Automation and Remote Control最新文献

A system of nonlinear stochastic functional-difference equations with finite delay is considered. By assumption, this system has a “partial” trivial equilibrium (with respect to part of the state variables). The problem under study is to analyze partial stability in probability of this equilibrium: stability is considered with respect to part of the variables determining it. The problem is solved using a discrete-stochastic modification of the method of Lyapunov–Krasovskii functionals. Conditions for partial stability in probability are established. An example is provided to illustrate the features of the proposed approach and the rationale for introducing a one-parameter family of functionals.

In this paper, the concept of weak active equilibrium, which was introduced in the eighties of the twentieth century by Smol’yakov, is used for the first time for a study of Bertrand–Edgeworth oligopoly (that is, competition among firms when firms’ strategies are prices and firms’ production capacities are limited). All symmetric weak active equilibria are found for the basic model of Bertrand–Edgeworth duopoly, which was analysed in the sixties of the twentieth century by Beckmann. However, this model is highly simplified. Also, the question of existence of nonsymmetric weak active equilibria is studied.

This paper considers discrete time-invariant systems (with constant parameters) described by dynamic models in the presence of exogenous disturbances. For such systems, the problem of estimating unknown inputs using interval observers is studied. The solution is based on a minimal-dimension disturbance-insensitive model of the original system. For this model, an interval observer is designed and then used to estimate the unknown inputs. The theoretical results are illustrated with a practical example.

The problem of parametric synthesis of a model predictive control (MPC) system by the chemical process of production of the kerosene fraction of an industrial fractionator under conditions of constraints and uncertainty is considered. The optimal parameters of the MPC algorithm are obtained as a result of solving the problem of multi-criteria optimization, taking into account the intervally specified parameters of the plant model.

Connected systems with switching between three linear discrete-time subsystems are considered, and a new frequency-domain criterion for the existence of a quadratic Lyapunov function ensuring the stability of such systems under arbitrary switching is proposed. The application of this criterion is demonstrated on an example of a third-order system.

This paper is devoted to the optimal control of mixed (stationary and periodic impulse) harvesting of a renewable resource distributed on the Earth’s surface. Examples of such a resource are biological populations, including viruses, chemical contaminants, dust particles, and the like. It is proved that on an infinite planning horizon, there exists an admissible control ensuring the maximum of time-averaged harvesting.

This paper considers technical systems described by nonlinear dynamic models. The fault tolerance property of such systems is ensured by introducing feedback with full or partial fault decoupling. The solution is based on separating a subsystem insensitive or minimally sensitive to faults and its subsequent analysis. For this purpose, a logical-dynamic approach is used, which operates only linear algebra methods. An illustrative practical example is provided.

This paper considers a noncooperative game of quantity competition among firms in an oligopoly market under general demand and cost functions. Each firm’s optimal response to the strategies of other firms is assessed by the magnitude and sign of its conjectural variation, expressing the firm’s expectation regarding the counterparty’s supply quantity change in response to the firm’s unit change in its supply quantity. A game of n firms with the sum of conjectural variations (SCV) regarding all counterparties as the generalized response characteristic is studied. The existence of a bifurcation of the players' response is revealed; a bifurcation is a strategy profile of the game in which both positive and negative responses are possible with an infinite-magnitude SCV value. Methods are developed for calculating the SCV value under different types of inverse demand functions (linear and power) and cost functions (linear, power, and quadratic), and the impact of these characteristics of firms on the bifurcation state is comparatively analyzed.

The problem of stabilizing a chain of three integrators subject to a phase constraint is studied. Continuous constrained control in the form of nested sigmoids, which guarantees the fulfillment of the phase constraint, is synthesized. A Lyapunov function is constructed, and necessary and sufficient conditions of global stability of the closed-loop system are established. The discussion is illustrated by numerical examples.

The analytical method for the synthesis of a generator of a random process with a given spectrum in the form of a linear system of Itô’s equations is proposed. The stationarity of a random process is assumed, the spectral and corresponding transfer functions of which are defined in the form of rational fractions. The coefficients of the system of Itô’s equations of the generator are found from recurrent algebraic relations. The method is focused on working with mathematical models of nature random processes, such as the Dryden’s wind model. The transformation of the spectra of the wind gust model in three directions is presented in detail and the corresponding stochastic equations are given.