Homogeneous Approximation of One- Dimensional Series of Iterated Integrals and Time Optimality

In the paper we consider nonlinear systems depending linearly on control with one-dimensional output. As is well known, under the analyticity requirement, the output can be expressed as a series of iterated integrals of controls with scalar coefficients. Since iterated integrals generate a free associative algebra, algebraic and combinatorial tools can be applied. Developing ideas of the algebraic approach to homogeneous approximation of nonlinear control systems, we propose the definition of a homogeneous approximation for series of iterated integrals with one-dimensional coefficients and study its algebraic properties. In addition, we describe relations between the homogeneous approximation of one-dimensional series of iterated integrals and an approximation in the sense of time optimality. Namely, we give conditions under which the optimal time and optimal controls for the minimal realization of the initial series are approximated by the optimal time and optimal controls for the minimal realization of its homogeneous approximation in a neighborhood of the origin

The labor protection specialist competence influence on the professional risk management state

The results of the authors’ research in more than 600 organizations have shown the labor protection specialist competence influence on the occupational risk management system state and the overall labor protection management system. It is revealed that the leading role in the labor conditions and safety improving strategy choosing and formation, as well as in the scientifically based method of professional risk assessment belongs to a labor protection specialist with a certain competence. The paper describes 16 occupational safety specialists’ professional competence levels and the main factors that determine their formation. The possibilities and abilities of specialists’ with different professional competence levels to assess professional risks are considered and presented in tabular form. About 100 data of different approaches and methods for assessing occupational risks are given, from which only a competent occupational safety specialist can choose the best method for his organization. His decision influences not only the assessing and managing professional risks procedure costs, determined by the particular method choosing, but also the overall occupational safety management system effectiveness in the organization. The conducted research has shown a significant occupational safety competent specialists role in ensuring the professional risks management in the organization and allowed to link his capabilities in assessing professional risks with his professional competence level. This information can motivate the employer to pay attention to the labor protection specialists’ role in ensuring the industrial safety and take care of their timely skills improvement