This paper discusses whether laser technology holds promise for use in marking steel billets in a continuous-production environment. A laser-marking experiment was performed on “dull metal” and “bright metal,” which have different oxidation layers. The experiment was performed on rolled-shape samples produced using a wide variety of carbon steels and differing scale produced by using different cooling rates during heat treatment (in water, or in a furnace). A QR code or bar code was applied to the heat-treated samples using laser markers where the laser exposure and laser power used for application of the code were varied. The experimental results revealed significant technical difficulties preventing use of this technology with “dull metal” (application of the code to areas coated with scale causes the corresponding areas to change color — gray instead of bronze resulting in the code being impossible to read using standard equipment). Delamination of the oxide coating on the billet will lead to loss of code, and make the code impossible to subsequently read. Successful laser marking of “dull metal” requires initial preparation of the surface for marking in order to remove scale inclusions, so that the code will have uniform color and contrast. A clean surface requires less time to laser mark and lower laser-marker power because of the high contrast between the code and the surface. The code remained intact and readable after long storage (on the order of 9 months) under standard conditions.

An optimization approach to linear control systems has recently become very popular. For example, the linear feedback matrix in the classical linear-quadratic regulator problem can be viewed as a variable, and the problem can be reduced to the minimization of the performance indicator for this variable. To this end, one can apply the gradient method and obtain a justification of the convergence. This approach has been successfully applied to a number of problems, including output feedback optimization. The present paper is the first to apply this approach to the peak-to-peak gain minimization problem. A gradient method for finding a static state or output feedback is written out and justified. A number of examples are considered, including the single and double pendulums.

We propose a test procedure for distinguishing between two separable classes of arbitrary distribution tails and, moreover, prove its consistency. The method is based on the goodness-of-fit test for an arbitrary distribution tail, and properties of this test are also discussed. This is the first goodness-of-fit test for distribution tails proposed in the literature that can be applied for testing the goodness-of-fit hypothesis with a discrete distribution tail. In contrast to the overwhelming majority of works related to statistics of extremes, we do not assume that the distributions belong to any of maximum domains of attraction.

Robust stability conditions are established for a family of linear discrete-time systems subjected to uncertainties. The traditional approach, which involves the construction of a common quadratic Lyapunov function for the entire family of systems with uncertainty, often leads to the problem of conservatism. In this connection, constructing parametric quadratic Lyapunov functions seems promising. The main tools of the proposed approach are the apparatus of linear matrix inequalities and a modification, presented here, of the well-known Petersen’s lemma. A simple approach to finding the robust quadratic stability radius of the family in question is proposed in the paper as well. The corresponding optimization problems have the form of semidefinite programming and one-dimensional minimization, which can be easily solved numerically. The efficiency of our approach is demonstrated via a numerical example. The results obtained can be generalized to design problems for linear discrete-time systems subjected to uncertainties, to other robust statements, and to the case of exogenous disturbances.

We consider the problem of minimizing the fuel consumption of subsonic passenger and transport aircraft at the cruise flight phase. An optimization problem is stated to form the altitude and speed flight profile. It is proposed to solve this problem by the coordinate descent method (taking into account the constraints) combined with the use of a set of auxiliary candidate points. The calculation of fuel consumption as an objective function of optimization is realized by numerical modeling with a fixed step for speed and altitude transients and by a simplified calculation of the per second consumption based on the static equations on flight intervals with constant speed and altitude.