Vol 78, No 9 (2017)

We consider stabilization of bilinear control systems by means of linear output dynamical controllers. Using the linear matrix inequality technique, quadratic Lyapunov functions, and a special iterative method, we propose a regular approach to the construction of the stabilizability ellipsoid having the property that the trajectories of the system emanating from the points of this ellipsoid asymptotically tend to zero. The developed approach enables for an efficient construction of nonconvex inner approximations of domains of stabilizability of bilinear control systems.

We consider the problem of compensation for a multisinusoidal disturbance for a linear stationary system with a given nominal control law. We consider the general structure of a controller that lets one use arbitrary algorithms for identification of disturbance parameters satisfying certain assumptions. The proposed structure is based on the Youla–Kucera parametrization and lets one compensate for a disturbance while preserving nominal behavior of a control system with respect to the reference.

Consideration was given to the problem of optimizing the locations of the control points over the object state within the framework of the optimal feedback control problems of the distributed parameter objects. For certainty, considered was heating of a rod in furnace where the temperature of controlled vs. the temperature measured at certain points of the rod. The problem is reduced to that of parametric optimal control of an initial-boundary value problem where unknown current values of temperature at the measurement points occur at the right side of its equation and the boundary conditions. Formulas were derived for the components of the objective functional gradient with respect to the coordinates of the control point locations and the parameters of the measurement-dependent current control. The results of the carried out numerical experiments were given.

The possibility of diagnosis of the multiprocessor systems under multiple, up to n−2, failed processors within the framework of the Preparata–Metze–Chien model and method was analyzed. The complete system diagnosis, that is, determination of the good–failed state of all processors, is sometimes possible using the proposed method of analysis of the system diagnostic graph. More precisely, the conditions were determined for impossibility of system diagnosis.

We present the Stackelberg model with linear demand and cost functions for the agents where the leader agent and follower agents have imprecise initial information regarding the marginal costs of competitors. Agents dynamically refine their perceptions and actions based on observing the actions other agents. We obtain necessary and sufficient conditions of the event that the dynamic converges to a Stackelberg equilibrium with true values of marginal costs. We also clarify the situations when agents cannot come to an equilibrium.

Consider a region on a plane with a set of points with positive weights and rectangles that have to be place in that region without intersections. Either the maximal sum of weights of the points in rectangles or the total sum must be minimal. We consider the case of two rectangles. The original continuous problem is reduced to a discrete one by introducing equivalence classes. We propose polynomial combinatorial algorithms for solving the problem. We conduct a computational experiment to compare the efficiency of developed algorithms with the IBM ILOG CPLEX suite with an integer programming model.

This paper considers the design issues of large system area networks of small diameter based on routers with small port count. We suggest a basic structure of a 2D–4D generalized hypercube with sparse dimensions that are implemented as a non-blocking multiring of unit diameter. All designs employ Angara series routers developed in Russia.

We propose a novel approach to constructing characteristic functions in cooperative differential games. A characteristic function of a coalition S is computed in two stages: first, optimal control strategies maximizing the total payoff of the players are found, and next, these strategies are used by the players from the coalition S, while the other players, those from NS, use strategies minimizing the total payoff of the players from S. The characteristic function obtained in this way is superadditive. In addition, it possesses a number of other useful properties. As an example, we compute values of a characteristic function for a specific differential game of pollution control.

In this paper, we consider a Cournot auction with uniform nodal prices for a two-node market. The structure of each local market is an oligopoly. We demonstrate how the type of Nash equilibrium depends on the throughput. Finally, we investigate the optimum throughput problem under an imperfect competition in the market.