Vol 80, No 1 (2019)

We consider the robust anisotropic filtering problem for a linear discrete nonstationary system on a finite time interval. We assume that external disturbances acting on the object have anisotropy bounded from above and additionally satisfy two constraints on the moments. Our solution of the filtering problem is based on the boundedness criterion for the anisotropic norm in reverse time and reduces to finding a solution for a convex optimization problem. We illustrate the operation of a suboptimal anisotropic estimator with a numerical example.

The problem of optimal control of a harmonic oscillator is considered. The energy of oscillator at the final time instant is used as the optimization criterion. The optimal control and optimal value of energy as function of this time instant is determined. The result obtained was compared with the solution of the problem of time-optimal operation at bringing the oscillator in the state of rest.

Consideration was given to the design of the optimal control of the general discrete stochastic system with a criterion as the probability of the state vector sojourn in the given sets at each time instant. Derived were relations of the dynamic programming enabling one to establish an optimal solution in the class of Markov strategies without extension of the state vector with subsequent reduction to an equivalent problem with the probabilistic terminal criterion. Consideration was given to the problem of one-parameter correction of the flying vehicle trajectory. An analytical solution was established.

We propose a model of a queueing system with a single server, perishable inventory and repeated customers that can form an orbit of infinite size. In the absence of inventory in the system, primary customers according to the Bernoulli scheme either enter the queue or go into the orbit. The system uses the (s, S)-policy of replenishing the inventory. We develop a method for calculating system characteristics and solve the problem of minimizing total costs by choosing the critical level of inventory.

We consider a solution of the optimal control problem for an adaptive multidirectional mirror antenna. With the Pontryagin maximum principle, we reduce the problem to solving a system of ordinary differential equations. The resulting system can be solved numerically using modern approaches such as the Runge–Kutta methods or hybrid evolutionary algorithms. Estimation of the state vector is performed by the maximum likelihood criterion with solving the generated Fokker–Planck–Kolmogorov stochastic differential equation. In this case, the posterior probability density function is associated with the normalized value of the energy flux density in the aperture of antenna feeders. We determine the ability to suppress interference with an adaptive multidirectional mirror antenna and give an example of solving the control problem.

We consider the task of assigning teams of specialists who jointly perform certain types of jobs (consulting services, compliance assessment for products, goods or services according to given requirements etc.). The team performing this work is composed of a set of specialists of various types (specialties), and their total number is limited. The problem is to design a team work plan for which the time to complete all jobs is minimal. We reduce this task to a linear programming problem and also consider heuristic algorithms and special cases of the problem.

We present the basic properties of the a new pattern analysis method in parallel coordinates; results of the method do not depend on the ordering of data in the original sample of objects being analyzed. We prove that clusters obtained with this method do not overlap. We also show the possibility of representing objects of one cluster in the form of monotonically increasing/decreasing functions.

The measure is proposed of discrete real sequences similarity in the extended space of states. The measure is based on the symbolic CTQ-analysis methods and is applicable to a chaotic and stochastic multidimensional non-equidistant time series as well. The analysis of the proposed metrics is carried out and their basic properties are described. The method efficiency is tested on the model systems differing in complexity and topology of the attractor. The high sensitivity of the developed similarity measures is demonstrated on the example of the financial time series analysis.

In this paper, we present and numerically study an adaptive coding procedure for data transfer among quadrotors moving in a formation. The quadrotor’s parameters are identified using experimental data from a digital communication channel with limited bandwidth. We compare the obtained results with theoretical expectations and illustrate the efficiency of the adaptive coding procedure.

Part II of the paper considers a game between a group of n pursuers and one evader that move along the 1-Skeleton graph M of regular polyhedrons of three types in the spaces ℝ^d, d ≥ 3. Like in Part I, the goal is to find an integer N(M) with the following property: if n ≥ N(M), then the group of pursuers wins the game; if n < N(M), the evader wins. It is shown that N(M) = 2 for the d-dimensional simplex or cocube (a multidimensional analog of octahedron) and N(M) = [d/2] + 1 for the d-dimensional cube.

The method of generating control circuits for self-use mechanisms is considered. It shows the techniques efficiency where CAD system is applied. CAD-based technology of control scheme design is described.