Ural Mathematical Journal (UMJ)
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AN APPLICATION OF MOTION CORRECTION METHODS TO THE ALIGNMENT PROBLEM IN NAVIGATION
Get PDFIn this paper, we apply some motion correction methods to the alignment problem in navigation. This problem consists in matching two coordinate systems having the common origins. As a rule, one of the systems named as basic coordinate system is located at a ship or airplane. The dependent coordinate system belongs to another object (e.g. missile) that starts from the ship. The problem is considered with incomplete information on state coordinates which can be measured with disturbances without statistical description
GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
Get PDFWe consider a family of equations with two free functional parameters containing the classical Black–Scholes model, Schönbucher–Wilmott model, Sircar–Papanicolaou equation for option pricing as partial cases. A five-dimensional group of equivalence transformations is calculated for that family. That group is applied to a search for specifications' parameters specifications corresponding to additional symmetries of the equation. Seven pairs of specifications are found.
DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE
Get PDFThe existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal control problems to a system described by the degenerate semilinear fractional evolution equation. Abstract results are applied to the research of an optimal control problem solvability for the equations system of Kelvin–Voigt fractional viscoelastic fluids
IMPULSE–SLIDING REGIMES IN SYSTEMS WITH DELAY
Get PDFThe paper is devoted to the formalization of a concept of impulse-sliding regimes generated by positional impulse controls for systems with delay. We define the notion of impulse-sliding trajectory as a limit of a sequence of Euler polygonal lines generated by a discrete approximation of the impulse position control. The equations describing the trajectory of impulse-sliding regime are received
REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS
Get PDFThis article is devoted to studying dual regularization method applied to parametric convex optimal control problem of controlled third boundary–value problem for parabolic equation with boundary control and with equality and inequality pointwise state constraints. This dual regularization method yields the corresponding necessary and sufficient conditions for minimizing sequences, namely, the stable, with respect to perturbation of input data, sequential or, in other words, regularized Lagrange principle in nondifferential form and Pontryagin maximum principle for the original problem. Regardless of the fact that the stability or instability of the original optimal control problem, they stably generate a minimizing approximate solutions in the sense of J. Warga for it. For this reason, we can interpret these regularized Lagrange principle and Pontryagin maximum principle as tools for direct solving unstable optimal control problems and reducing to them unstable inverse problems
THE PROGRAM ITERATIONS METHOD IN GAME PROBLEM OF GUIDANCE AND SET-VALUED QUASISTRATEGIES
Get PDFWe consider a differential game of guidance-evasion, which is solved with the program iterations method. The iterated procedure is realized in the space of sets, the elements of which are the game's positions. The objective of this procedure is to construct the alternative partition of the space of positions as established by N.N. Krasovskii and A.I. Subbotin. In addition, more general assumptions on topological properties of the set defining the phase constraints are considered. The connection with the game's solution in the class of quasistrategies is investigated. These quasistrategies are defined as set-valued mappings on spaces of strategic (countably additive) Borel measures
A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY
Get PDFFor two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank–Nicholson method, and also uses interpolation and extrapolation of the prehistory of model with respect to time
PARALLEL ALGORITHM FOR CALCULATING GENERAL EQUILIBRIUM IN MULTIREGION ECONOMIC GROWTH MODELS
Get PDFWe develop and analyze a parallel algorithm for computing a solution in a multiregion dynamic general equilibrium model. The algorithm is based on an iterative method of the Gauss–Seidel type and exploits a special block structure of the model. Calculation of prices and input-output ratios in production for different time steps is carried out in parallel. We implement the parallel algorithm using the OpenMP interface for systems with shared memory. The efficiency of the algorithm is studied with the numbers of cores varying in the full range from one to the number of time steps of the model
ON CALCULATING THE VALUE OF A DIFFERENTIAL GAME IN THE CLASS OF COUNTER STRATEGIES
Get PDFFor a linear dynamic system with control and disturbance, a feedback control problem is considered, in which the Euclidean norm of a set of deviations of the system’s motion from given targets at given times is optimized. The problem is formalized into a differential game in “strategy-counterstrategy” classes. A game value computing procedure, which reduces the problem to a recursive construction of upper convex hulls of auxiliary functions, is justified. Results of numerical simulations are presented.
OPTIMAL MULTIATTRIBUTE SCREENING
Get PDFWe provide a technique for constructing optimal multiattribute screening contracts in a general setting with one-dimensional types based on necessary optimality conditions. Our approach allows for type-dependent participation constraints and arbitrary risk proles. As an example we discuss optimal insurance contracts