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Nº 2 (2023)
Articles
About the Method for Constructing External Estimates of the Limit Controllability Set for the Linear Discrete-Time System with Bounded Control
Resumo
This article discusses the problem of constructing an external estimate of the limit set of controllability for a linear discrete system with convex control constraints. We have proposed a decomposition method that allows us to reduce the problem for the initial system to subsystems of smaller dimension by switching to the normal Jordan basis of the matrix of the system. The statement about the structure of the reference hyperplane to the limit set of controllability is formulated and proved. A method for constructing an external estimate of the limit set of controllability with an arbitrary order of accuracy in the sense of the Hausdorff distance is proposed based on the principle of contraction mappings. The paper provides examples.
3-34
On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems
Resumo
As shown below, the linear operator norms in the deterministic and stochastic cases are optimal values of the Lagrange-dual problems. For linear time-varying systems on a finite horizon, the duality principle leads to stochastic interpretations of the generalized H2 and H∞ norms of the system. Stochastic minimax filtering and control problems with unknown covariance matrices of random factors are considered. Equations of generalized H∞-suboptimal controllers, filters, and identifiers are derived to achieve a trade-off between the error variance at the end of the observation interval and the sum of the error variances on the entire interval.
35-53
Neobkhodimye usloviya optimal'nosti pervogo i vtorogo poryadkov v odnoy zadache upravleniya, opisyvaemoy nelineynymi raznostnymi uravneniyami drobnogo poryadka
Resumo
54-65
Boundary Control of Some Distributed Heterogeneous Vibrating System with Given States at Intermediate Time Instants
Resumo
This paper considers the boundary control problem for a distributed heterogeneous vibrating system described by a one-dimensional wave equation with piecewise constant characteristics. The travel time of a wave through each homogeneous section is assumed the same. The control is implemented by displacement at the two ends. A constructive control design approach is proposed to transfer the vibrations on a given time interval from the initial state through the multipoint intermediate states to the terminal state. The control design scheme is as follows: the original problem is reduced to a control problem with distributed actions and zero boundary conditions. Then the variable separation method and control methods for finite-dimensional systems with multipoint intermediate conditions are used. The results are illustrated by an example.
66-80
Design of Nonlinear Selectively Invariant Control Systems Based on Quasilinear Models
Resumo
An original analytical method is developed to design the selectively invariant control systems for nonlinear plants with differentiable nonlinearities. To solve the design problem, the method of designing nonlinear control systems is applied on the base of a quasilinear model of nonlinear plants and the internal models principle of external impacts is used, taking into account the requirements for the relative order of the control device and the fast response of the designed system. The system of linear algebraic equations is solved to determine the parameters of the nonlinear control device. The suggested method can be applied to design the control systems for nonlinear plants of various purposes, operating under conditions of regular external impacts of the known form.
81-102
Matrichnye neravenstva v teorii ustoychivosti: novye rezul'taty na osnove teoremy o svertyvanii
Resumo
103-121
Optimal'noe vosstanovlenie kvadratichno integriruemoy funktsii po nablyudeniyam za ney s gaussovskimi oshibkami
Resumo
122-149
The Interaction of Economic Agents in Cournot Duopoly Models under Ecological Conditions: A Comparison of Organizational Modes
Resumo
This paper presents a comparative analysis of the efficiency of organizational modes (information structures) for the interaction of economic agents in static and dynamic Cournot duopoly models. We compare the independent behavior of equal players, their cooperation, and the hierarchy formalized as Germeier games. The efficiency of individual players and the entire society is quantitatively assessed using the private and social relative efficiency indices. The ecological safety conditions of the system are investigated. An organizational and economic interpretation of the results is proposed
150-168