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.     

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.     

A class of systems of bilinear integral Volterra equations of the first kind of the second order

A class of bilinear systems of integral Volterra equations of the first kind related to the problem of automatic control of a nonlinear dynamic system (object) with unknown structure and vector input and output is studied. Algorithms for an analytic solution to corresponding bilinear systems and its numerical approximation are developed. A special character of the algorithms is illustrated by model examples.     

On the properties of the identically singular Lagrange problem

We consider the identically singular Lagrange problem of the calculus of variations. It is investigated how the conjugate points and the Jacobi equation index are related to the solvability conditions of the appropriate matrix Riccati equation and the reducibility of the functional to a perfect square. The criterion of the trajectory variation smallness at a small variation of the functional in the neighborhood of the extremal is obtained.     

Control of complex ecological-economic systems

The paper is devoted to developing methods for control of ecological-economic systems consisting of three hierarchically subordinate subjects of control. In describing the dynamics of a system state, equations in partial derivatives that are solved numerically according to a semi-implicit scheme of the finite-difference method are used. To achieve its main goal (maintenance of an ecological subsystem in stable state), the subject of control of the upper level applies different control methods. Methods of hierarchical control (motivation, enforcement, and persuasion) that differ in the direction of action (on the objective function or domain of admissible controls) are proposed; examples of their use are represented and a comparative analysis of the obtained results is made.     

Minimum of power consumption in the problem of oscillation damping

Consideration was given to minimization of the L ¹-norm of control of the linear oscillatory system. For consumption of the energy resources required to damp oscillations, bilateral estimates were obtained.     

Specific optimal estimation of special Markov jump processes

A solution to the filtering problem of states of special Markov jump processes that is optimal in the mean-square sense at the class of polynomial observation functions is presented. A comparison of the proposed estimates with the known estimates of optimal linear and nonlinear filtering is given.     

基于心态指标的区间灰数关联度模型

针对已有的灰色关联度模型仅适用于实数序列而不能应用于区间灰数序列的情况,通过引入决策者心态指标,将区间灰数序列转化为决策者心态指标序列,并且当决策者的心态指标确定时,心态指标序列就转化为实数序列,于是通过对体现决策者心态的实数序列建立灰色关联度模型,得到了反映出决策者心态的灰色关联度,从而构建了基于心态指标的区间灰数关联度模型。决策者处于不同心态时,可以通过调整其心态计算灰关联度,从而使建立的关联度模型更加符合实际。最后,通过计算实例说明了模型的可行性。