Abstract
This paper examines the controllability problem of quasilinear integro-differential systems with impulse effects. The influence of weak nonlinear perturbations included in the equations that determine the moments of impulse effects is studied, leading to the necessity of analyzing systems with variable impulse moments. The method of reduction to equations with fixed impulse moments is applied, allowing for the use of classical control approaches. Methods for constructing admissible control that ensures the transition of the system from an initial state to a given final state are developed. The conditions for the existence and uniqueness of solutions, as well as the optimization of control in the mean, aimed at minimizing a given cost functional, are considered. The obtained results can be applied in automatic regulation tasks, modeling of dynamic systems with discrete and continuous influences, as well as in the control of technological and economic processes. This work will be of interest to specialists in differential equations, control theory, and applied mathematics.