Vol 80, No 12 (2019)

It is demonstrated how to design optimal digital controllers on a finite horizon for the linear time-varying objects with uncertain initial conditions and external disturbances. The square of an optimality criterion, called the maximum output deviation, represents the exact guaranteed maximum value of the squared Euclidean norm of the system output normalized by the sum of the squared Euclidean norms of disturbances and a quadratic form of the initial state of a system. The maximum output deviations and the worst-case disturbances and/or initial conditions causing them, as well as the minimax controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) are calculated as solutions to a semidefinite programming problem. The necessary and sufficient conditions for the finite-time stability and boundedness of a system are established; they can be used for controller design.

A nonlinear autonomous system near an equilibrium is considered. The matrix of its linearized counterpart is supposed to have imaginary eigenvalues without internal resonances up to the fourth order inclusive. The oscillations of this system caused by periodic controls with a small gain k are investigated, and isolated resonant oscillations are found. The amplitudes of the oscillations in terms of the parameter k are estimated, and their stability is analyzed. It is shown that the existence of a resonant oscillation is guaranteed by the control action, while its asymptotic stability is determined by the uncontrolled system.

For the linear autonomous differential-difference systems of neutral type, a finite observer that estimates in finite time the solution to an original system with zero error is suggested. A criterion for the existence of such an observer and a corresponding design method are developed.

We analyze the construction of a system for processing space-time signals in a radio system that takes into account technical limitations in the measurement of the bearing. A desired efficiency can be achieved by using simplified processing procedures with stochastic controlled bearing interpolation. For implementation, we use processing based on truncated (low-element) managed apertures of antenna arrays and coarse (“binary”) robust signal statistics. We propose an alternative approach that involves applying the Monte Carlo method with feedback in the process of digital processing: we implement randomization and incremental stochastic control for the phase center position by sequentially activating a small number of elements during the accumulation and averaging of rough samples of the input signal. We also present quantitative results of reducing instrumental errors in bearing measurement.

We study additional flows of events that are generated by claims located in the queuing system with an unlimited number of devices and arbitrary claim servicing time. We propose and carry out the Markov summation method to obtain the characteristics of the additional flows in question.

We consider the motion of a spacecraft described by the differential equations of the three-body problem in the Earth-Moon system. The goal is to stabilize the spacecraft in the neighborhood of the collinear Lagrangian points (which are know to be unstable equilibria) via use of minimum fuel-consumption control. The adopted approach is based on l₁-optimization of linearized and discretized equations with terminal conditions being the target Lagrangian point. Therefore, the problem reduces to a linear program, and its solution defines pulse controls for the original three-body equations. Upon reaching the desired neighborhood, the spacecraft performs control-free flight until its deviation from the Lagrangian point exceeds certain prespecified threshold. The correction is then applied repeatedly, so that the spacecraft is kept within a small neighborhood of the unstable equilibrium point.

The models of network active systems are introduced and studied. A network active system consists of a finite set of agents interacting within a given network; each agent is characterized by the technology of his activity (a dependence of the output on his own action and also the outputs of other agents). The problems of incentives and planning are stated and solved. Applications of network active systems for the modeling and optimization of extended enterprises are discussed.

The paper describes the results of the comparative analysis of the applicability of several methods for solving dynamic DEA-models to the problem of monitoring of the ecological and economic efficiency of economic activities of regional economic systems (on the example of the regions of the Central Federal District). The method of forming time series based on point estimates of environmental and economic efficiency the Malmquist method and the window method is considered. The results obtained for different window widths are analyzed for stability and adequacy. A comparison of the obtained results allows us to conclude that the window method is uniquely preferable for solving problems of monitoring the ecological and economic efficiency of regions not only from a computational but also from a substantive point of view.

A high-accuracy fast-acting simple in implementation and invariant to interferences in the form of direct current signal method of non-coherent harmonic alternating current signals vectors sets measurement is described. The solution of stated in the general view problem is gained on the base of so called the splitting sets of samples method and invariant theory approach to measurement process organization. The implementation of the method is illustrated on example of a synthesis of the measurement algorithm for the case of three harmonic signals. The analysis of the gained results is given.