The paper presents the results of the discussion of related issues of justification of phasing and preparation of proposals for the advanced implementation of integration components of Aerospace Technologies in a particular subject area of Space Debris. The problem of multi-stage evaluation of production efficiency using the Free Disposal Hull model is considered. The approach to the management and maintenance of products, as well as some case of Data Envelopment Analysis application in the aerospace industry, are presented. An adaptation of the idea of the Quality Function Deployment in the context of topical issues of the development of advanced space technologies is proposed. The report includes a brief overview of European projects to reduce the level of man-made contamination of near-Earth space. Selected examples of diversified solutions are shown including a method of increasing the duration of the operation of spacecraft, an Instrumental Modeling Complex, etc. This formation of a bi-directional vision from theory to practice is of permanent interest to the transformation in the digital age.

The application of DEA technologies is considered in the interests of studying the complex structure of risks in modeling the dynamics of crisis situations and the complex improvement of providing algorithms for strategic management and operational management in modern conditions. The scale effect is studied together with the specifics of hybrid models that correspond to the joint monitoring problem.

We introduce the concept of local controllability of a dynamical system and present sufficient conditions for such controllability. As an immediate consequence, we prove necessary second-order conditions for a local infimum trajectory in an optimal control problem. These conditions strengthen the well-known second-order optimality conditions and extend them to more general classes of problems.

The article considers the problem of combinatorial optimization of interception of rectilinearly moving targets as a modification of the traveling salesman problem. New macro characteristics and definitions for this problem are introduced and used to classify the obtained solutions. Vector criteria composed of several important for applications functionals are described. The principles of no-waiting and maximum velocity are proved for two types of criteria. An intelligent brute-force algorithm with dynamic programming elements for finding optimal plans according to the introduced intercept criteria is proposed and implemented. Statistics of solutions of the developed algorithm is collected for a set of different initial parameters and the proposed macro characteristics are investigated. The conclusions about their applicability as local rules for the greedy algorithm for finding a suboptimal intercept plan are drawn.