Vol 77, No 4 (2016)

We consider a method of structural decomposition for an object’s polynomial transition function obtained from an output transition function into a set of structural circuits consisting of standard automation links. The choice of an “optimal” structural circuit is done with the minimal “entropy” criterion.

Consideration was given to an autonomous model with weakly coupled identical subsystems. Existence of a family of periodic solutions which is similar to the family in a subsystem was established. A scenario of bifurcations of the characteristic exponents was given, and the stabilization problem was solved. An example was given.

Stabilization of motion of a wheeled robot with constrained control resource by means of a continuous feedback linearizing the closed-loop system in a neighborhood of the target path is considered. We pose the problem of finding the feedback coefficients such that the phase portrait of the nonlinear closed-loop system is topologically equivalent to that of a linear system with a stable node, with the asymptotic rate of decrease of the deviation from the target path being as high as possible. On this family, we pose the problem of minimization of “overshooting” for arbitrary initial conditions. The solution of this optimization problem is proved to be a limit discontinuous control law. A hybrid control law is proposed that, on the one hand, ensures the desired properties of the phase portrait and minimal overshooting and, on the other hand, does not result in a chattering inherent in systems with discontinuous feedbacks.

We consider the parametric synthesis problem for analog technical devices and systems, where tuning the elements is necessary to ensure required quality and reliability parameters. We pay the most attention to choosing optimal values of variable parameters established during industrial or maintenance tuning.

We consider a system where servicing of a collection of stationary objects distributed inside a one-dimensional zone is done by a moving processor. One-time servicing of each object must be performed during two runs of the processor, direct and reverse. Servicing of any object cannot begin before a predefined time moment; each object is also associated with an individual penalty which is a monotone increasing function of the moment when servicing ends. For the resulting optimization problems, we propose algorithms based on dynamic programming, give examples of their implementation, show results of numerical experiments; we study the computational complexity of these algorithms and the problems themselves.

Consideration was given to the hierarchical two-person game where the lower-level player informs the principal about his decisions, and at that it can communicate invalid information. The principal, however, can verify at random the presented information and penalize its partner for the distorted information. Calculation of the maximal guaranteed result in a corresponding game is a complicated variational game. The present paper reduced this problem to calculation of multiple maximins in the “finite-dimensional” spaces. This result enables one to gain an insight into the logical structure of the optimal strategy of the upper-level player.

Consideration was given to the classical NP-hard problem 1|r_j|L_max of the scheduling theory. An algorithm to determine the optimal schedule of processing n jobs where the job parameters satisfy a system of linear constraints was presented. The polynomially solvable area of the problem 1|r_j|L_max was expanded. An algorithm was described to construct a Pareto-optimal set of schedules by the criteria L_max and C_max for complexity of O(n³logn) operations.

Consideration was given to the problem of relative positioning with the use of variable magnetic field. Preliminary calibration of the positioning system was shown to be necessary to increase precision in determination of the navigation parameters. Various approaches to the calibration experiment were discussed. Efficient calibration algorithms were proposed, and a numerical example of solving a calibration problem was presented.

This paper considers the game problem of biological community control. A set of players with individual utility criteria control a biological community. All players are mutually independent and possess information on the current state of the community. In a special case, this can be a fish community (ichtyocenosis) in an ocean or sea under the impact of different types of harvesting. And finally, the proposed game structures are illustrated using numerical simulation results for populations and communities of marine fish.

This paper derives necessary and sufficient conditions of simultaneous multiple capture in a simple group pursuit problem with equal opportunities and the presence of evader’s defenders.

This paper establishes the uniform Tauberian theorem for differential zero-sum games. Under rather mild conditions imposed on the dynamics and running cost, two parameterized families of games are considered, i.e., the ones with the payoff functions defined as the Cesaro mean and Abel mean of the running cost. The asymptotic behavior of value in these games is investigated as the game horizon tends to infinity and the discounting parameter tends to zero, respectively. It is demonstrated that the uniform convergence of value on an invariant subset of the phase space in one family implies the uniform convergence of value in the other family and that the limit values in the both families coincide. The dynamic programming principle acts as the cornerstone of proof.