

This paper concerns a dynamic system described by a nonlinear differential equation with two controllers. One control is not bounded in norm and is chosen arbitrarily close to a \(\delta\)-type impulse control. The author has defined the concept of solution for such a differential equation. Application of the time discontinuous substitution method transforms the initial optimization problem to an optimal control problem with bounded controls. The result is applied to study the existence of solutions of generalized optimization problems under various constraints.