Estimation of non-stationary delay for a linear discrete dynamic plant

A nonlinear recurrent gradient-type algorithm is proposed for estimation of nonstationary delay arising in finite impulse response of a linear discrete dynamic plant. Convergence of the algorithm is investigated. Using linear matrix inequalities, its optimal functioning is investigated in order to provide for the maximal rate of convergence of the estimation error to zero.     

Studying the stability boundaries of the gyro-stabilized satellite on a circular orbit

Consideration was given to all parts of the stability boundaries of stationary motion of the gyro-stabilized manyaxis satellite. For each of the necessary stability conditions, conversion to zero or equality was analyzed using the second Lyapunov method. Terms of orders higher than two were used to check sign-definiteness of the Lyapunov function on the stability boundaries. Using the terms up to the sixth order, analysis established asymptotic stability on some parts of the boundaries. Terms of the order at most four enabled us to prove instability on other parts of the boundary.     

Approximate solution of two-point boundary value problems for linear in control systems

The two-point boundary value problem for nonlinear systems, linear in unbounded control, is considered. For three-dimensional systems we present a local algorithm of approximate solution to the control problem. On the basis of this algorithm were constructed algorithms of approximate solution to the control problem on the 3-dimensional integral manifold (orbit) of n-dimensional systems with 2-dimensional control. Demonstrating examples are presented.     

Operating ratio of the technical systems,subjected to failures

The original way of definition of operating ratio in view of reliability of the equipment of the control, time of the control over periodic checks and time of restoration is offered. The received results allow to define the best value of operating ratio of system both in view of, and without taking into account operational expenses.     

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.     

Linear systems with multiple singular values

Properties of linear dynamical systems are studied in the case of Hankel singular values of high multiplicity for monosingular and bisingular systems. Singular values of the Hankel operator take only one or two values for such systems. Properties of transfer functions are analysed. Algorithms of transfer function analysis and design are developed. Relations between frequency characteristics and Hankel singular values are established.     

Local search of orthogonal packings using the lower bounds

Consideration was given to the problem of packing the rectangular half-infinite strip. It was suggested to solve it using a one-point evolutionary algorithm with search of the best solution in the neighborhood of the local lower bound. Proposed was an algorithm to construct this neighborhood including the packings obtained by solving a special problem of one-dimensional cutting. Its solution was shown to be the local lower bound in the considered neighborhood. An improved global lower bound was proposed. The results of numerical modeling were presented. The record value obtained was compared with the global bounds.     

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.     

Models of closed multimachine computer systems with transient-fault-tolerance and fault-tolerance on the basis of replication under byzantine faults

Consideration was given to the key definitions, notions, and models that may be useful for transient-fault-tolerant and fault-tolerant computing in the unmanned multimachine computer systems having many interconnected autonomous computers without shared memory and centralized control organ and operating with high degree of computational parallelism, that is, executing on different computers simultaneously various tasks which interchange their information. These computations should establish reliable results under byzantine faults and controllable degradation of the system at detection of faults.     

An alternative Kalman-Yakubovich-Popov lemma and some extensions

This paper introduces an alternative formulation of the Kalman-Yakubovich-Popov (KYP) Lemma, relating an infinite dimensional Frequency Domain Inequality (FDI) to a pair of finite dimensional Linear Matrix Inequalities (LMI). It is shown that this new formulation encompasses previous generalizations of the KYP Lemma which hold in the case the coefficient matrix of the FDI does not depend on frequency. In addition, it allows the coefficient matrix of the frequency domain inequality to vary affinely with the frequency parameter. One application of this results is illustrated in an example of computing upper bounds to the structured singular value with frequency-dependent scalings.