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.     

Adaptive suboptimal robust control of the first-order plant

For a linear first-order plant, consideration was given to minimization of the deviation of its output from the specified value in an uncertain environment. Both the parameters of the plant itself and the upper bounds of the external disturbances and operator perturbations in output and control were assumed to be unknown. The suboptimal adaptive control was constructed on the basis of an approximate solution of the problem of optimal identification from the measurement data where the performance of the problem of control was used as an identification criterion.     

Markov model of a digital stochastic generator

A stochastic process generator based on a chain of modulo-two adders with asynchronous feedback loops is investigated. The generator dynamics is described by the Erlang equations. A mathematical model of the generated stochastic process is proposed. The implementation of the generator using modern electronic devices is considered.     

Output control algorithm with the compensation of biased harmonic disturbances

The paper develops the methods of harmonic disturbance compensation using the measurements of plant output variable. An approach for biased harmonic disturbance compensation is proposed. This approach is superior to known ones in some characteristics.     

A note on application of the method of supplementary variables to the analysis of a processor sharing system

We present a new proof of Theorem of 1989 about non-stationary (transient) distribution of the number of jobs in the M/G/1 queue with egalitarian processor sharing. To get this goal, we use the well-known method of supplementary variables. The complete proof of that non-trivial Theorem of 1989 (see Theorem 2.1) was first given in the author’s monograph [12, §2.8] (1989) by means of essentially novel analytic method. Before appearing author’s work, this problem had been considered from analytic viewpoint as insoluble one. In essence, Theorem 2.2 almost repeats Theorem 2.1, but with other proof. In Section 3, Theorem 2.2 is extended to the case of an M/G/1-EPS queue with catastrophes which appear according to a Poisson process.     

Accounting of heterogeneity in the estimation of radiation risks

The problem is considered of taking account of heterogeneity in the individual radiosensitivity in evaluating the radiation risk of the origin of a disease in a group of persons subjected to the radiation action. Mathematical models are described for the estimation of the radiation risk of the origin of the disease with and without regard for heterogeneity. The use of the described method is demonstrated with an example of the estimation of the risk of the origin of radiation-induced diseases from the class of “solid cancers” among the persons taking part in the liquidation of consequences of the accident at the Chernobyl’ Atomic Power Station (CAPS) in the years 1986–1991. It is shown that the heterogeneity disregard leads to understated estimates of the radiation risk of the origin of radiation-induced solid cancers. The effect is investigated of the length of the latent period in the origin of radiation-induced “solid cancers” in taking account of heterogeneity.     

Evasion of multiple target in three-dimensional space

Consideration was given to the differential game of one pursuer against a group of one true and one false target in the three-dimensional space where the concordant targets solve the problem of evasion of the true target from being detected by the pursuer.     

Petersen’s lemma on matrix uncertainty and its generalizations

Various generalizations and refinements are proposed for a well-known result on robust matrix sign-definiteness, which is extensively exploited in quadratic stability, design of robustly quadratically stabilizing controllers, robust LQR-problem, etc. The main emphasis is put on formulating the results in terms of linear matrix inequalities.     

Multidimensional analogs of the kendall equation for priority queueing systems: computational aspects

An analogy between celebrated Kendall equation for busy periods in the system M|GI|1 and analytical results for busy periods in the priority systemsM _r |GI _r |1 is drawn. These results can be viewed as generalizations of the functional Kendall equation. The methodology and algorithms of numerical solution of recurrent functional equations which appear in the analysis of such queueing systems are developed. The efficiency of the algorithms is achieved by acceleration of the numerical procedure of solving the classical Kendall equation. An algorithm of calculation of the system workload coefficient calculation is given.     

Adaptive algorithms to estimate parameters of the optimal policies of inventory control under limited stock-out

Consideration was given to the inventory control by the criterion for minimum of the cumulative mean costs over a sufficiently long planning horizon in conditions of uncertain demand characteristics. Adaptive algorithms to estimate the parameters of the optimal two-level control policies oriented to the supply systems with high level of customer servicing were constructed for the stationary mode of operation.