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The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

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In this work, a hybrid-forecasting model is proposed. The model includes a recursive penalty P-spline with parameters adaptation based on evolutionary optimization algorithms. In short-term forecasting, especially in real-time systems, the urgent task is to increase the forecast speed without compromising its quality. High forecasting speed has been achieved by an economical computational scheme of a recurrent P-spline with a shallow depth of prehistory. When combined with the adaptation of some parameters of the P-spline, such an approach allows you to control the forecast accuracy.