On the “soft” capture in one group pursuit problem

For the generalized L.S. Pontryagin example, sufficient conditions for a “soft” capture of one evader by a group of pursuers are obtained.     

Simple pursuit of one evader by a group

The pursuit of one evader by a group of controlled pursuers is considered for the case of simple motion of the players in nonempty compact sets. Sufficient solvability conditions are derived. These conditions are sometimes also necessary.Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 131–137, May–June, 1992.     

A problem of pursuit and evasion

A trajectory problem of pursuit and evasion on a plane is considered for the case of equal absolute velocities of the players. Exact solutions are obtained for fixed initial conditions.Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 138–143, May–June, 1992.     

A non-stationary problem of group pursuit

A linear non-stationary conflict-interaction problem for controlled objects with n pursuers and m evaders with equal dynamical potency of each participant is considered. The objective of the pursuers is to capture all the evaders; the objective of the evaders is to avoid overtaking of at least one of them. Sufficient conditions for the global evasion problem solvability are stated.     

To a nonstationary group pursuit problem with phase constraints

We consider two linear nonstationary pursuit-evasion problems with one evader and a group of pursuers under the conditions that the players have equal dynamic abilities and that the evader cannot leave a certain set. We prove that if the number of pursuers is less than the space dimension, then the evader can avoid capture in the interval [t ₀,∞).     

Conditional spectral moments in matching pursuit based on the chirplet elementary function

In this paper, we derive closed form formulae for the first- and the second-order conditional spectral moments, which are generalizations of the concept of instantaneous frequency (IF) and instantaneous bandwidth (IB). We prove that for the matching pursuit (MP) distribution, based on the chirplet elementary function, the first-order conditional spectral moment or the IF is guaranteed to be real valued and the IB is always positive. In addition, not only is the second-order conditional spectral moment positive but so also are all even higher-order conditional spectral moments. These new properties are shown to be additional reasons for using the MP decomposition. We also compare the chirplet and Gaussian atoms, because both always give positive values for the Wigner–Ville distribution (WVD), and therefore the MP distribution is also always positive. We show that when the chirplet atom is used, the MP distribution has superior resolution and the convergence is faster when compared with the Gaussian atom. Finally, as the MP algorithm is computationally demanding, we study how to overcome this limitation when using the chirplet atom.     

An approach to the pursuit problem on a heterogeneous multiagent system using reinforcement learning

Cooperation among agents is important for multiagent systems having a shared goal. In this paper, an example of the pursuit problem is studied, in which four hunters collaborate to catch a target. A reinforcement learning algorithm is employed to model how the hunters acquire this cooperative behavior to achieve the task. In order to apply Q-learning, which is one way of reinforcement learning, two kinds of prediction are needed for each hunter agent. One is the location of the other hunter agents and target agent, and the other is the movement direction of the target agent at next time step t. In our treatment we extend the standard problem to systems with heterogeneous agents. One motivation for this is that the target agent and hunter agents have differing abilities. In addition, even though those hunter agents are homogeneous at the beginning of the problem, their abilities become heterogeneous in the learning process. Simulations of this pursuit problem were performed on a continuous action state space, the results of which are displayed, accompanied by a discussion of their outcomes’ dependence upon the initial locations of the hunters and the speeds of the hunters and a target.     

Remark on one problem in extremal combinatorics

We reduce the problem of determining the maximum number of permutations of a finite set such that any pair of permutations has at least t common transpositions to the problem of determining the maximum number of permutations of finite set such that any pair has at least t common fixed points. The latter problem was solved by the author in [1].     

Algorithm for one classification problem

Conclusions We have examined a class of optimal classification problems with an objective function based on a loss functional defined directly on the set of all subsets of the given set of objects without resorting to distance between objects.A fast algorithm MATCHING was proposed for approximate solution of the optimal class fication problem. The algorithm is iterative, and the number of partitioning classes analyzed is roughly halved from iteration to iteration. The assignment problem is solved in each iteration.Computer experiments have shown that in many cases (over 75% for problems of dimension from 4 to 15) a symmetric initial matrix in the assignment problem produces a symmetric optimal assignment.The relative error of the proposed algorithm investigated for some model problems does not exceed 12% in most of the cases (Figs. 4 and 5) and, in general, depends on the dimension of the problem (n) and the location of k^* on the interval [1, n], where k^* is the number of classes in the optimal classification.Translated from Kibernetika, No. 6, pp. 90–95, November–December, 1988.     

On one variational Butkovskii problem

One of the unsolved problems of the theory of optimal control, the Butkovskii variational problem which is of importance for applications, was solved.     

On one problem of integer optimization

A recognition problem of the following form is studied: to find put for the prescribed polyhedron whether the maximum of the linear objective function is achieved at its integral point. It is established that this problem is NP-hard in the general case and polynomially solvable in the class of rooted semimetric polyhedra.     

Sufficient conditions of capture in differential games of m-person pursuit of one evader

Cybernetics and Systems Analysis -