Введение в оптимальное управление
An optimal control problem is formulated for a class of nonlinear systems which can be presented by system with linear structure and state-depended coefficients (SDC). The system being under the influence of uncontrollable disturbance is supposed. The linearity of the transformed system structure and the quadratic functional make it possible to pass over from the Hamilton–Jacoby–Bellman equation (HJB) to the state dependent Riccati equation (SDRE) upon the control synthesis. In thus paper the optimal control problem by nonlinear system in a task of Keeping Tabs on Reference Trajectory we decide in a key of differential game. The presented example illustrates the application of the proposed control method.
Optimization, simulation and control are very powerful tools in engineering and mathematics, and play an increasingly important role. Because of their various real-world applications in industries such as finance, economics, and telecommunications, research in these fields is accelerating at a rapid pace, and there have been major algorithmic and theoretical developments in these fields in the last decade.
This volume brings together the latest developments in these areas of research and presents applications of these results to a wide range of real-world problems.- Collection of selected contributions giving a state-of-the-art account of recent developments in the field - Covers a broad range of topics in optimization and optimal control, including unique applications - Written by an international group of experts in their respective disciplines - Broad audience of researchers, practitioners, and advanced graduate students in applied mathematics and engineering
This research work deals with the problem formulation of control of complex organizational structures. The mechanism of functioning of such systems is described by example of a vertically integrated company (VIC). The problems of strategic and operative control of VIC are considered. The methods for solving such problems based on genetic algorithms and neural networks are suggested. A new iterative procedure for coordination of strategic and operative control goals based on the estimation of imbalance between shareholder value and net profit distributed for payment of dividends to shareholders is suggested.
The considered system is a double criterion optimization problem with complex multiparameter restrictions.
We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer value.
The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G1(p). We offer the solutions for these games.
We begin with constructing solutions for these games with distributions p having two and three-point supports. Next, we build the optimal strategies of Player 1 for bidding games G1(p) with arbitrary distributions p as convex combinations of his optimal strategies for such games with distributions having two- and three-point supports. To do this we construct the symmetric representation of probability distributions with fixed integer expectation vectors as a convex combination of distributions with not more than three-point supports and with the same expectation vectors.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
Summarizes the latest applications of robust optimization in data mining.
An essential accompaniment for theoreticians and data miners Data uncertainty is a concept closely related with most real life applications that involve data collection and interpretation. Examples can be found in data acquired with biomedical instruments or other experimental techniques. Integration of robust optimization in the existing data mining techniques aims to create new algorithms resilient to error and noise.