Vol 78, No 6 (2017)

A method to design controllers of one-dimensional nonminimal-phase plants under unknown bounded external perturbations was proposed. It is based on determining the parameters of the Bézout identity. The attainable indices of precision and speed were determined.

The method of localization of invariant compact sets was proposed to study for asymptotic stability the equilibrium points of an autonomous system of differential equations. This approach relies on the necessary and sufficient conditions for asymptotic stability formulated in terms of positive invariant sets and invariant compact sets, and enables one to study the equilibrium points for asymptotic stability in the cases where it is impossible to use the first approximation or the method of Lyapunov functions. The possibilities of the method were illustrated by examples.

A modification was proposed for the relations of the method of dynamic programming in the problems of optimal stochastic control of the discrete systems by the probabilistic performance criterion. It enabled one to simplify the process of finding the optimal Markov strategy and obtain a suboptimal solution. Its efficiency was verified by the examples of maneuver optimization of the stationary satellite in the neighborhood of a geostationary orbit. An explicit form of the optimal control for the bilinear system with probabilistic terminal criterion was determined using the results obtained.

Consideration was given to construction of a nonlinear robust control law for a multivariable dynamic plant distinguished for control nonlinear mathematical model, the socalled nonaffinity. The design of the robust law for the nonaffine control plant operating in the environment of external and parametric perturbations relies on the hyperstability criterion and the conditions for L-dissipativity, as well as on using in the main loop an explicit two-output reference model and fast correcting filter.

We study dynamical game-theoretic models of two-level control systems accounting for the conditions of sustainable development. As the hierarchical control mechanisms we consider compulsion and impulsion methods. We give definitions of equilibria and show algorithms for constructing them with simulation modeling for various information regulations. We show a comparative analysis of the efficiency of the proposed control mechanisms for the model of an ecosystem of a shallow body of water (with the example of the Azov sea).

We propose an algorithm for computing parameter estimates for a smoothing cubic spline that minimize the estimated expectation of losses. Instead of the usual assumption that the noise is centered we use an assumption which is more realistic for many practical smoothing problems, namely that it is zero median. The problem setting is augmented by prior deterministic information in the form of constraints on linear combinations of parameters of spline functions. We obtain explicit representations of such estimates and give their qualitative interpretation. Based on the results of a numerical experiment, we establish a high degree of robustness of the solutions to the presence of outliers in the measurements, including same sign outliers, and the possibility to fairly reliably determine the actual accuracy of the resulting estimates of spline parameters by the attained minimum risk value.

We consider the resource-constrained project scheduling problem with respect to the makespan minimization criterion. The problem accounts for technological constraints of activities precedence together with resource constraints. We propose a genetic algorithm with two versions of crossovers based on the idea of most rational use of constrained resources. The crossovers uses a heuristic that takes into account the degree of criticality for the resources, which is derived from the solution of a relaxed problem with a constraint on accumulative resources. A numerical experiment with examples from the PCPLIB library has shown that the proposed algorithm has competitive quality. For some examples from the j120 test series the best known solutions were improved and for j60 (50 000 and 500 000 iterations) and for j120 (500 000 iterations) we have obtain the best average deviations of the solutions from the critical path value.

The airborne measurement systems of geophysical fields are considered. The applicability of such systems in navigation and geophysics is analyzed. The existing gravimetric, magnetometric and electromagnetic systems are briefly overviewed. The structure of the airborne measurement systems of geophysical fields and the associated mathematical models are discussed in detail. Finally, the issues of data processing are studied and the solution approaches to the ill-posed problems are described.

In this paper adhesion is considered as a factor that to a large extent defines the reliability of technological processes in microelectromechanical systems (MEMS) manufacturing using superficial technology. The physical and chemical conditions of its emergence are investigated, as well as the short-range and superficial forces causing adhesive collapse in MEMS are assessed in quantitative terms. Some suggestions on adhesion prevention at the final stages of the technological process are formulated. The existing and prospective methods used to prevent adhesion in electronic industry are also discussed.

In the group pursuit problem for rigidly coordinated targets pursued by a group of inertial objects, we construct a control that guarantees evasion.