Рассматривается задача реконструкции управлений для динамических детерминированных аффинно-управляемых систем. Эта задача состоит в построении по дискретным неточным замерам наблюдаемой траектории кусочно-постоянных аппроксимаций нормального управ- ления, порождающего эту траекторию и определяемого единственным образом. Управления стеснены известными невыпуклыми геометрическими ограничениями. Для такого случая сходимость аппроксимаций понимается в смысле слабой сходимости в пространстве L^2. Предложено решение задачи реконструкции управлений. Его построение основано на использовании конструкций из вспомогательных задач реконструкции управлений с выпуклыми ограничениями и разложении их по теореме Каратеодори о структуре выпуклого множества. The control reconstruction problem for dynamic deterministic affine-controlled systems is considered. This problem consists in constructing piecewise constant approximations of the normal control generating this trajectory that is determined uniquely from discrete inaccurate measurements of the observed trajectory. The controls are constrained by known non-convex geometric constraints. For this case, the convergence of the approximations is understood in the sense of weak convergence in the L^2 space. A solution to the control reconstruction problem is proposed. Its construction is based on the use of constructions from auxiliary problems of control reconstruction with convex constraints and their expansion according to the Caratheodory theorem on the structure of a convex set. The control reconstruction problem for dynamic deterministic affine-controlled systems is considered. This problem consists in constructing piecewise constant approximations of the normal control generating this trajectory that is determined uniquely from discrete inaccurate measurements of the observed trajectory. The controls are constrained by known non-convex geometric constraints. For this case, the convergence of the approximations is understood in the sense of weak convergence in the L2 space. A solution to the control reconstruction problem is proposed. Its construction is based on the use of constructions from auxiliary problems of control reconstruction with convex constraints and their expansion according to the Caratheodory theorem on the structure of a convex set.