Agent-based modeling and simulation was applied to investigate a set of problems in the energy context. The paper shows advantages of the agent based modeling approach. The method to define agents-consumers in simulation tool AnyLogic and the approach to simulating investment project risk are suggested.
A majority of the real voting rules are (or may be written as) voting with a quota (i.e. weighted game). But the axioms for the power indices defined on simple games are not directly transferred to the weighted games, because the operations used there are defined incorrectly in this case. Nevertheless, most of the axiomatics can be adapted for the weighted games. The main goal of this article is to answer the question: how to do it?
As a part of managing behavior of an active consumer of electric power in prospective smart grids it is necessary to create a mathematical model that meets his or her economic interests. Existing models either do not take into account all relevant aspects or turn out to be too complicated for the purposes of multi-agent modeling. We suggest a mathematical model of an active consumer and use it to investigate the problem of consumption and local generation regimes optimization. We derive conditions when the consumer’s problem has a pretty simple and efficient solution. The proposed approach is illustrated by optimizing the operating modes of equipment for a single household.
The problem of optimal control for a class of nonlinear objects with uncontrolled bounded disturbances is formulated in the key differential game. For problems with a quadratic quality functional task of searching for the optimal control reduces the need to find solutions to the scalar partial differential equation Hamilton-Jacobi-Isaacs. Finding solutions to this equation in tempo operation of the facility by means of special algorithmic procedures. The results can be used to solve theoretical and practical problems encountered in mathematics, mechanics, physics, biology, chemistry, engineering sciences, management and navigation.
The paper proposes decision rules that allow comparing alternatives by preference for different cases of information regarding criteria importance and growth of preferences along criteria scale. These rules work within the framework of the new model of decision making situation with criteria forming a multi-level structure. This model was previously developed by the authors. The created methodology is free from fundamental drawbacks that cannot be avoided in principle, which are intrinsic to the analytic hierarchy process and all other known methods ofproblem solving with hierarchical structure.
The paper presents a modification of the pattern analysis method that allows allocating separate clusters of objects with similar structure as well as with close values of their parameters. A description of the method and its algorithm realization are given.
This paper surveys some parts of approximation theory for functions of one and several real variables. Approximation of functions by algebraic polynomials is a classical theory. The paper contains some results from this theory. First results on approximation of functions by neural networks and fuzzy systems have appeared as responses on practical requirements. It was necessary to know is it possible to approximate an arbitrary continuous function by such aggregates. Later, these fields were developed like the theory of approximation of functions by algebraic polynomials. In this paper we consider some results on approximation of functions by neural networks and fuzzy systems.
The human immunodeficiency virus infection, that causes Acquired Immune Deficiency Syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The paper introduces
a methodological problem of use of modern mathematical and information methods to boost the response of the immune system by means of drug scheduling. The control purpose is to steer the system
to an equilibrium condition, known as long-term nonprogressor, which corresponds to an infected patient that does not develop AIDS symptoms. To show the feasibility of the control methodology a human
immunodeficiency virus model computer simulations are presented.
In authors' previous paper published in 2011 in «Control Sciences» journal one example of a bi-criterion decision analysis problem demonstrating that the use of Analytic Hierarchy Process (AHP) may lead to a clearly erroneous result is given. However, the author of another paper published in 2012 in the same journal suggested that he found an error in our use of AHP and, consequently, our criticism of AHP is unsubstantiated. In this new paper the authors show that there was no mistake in the use of AHP in their original counter-example, and provide two further counter-examples that support their original conclusion.