In this work, an optimal control problem with state constraints of equality type is considered. Novelty of the problem formulation is justified. Under various regularity assumptions imposed on the optimal trajectory, a non-degenerate Pontryagin Maximum Principle is proven. As a consequence of the maximum principle, the Euler–Lagrange and Legendre conditions for a variational problem with equality and inequality state constraints are obtained. As an application, the equation of the geodesic curve for a complex domain is derived. In control theory, the Maximum Principle suggests the global maximum condition, also known as the Weierstrass–Pontryagin maximum condition, due to which the optimal control function, at each instant of time, turns out to be a solution to a global finite-dimensional optimization problem

Electromyography (EMG) signals have been extensively used as a control signal in robotics, rehabilitation and health care. Creating an prosthetic hand requires many steps, beginning with a way for the prosthesis to detect the EMG signal. Unfortunately, signal detection may cause some troubles. Among them there are sensor faults that may lead to serious distortion of the signal and malfunction of the prosthetic hand. This paper is devoted to the development of algorithmic software that allows to detect faults of EMG sensors of prosthetic hand. To solve the problem modules of fault detection and signal correction were developed. These modules not only carefully supervise records from individual EMG electrodes, but, if necessary, replace them in systems if one or more signals are violated. This approach is based on signal processing methods with low computational complexity, that allows to reduce hardware requirements.

We consider a problem of finding a covering constant for a restriction of a linear operator to a polyhedral set. The obtained result allows to reduce the initial problem to the problem of finding a covering constant for some linear bijective operators.

Some properties of Hausdorff distance are studied. It is shown that, in every infinite-dimensional normed space, there exists a pair of closed and bounded sets such that the distance between every two points of these sets is greater than the Hausdorff distance between these sets. A relation of the obtained result to set-valued analysis is discussed.

We prove a theorem on the coincidence points of two mappings acting on spaces equipped with a vector metric. By way of application, we obtain sufficient conditions for the existence of a solution of an ordinary differential equation unsolved for the derivative of the unknown function and local solvability conditions for a control system with mixed constraints.