Automation and Remote Control最新文献

A comparative analysis of the efficiency of various ways of organization of economic agents is carried out, taking into account the structure and regulations of their interaction in the models of the Cournot oligopoly. The Cournot oligopoly models in the form of a supply chain are constructed and analytically investigated, taking into account the green effect and concern for fairness. For symmetric models of the Cournot oligopoly with different ways of organization of economic agents, the respective structures of social and individual preferences are analytically obtained. A numerical study of the Cournot oligopoly models in various forms with asymmetrical agents has been carried out, and the corresponding structures of social and individual preferences have been obtained.

The paper proposes a game-theoretic model of competition and cooperation, including partial cooperation, of vaccine producers. Various versions of players’ cooperation (partial and full) have been studied. The differential game has an infinite duration. For each possible coalition of players, the profits and production quantities of its members are determined. An stability analysis of possible coalition structures, as well as coalitions that are most attractive to customers has been made.

Centrality is a numerical measure that characterizes the structural properties of a graph. In the presented work, centrality is used to analyze the load of the graph of urban roads in the city of Petrozavodsk. In the paper, we describe the method used to construct the road graph, present a modified centrality measure that takes into account the features of the transport network and the distribution of passenger traffic, and demonstrate the results of numerical simulations. For the transport graph, betweenness centralities were calculated with and without regard to the distribution of passenger traffic; a connectivity analysis was performed to identify critical, overloaded and reserve roads, and the routes that make the greatest contribution to the centrality of the most loaded roads. The results show that centrality can be used for the analysis of the structural features of the graph of urban roads, modeling sustainability and planning the development of the transport network.

In this paper, we consider finite- and infinite-dimensional optimization problems with constraints of general type. We obtain sufficient conditions for stability of a strict solution and conditions for stability of a set of solutions with more than one point in it according to small perturbations of the problem parameters. For finite-dimensional extremal problems with equality-type constraints, we obtain stability conditions based on the construction of λ-truncations of mappings.

This paper proposes a novel method for recognizing a set of signals with linearly and nonlinearly included parameters from a given ensemble of signals under essential a priori uncertainty. Due to this uncertainty, well-known statistical methods become inapplicable. Signals may be present in an additive mixture containing an observation noise and a singular interference; the distribution law of the noise is unknown, and only its correlation matrix is specified. The novel method is invariant to this interference, does not require traditional state-space expansion, and ensures the decomposition and parallelization of the computational procedure. The signals and interference are represented using conventional linear spectral decompositions with unknown coefficients and given basis functions. Random and methodological errors, as well as the resulting computational effect, are analyzed. An illustrative example is provided.

Considering a piecewise smooth map describing the behavior of a pulse-modulated control system, we discuss border-collision related phenomena. We show that in the parameter space which corresponds to the domain of oscillatory mode a mapping is piecewise linear continuous. It is well known that in piecewise linear maps, classical bifurcations, for example, period doubling, tangent, fold bifurcations become degenerate (“degenerate bifurcations”), combining the properties of both smooth and border-collision bifurcations. We found unusual properties of this map, that consist in the fact that border-collision bifurcations of codimension one, including degenerate ones, occur when a pair of points of a periodic orbit simultaneously collides with two switching manifolds. This paper also discuss bifurcations of chaotic attractors such as merging and expansion (“interior”) crises, associated with homoclinic bifurcations of unstable periodic orbits.

The article is devoted to the development of an algorithm for the approximate solution of the time-optimal control problem for a system of ordinary differential equations, under the condition of avoiding collisions with stationary obstacles and subject to the specified point-wise constraints on the possible values of the control parameters. The main idea is to use a modification of the algorithm for finding suboptimal paths using rapidly growing random trees (RRT*). The most difficult part of this algorithm is to find the optimal trajectories for the problems of transferring the system from one fixed position to another, close to it, without taking into account state constraints. This subproblem is proposed to be solved using the methods of ellipsoidal calculus. This approach makes it possible to efficiently search suboptimal trajectories both for linear systems with large state space dimension and for systems with nonlinear dynamics. Algorithms for the linear and non-linear cases are sequentially analyzed in the paper, and the corresponding examples of calculations are presented.

The problem of drawing up a bypass plan for targets moving rectilinearly to one point for simple movements of an interceptor (traveling salesman) is considered. A new criterion of the problem is proposed based on the initial partition of the possible intercept area, as well as an algorithm for finding a sub-optimal bypass plan based on the construction of a solution search tree by the Monte Carlo method. A numerical implementation of the algorithm has been developed, modeling has been carried out and the obtained plans for bypassing targets have been statistically analyzed.

The paper considers a game theory approach to calculating the centrality value of the vertices in a directed graph, based on the number of vertex occurrences in fixed length paths. It is proposed to define vertex centrality as a solution of a cooperative game, where the characteristic function is given as the number of simple paths of fixed length in subgraphs corresponding to coalitions. The concept of integral centrality is introduced as the value of a definite integral of the payoff function. It is shown that this centrality measure satisfies the Boldi–Vigna axioms.

In precision agriculture, path planning for agricultural robots with complete covering a three-dimensional landscape is an essential task. For robots with front wheels steering the normal curvature of the trajectories should be limited to some value determined by the characteristics of the vehicle. The paper considers a method of deformation of these paths to account for obstacles for trajectories described by homogeneous cubic B-splines. We propose an optimization problem that allows calculating paths with minimizing skips in the coverage. The considered problem is convex and belongs to the class of second-order cone programming, which entails the possibility of its computationally efficient solution. The computational examples are presented.