Some problems of on-target control for a class of continious-discrete systems
For a functional differential system with continuous and discrete times, the problem of control with respect to an on-target vector-functional is considered. Conditions for the solvability of the problem are obtained.
For a functional differential system with continuous and discrete times, the general linear boundary value problem and the problem of control with respect to an on-target vector-functional are considered. Conditions for the solvability of the problems are obtained. Questions of computer-aided techniques for studying these problems are discussed.
For degenerate Hybrid Stochastic Systems with full Dependence of all components exponential convergence to the stationary regime has been established.
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.
Dynamic models under consideration cover a wide class of models in mathematical Economics and Ecology taking into account some aftereffects and including equations with both continuous and discrete times. Control problems are considered in a general case when the aimes of control are given by a system of linear functionals with an arbitrary number of functionals. Complete description of all control actions that solve the control problem is given for the case when only discrete control is applied.
This book constitutes the refereed proceedings of the 18th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2017, held in Paris, France, in January 2017. The 27 full papers together with 3 invited keynotes presented were carefully reviewed and selected from 60 submissions. VMCAI provides topics including: program verification, model checking, abstract interpretation and abstract domains, program synthesis, static analysis, type systems, deductive methods, program certification, debugging techniques, program transformation, optimization, hybrid and cyber-physical systems.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.