The dependence of the radius of a ball centered at zero inscribed in the values of the integral of a set-valued mapping on the upper integration limit is studied. For some types of integrals, exact asymptotics of the radius with respect to the upper limit are found when the upper limit tends to zero. Examples of finding this radius are considered. The results obtained are used to derive new sufficient conditions for the uniformly continuous dependence of the minimum time and solution-point in the linear minimum time control problem on the initial data. We also consider applications in some algorithms with a reachability set of a linear control system.

In this study, a pursuit-evasion game of two players, known as a game of two identical cars, is examined. It is assumed that the game proceeds in a two-dimensional plane. Both players have a constant speed and a limited turn radius. The goal of the first player (pursuer) is to ensure that the second player (evader) enters the capture circle as quickly as possible. The goal of the evader is to avoid or delay capturing for as long as possible. The kinematics of both players are described using the same equations. Thus, the game has only one free parameter: capture radius. This study aims to provide an exhaustive analytical description of the barrier surface for all values of capture radius. Previously, Merz analytically investigated the barrier in a game of two identical cars. In this work, it was found that there is a certain critical value of the capture radius, above which the barrier is qualitatively different from Merz’s example. In addition, we obtained an explicit analytical description of the optimal feedback controls for the barrier.

In this paper, design problems are considered for bilinear control systems subjected to arbitrary-but-bounded exogenous disturbances and containing structured matrix uncertainty. We formulate and solve the problem of efficient construction of robust stabilizability ellipsoids and the domain of robust stabilizability of bilinear systems, both in continuous and discrete time; the basic tool is the linear matrix inequality technique.

We consider the problem of minimizing the fuel consumption of a subsonic turbojet passenger aircraft at the climb phase. In addition to fuel consumption, the objective function to be optimized includes the time spent at the climb phase, since climb optimization is part of the optimization problem for the entire flight with the requirement to arrive at a given point at a given time. Since at the end of the phase it is necessary to reach the given values of speed and altitude from which the cruising flight should begin, penalties for not reaching these values are added to the objective function. The value of the objective function is the result of a numerical solution of a system of differential equations; therefore, for optimization, a gradient-free search method is proposed using candidate points and taking into account constraints. An example of optimizing fuel consumption in comparison with a standard climb profile is considered for two options for the possible implementation of the control system: thrust and pitch control or only pitch control at a constant value of thrust control.

The article “Observer-Aided Output Feedback Synthesis as an Optimization Problem” by B. T. Polyak and M. V. Khlebnikov was originally published in Autom. Remote Control, 2022, volume 83, issue 3, pages 303–324. The formula for the gradient of f(K, L, α) by L in Lemma 3 is given inaccurately; below find the full derivation of this result.