Purpose: to find out the features of hip girth (distal) of both limbs of young boys and young girls of Bukovynian higher educational institutions, depending on the sport type. Materials and methods: 115 students of Bukovynian higher education institutions aged from 16 to 21 years old participated in the study, 78 (67.82%) of them were young boys and 37 (32.18%) were young girls. The main group was 75 (65.22 %) students of the I-II courses of the Faculty of Physical Culture and Human Health (the Yuriy Fedkovich Chernivtsi National University), the control group - 40 (34.78%) college students and students of the Stomatological Faculty of the Bukovynian State Medical University, who underwent an anthropometric study, according to the method of V.V. Bunaka in the modification of P.P. Shaparenko (determination of body weight and hip girth distally). Results: a comparison of the length of the distal right and left hip girth of young boys and young girls of both groups shows that the length of the right hip girth of young boys and young girls is bigger than the left: the main group (right in young boys - 48.50±2.0 cm, left - 42.25 ±2.0 cm; right in young girls – 48.59±2.0 cm; left – 41.74±2.0 cm), control group (right in young boys – 49.19±2.0 cm, left – 44 ,42±2.0 cm; young girls' right - 46.57±2.0 cm; left - 41.52±2.0 cm). The conducted regression analysis shows that gender and weight are significant factors for hip girth distally on the right and left. Conclusions: the model for predicting the circumference of the distal right thigh has the equation: y = β1+β2 +0.318*x, where y is the distal right thigh circumference, x is weight. Coefficient β1 = 29.848 for young girls and β2 = 25.95 for young boys. The coefficient of determination is 0.994. On the left, it has the equation: y = β1+β2 +0.292*x, where y is the hip girth on the distal left, x is weight. Coefficient β1 = 29.848 for women and β2 = 21.901 for men. The coefficient of determination is 0.991.

An optimal control for a dynamical system optimizes a certain objective function. Here, we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here, we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations. Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the construction of an optimal control. The method using a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel solution to the problem of optimal stabilization for a stochastic dynamical system with a random structure, Markov switches and Poisson perturbations.

The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.

The problem of synthesis of optimal control for stochastic dynamical system of random structures with the Markovian switchings is solved. For determination of the corresponding functions for construction of the Bellman functional and optimal control the system of differential equations is written, for which the existence of the unique solution was substantiated.

The problem of synthesis of the optimal control for a stochastic dynamic system of a random structure with Poisson perturbations and Markov switching is solved. To determine the corresponding functions for Bellman functional and optimal control the system of ordinary differential equation is investigated.