Technologies of parallel database systems for hierarchical multiprocessor environments

For the multiprocessor systems of the hierarchical-architecture relational databases, a new approach to data layout and load balancing was proposed. Described was a database multiprocessor model enabling simulation and examination of arbitrary multiprocessor hierarchical configurations in the context of the on-line transaction processing applications. An important subclass of the symmetrical multiprocessor hierarchies was considered, and a new data layout strategy based on the method of partial mirroring was proposed for them. The disk space used to replicate the data was evaluated analytically. For the symmetrical hierarchies having certain regularity, theorems estimating the laboriousness of replica formation were proved. An efficient method of load balancing on the basis of the partial mirroring technique was proposed. The methods described are oriented to the clusters and Grid-systems.     

The iteration method of data censoring in the regression estimation problem

A robust analog of the Nadaraya-Watson regression estimate is considered. A solution is obtained in the class of censor algorithms. A criterion and iteration procedure for determining a censored sample are proposed. The criterion is based on the analysis of residuals (errors) of estimation.     

Robust control of multidimensional nonstationary linear plants

Solved was the problem was of constructing a robust control system with linear nonstationary multidimensional control plant compensating the parametric and external bounded perturbations to within δ if the derivatives of the output vector are not measured and fully if the derivatives are measured.     

Estimating the latent time of fault detection in finite automaton tested in real time

The notions of potential and real latent times of fault detection in finite automata were introduced. The potential latent time is the minimal theoretical time of automaton fault detection, the real time is defined as the time of fault manifestation at a certain point. A method for determination of the statistical characteristics of both times for the automaton tested in the course of its real operation was proposed. It is based on selection of the trajectories of the Markov chain describing behavior of the operable and faulty automata. Additionally, a method for determination of the upper bound of the mean latent time in the case of limited information about the automaton characteristics was proposed.     

Some methods of automatic analysis and controllable transformation of programs

Principles and methods of the development of program systems are considered, which facilitate the analysis and transformation of the structure of programs. In the implementation of scale projects, it is impossible to have a complete concept of the structure of a program without the use of special systems. These systems contain the means of analysis of the initial program and, as a result of automatic transformation, produce another program displaying prescribed properties. As examples, the problems of fast automatic differentiation and the problems of obfuscation (“darkening,” intricacy) of programs are considered.     

Probabilistic model of the algorithms of distributed control protocol in the internet network

Consideration was given to a queuing system that models interaction of two basic algorithms of the TCP protocol. Within the framework of analysis of this system, semi-Markov process of the unified data transmission rate was constructed, recurrent analytical representation of the stationary distribution of a Markov chain embedded in this process was determined, and stationary distribution of the original semi-Markov process was obtained. In view of high complexity of the analytical representation of the stationary distribution, an exact numerical linear-complexity algorithm was constructed enabling one to calculate some important characteristics of the initial protocol.     

On instability of control systems for a certain class of objects and methods of its elimination

In practice of design of control systems, the cases occur when some of the roots of the transfer function of a controllable object are disposed on the imaginary axis of the complex plane. The optimal controller constructed for such objects, despite its realizability, will not afford the robustness properties in the system. The methods of removal of this phenomenon are given. The comparative estimate of the solution of this problem is provided both in the space of states and in the input-output relations (in the space of operators).     

Combinatorial methods for constructing bipartite uniform minimal quasicomplete graphs (symmetrical block designs)

Consideration was given to a specific family of bipartite graphs consisting of two disjoint subsets X and Y of vertices and characterized by that each vertex in X (Y) is connected to each of the remaining vertices in X (Y) by a unique path of length two passing through some vertex in Y (X). The prefix “quasi” reflects the fact that complete connection of the vertices is realized by paths of length two rather than by edges. The problem of constructing uniform minimal graphs with identical cardinalities of the subsets X and Y which is of practical interest for complex communication networks was discussed. It belongs to the class of combinatorial problems of construction of the so-called symmetrical block designs.     

Mathematical models of formation of rational organizational hierarchies

A survey of Russian and foreign papers devoted to one of the burning trends of the theory of control of social and economic systems, i.e., mathematical models of formational of rational organization hierarchies is made. The following lines of investigations are emphasized: multilevel symmetrical hierarchies, hierarchies of knowledge, multilevel hierarchies of data processing, hierarchies and command theory, hierarchies of decision-making, hierarchies and contracts theory, and general model of optimal hierarchies search.     

Constructive methods of control optimization in nonlinear systems

The paper investigates methods of optimal program and point-to-point control in nonlinear differential systems. The proposed methods are based on the idea of discretizing the continuous-time problem. In case of program control, the method of projected Lagrangian is used, which involves solution of an auxiliary problem with linearized constraints by the reduced gradient method; in case of point-to-point control, Bellman’s optimality principle is employed for a “grid” over an approximating solvability tube of the system for a specified goal set with approximation of the point-to-point control by families of controlling function or parameters. An example is given, where the optimal point-to-point control is calculated for a model of maneuvering aircraft.     

Randomized methods of stabilization of the discrete linear systems

Proposed was a new approach to system stabilization by low-order controllers based on generation of the stable random polynomials or matrices and their projection on the space of controller parameters.     

Exponential queuing system with negative customers and bunker for ousted customers

Consideration was given to the queuing system with Poisson flows of incoming positive and negative customers. For the positive customers, there is an infinite-capacity buffer. The arriving negative customer knocks out a positive customer queued in the buffer and moves it to an infinite-capacity buffer of ousted customers (bunker). If the buffer is empty, then the negative customer discharges the system without affecting it. After servicing the current customer, the server receives a customer from the buffer or, if the buffer is empty, the bunker. The customers arriving from both the buffer and bunker are distributed exponentially with the same parameter. Relations for calculation of the stationary distributions of the queues in the buffer and bunker were obtained.     

Decomposition of problems of optimal control and estimation for discrete systems with fast and slow variables

Consideration was given to the linear-quadratic problem of optimal control for the discrete linear system with fast and slow variables under incomplete information about system state. Decomposition of the discrete matrix Riccati equations was carried out. The proposed decomposition algorithm relies on a geometrical approach using the properties of the invariant manifolds of slow and fast motions of the nonlinear multirate discrete systems as basis. The splitting transformation was constructed in the form of asymptotic decomposition in the degrees of a small parameter.     

Invariance for impulsive control systems

The conventional concepts of invariance are extended in this article to include impulsive control systems represented by measure driven differential inclusions. Invariance conditions and some of their main features are derived. The solution concept plays a critical role in the extension of the conditions for conventional problems to the impulsive control context.     

Optimality conditions of sliding modes and the maximum principle for control problems with the scalar argument

Various types of optimality criteria and conditions, which define the set of admissible solution, are brought to the canonical form. For the problem set in this form, the optimality conditions of sliding modes are stated. It is shown that the optimality conditions emerge from these conditions in the form of the maximum principle for problems with a scalar argument and an arbitrary combination of the optimality criterion and constraints.     

Two strong equilibria for game problems

The paper presents two new definitions of equilibrium for arbitrary game problems. The new definitions allow finding a unique solution for a significantly wider class of problems.     

Topological method for analysis of periodic canards

Singularly perturbed systems of ordinary differential equations are studied. A method for analysis of canard-type trajectories in such systems based on the topological degree theory is suggested. The method does not require smoothness of the right-hand side of the system. A result on the existence of periodic canards in systems with non-smooth perturbations is obtained. The trajectories located in this way are not necessarily Lyapunov stable, and appropriate control algorithms are required to stabilize them, e.g., feedback control.     

Pontryagin principle of maximum for the quantum problem of speed

The Pontryagin principle of maximum as originally formulated for the classical dynamic systems, was extended to the quantum systems with a finite number of states of the discrete spectrum. The principle was derived on the basis of equivalence of the matrix representation of the Schrödinger equation to the system of ordinary differential equations. An example of the problem of speed for generation of the given-structure wave package was considered.