No 6 (2023)

One of the most important problems of game theory—the game of firms in an oligopoly market—is considered. The survey covers classical and modern formulations for the game-theoretic problem of choosing optimal player’s strategies and the recent methodological achievements in oligopoly games with applications, including publications over the past five years.

We present a model of a stochastic observation system that allows for time delays between the received observation and the actual state of the observed object that formed these observations. Such delays can occur when observing the movement of an object in a water medium using acoustic sonars and have a significant impact on the accuracy of position tracking. We present equations to solve the optimal mean square filtering problem. Since the practical use of the optimal solution is barely feasible due to its computational complexity, we pay the main attention to an alternative, suboptimal but computationally efficient approach. Specifically, we adapted a conditional minimax nonlinear filter (CMNF) to the proposed model and formulated sufficient existence conditions for its estimate. We conducted a computational experiment on a model that is close to practical needs. The results of the experiment show the effectiveness of CMNF in the model considered. However, they also show a significant decrease in the quality of estimation compared to the model without random observation delays, which can be considered as a motivation for further research into the model and related problems.

In modern smart manufacturing, robots are often connected via a network, and their task can change according to a predetermined program. Iterative learning control (ILC) is widely used for robots executing high-precision operations. Under network conditions, the efficiency of ILC algorithms may decrease if the program is restructured. In particular, the learning error may temporarily increase to an unacceptable value when changing the reference trajectory. This paper considers a networked system with the following features: the reference trajectory and parameters change between passes according to a known program, agents are subjected to random disturbances, and measurements are carried out with noise. In addition, the network topology changes due to the disconnection of some agents from the network and the connection of new agents to the network according to a given program. A distributed ILC design method is proposed based on vector Lyapunov functions for repetitive processes in combination with Kalman filtering. This method ensures the convergence of the learning error and reduces its increase caused by changes in the reference trajectory and network topology. The effectiveness of the proposed method is confirmed by an example.

In this paper, a heating process control law with steam supply is designed for a fluid in a heat exchanger. The process is described by a linear hyperbolic equation of the first order with a nonlocal boundary condition with a time-delayed argument. The temperature of the supplied steam is found as a linear dependence on fluid temperature values at measurement points in the heat exchanger. Explicit formulas are obtained for the gradient of the objective functional of the control problem in the space of the feedback coefficients (parameters) of this dependence. A numerical scheme is developed for determining the feedback parameters based on these formulas. Finally, an algorithm is proposed for determining the rational (optimal) number of measurement points.