The problem of intercepting a target moving along a prescribed trajectory by a Dubins car is stated and formalized as a time-optimal control problem with an arbitrary car velocity direction at the interception. The conditions available in the literature under which the optimal trajectory is a geodesic line drawn from the initial position of the car to the interception point are refined. Algebraic equations for calculating the optimal interception time are obtained. The optimal control is synthesized based on these equations. A software module is developed for constructing the optimal car trajectories for various target trajectories.

Consideration was given to the methods for solution of the differential and algebraic Lyapunov and Sylvester equations in the time and frequency domains. Their solutions are represented as various finite and infinite grammians. The proposed approach to calculation of the grammians lies in expanding them as the sums of the matrix bilinear or quadratic forms generated with the use of the Faddeev matrices and representing each the solution of the linear matrix algebraic equation corresponding to an individual matrix eigenvalue. A lemma was proved representing explicitly the finite and infinite grammians as the matrix exponents depending on the combined spectrum of the original matrices. This result is generalized to the cases where the spectrum of one matrix contains an eigenvalue of the multiplicity two. Examples illustrating calculation of the finite and infinite grammians were discussed.

This paper considers the appearance of indications of useful acoustic signals in the signal/noise mixture. Various information characteristics (information entropy, Jensen–Shannon divergence, spectral information divergence and statistical complexity) are investigated in the context of solving this problem. Both time and frequency domains are studied for the calculation of information entropy. The effectiveness of statistical complexity is shown in comparison with other information metrics for different signal-to-noise ratios. Two different approaches for statistical complexity calculations are also compared. In addition, analytical formulas for complexity and disequilibrium are obtained using entropy variation in the case of signal spectral distribution. The connection between the statistical complexity criterion and the Neyman–Pearson approach for hypothesis testing is discussed. The effectiveness of the proposed approach is shown for different types of acoustic signals and noise models, including colored noises, and different signal-to-noise ratios, especially when the estimation of additional noise characteristics is impossible.

Consideration was given to optimization of the laws of moving object evasion from detection under the coordinate and phase constraints.

Results of solution of optimization problems of a mobile object evasion at constant and variable velocities from detection by an immobile observers are presented.

The evasion problem of a mobile object from detection by a stationary observer in a passive mode is solved. For the case of power dependence of the level of the radiated signal on the motion velocity, a control law for velocity and the trajectory of the object that provide a minimum to the integral level of the signal coming to the observer input for the time of object motion are found in an explicit form.