Stability of continuous hybrid systems

The stationary state of a continuous hybrid system is analyzed for stability using the method of Lyapunov functions. Sufficient conditions of stability and instability are established. These conditions are constructive and can easily be calculated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 123–128, March–April 2007.     

Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics

Necessary and sufficient conditions of existence and uniqueness of solutions of integral equations are established for ruin probability as a function of the initial capital of an insurance company. Several sufficient conditions and correctness conditions of the problem of finding ruin probability are also established. A general method of successive approximations for solution of this problem is substantiated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 157–164, September–October 2006.     

Modeling convection–diffusion processes based on a multidimensional integro-differential equation with degenerate parabolicity

An initial–boundary-value problem for a multidimensional integro-differential equation with degenerate parabolicity is considered. Based on the maximum-principle theorem and splitting method, a nonlinear monotonic high-order (higher than the first) numerical scheme is constructed for an implicit two-layer scheme. For the error of a numerical solution, a priori estimates are obtained and the sufficient convergence conditions are proved. A posteriori estimates for the numerical error of the solution are analyzed. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 83–96, March–April 2009.     

Pursuit problem in distributed control systems

A pursuit problem in distributed parabolic control systems without mixed derivatives with variable coefficients is considered. The finite-difference method is used to solve this problem. Necessary conditions for the termination of a pursuit are obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 153–158, March–April 2009.     

Boundedness conditions for relative error in fast simulation of reliability of non-Markovian systems

A general model is considered that describes the functioning of non-Markovian systems. A new method is proposed for fast simulation of failure probability. The method allows obtaining estimates with a bounded relative error under some weak conditions. This method is used to evaluate the reliability of a specific class of systems. Numerical examples are considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 63–80, July–August 2006.     

The method of successive approximation applied to find the probability for an insurance company with random premiums

A risk process that describes the evolution of the capital of an insurance company is analyzed, random premiums and claims being available. Integral equations of nonbankruptcy probability as a function of the initial capital are derived. Necessary and sufficient conditions for the existence and uniqueness of solutions of these integral equations, and convergence conditions for the method of successive approximation for finding their solutions are established __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 112–127, January–February 2006.     

Comparison of guaranteed times in conflict-controlled motion

The paper proposes a modified scheme of the method of resolving functions for conflict-controlled processes with a cylindrical terminal set. This scheme ensures that the game is terminated in a definite guaranteed time in the class of stroboscopic strategies without any additional conditions. The guaranteed times of various schemes of the method of resolving functions are compared with that of the first Pontryagin method in terms of convex-valued mappings for a certain structure of the terminal set. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 89–100, July–August 2008.     

The asymptotic properties of estimates of the parameters of nonlinear time series

Asymptotic properties of nonlinear time series parameter estimators constructed on trajectories of stochastic systems under stationary and transient conditions are studied with the use of the least-squares method. The investigation method is based on the study of asymptotic properties of extremal sets of random functions. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 62–72, March–April, 2000     

Sufficient conditions of deterministic implementation of finite-state automata with retention of the numbers of their states

The following three conditions for nondeterministic finite-state automata are defined: input embeddability, output embeddability, and input decomposability. Automata satisfying these conditions are called nondeterministic automata with embeddability. A method for deterministic implementation of such automata with retention of the numbers of their states is proposed. These automata correspond to block-procedural high-level programming languages. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 55–62, May–June, 2000.     

Minimization of logical functions by the method of subimplicants

The method of subimplicants is described for minimization of logical functions that assume no less than three values. The distinctive features of the method are the improvement of results of minimization owing to the extension of gluing conditions and the possibility of minimization of functions that cannot be minimized by traditional methods. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–99, May–June, 2000.