This paper proposes a new method to provide the exponential convergence of both the parameter and tracking errors of the composite adaptive control system without the persistent excitation (PE) requirement. Instead, the derived composite adaptive law ensures the above-mentioned properties under the strictly weaker finite excitation (FE) condition. Unlike known solutions, in addition to the PE requirement relaxation, it provides better transient response under jump change of the plant uncertainty parameters. To derive such an adaptive law, a novel scheme of uncertainty filtration with resetting is proposed, which provides the required properties of the control system. A rigorous proof of all mentioned properties of the developed adaptive law is presented. Such law is compared with the known composite ones, which also relax the PE requirement, using the wing-rock problem to conduct numerical experiments. The obtained results fully support the theoretical analysis and demonstrate the advantages of the proposed method.

В терминах весовых функций v и w, заданных в первом квадранте декартовой плоскости, получены критерии ограниченности и компактности оператора Харди прямоугольного интегрирования, действующего из весового пространства Лебега с весом v и индексом суммирования p в пространство такого же типа с весом w и параметром суммирования q. При p

We consider the problem of constructing suboptimal filters (lower-order optimal filters, i.e., filters for linear vector functionals of the system state vector) for stochastic multivariable multicriteria plants. The method for constructing such filters is presented in the Luenberger canonical basis. Using a numerical example of a seventh-order system, we show that the proposed approach improves the optimality of filters compared to filters based on scalar observers.

Linked data structures combine a variety of most effective data structures used in a large number of algorithms. Any linked data structure represents a data structure which organized as a set of elements with links of each to other. Unlike one-dimensional array, in which all its elements are located in memory next to each other, in a linked data structure elements may be located in different memory locations. On the basis of linked data structures can be created new combined and modified data structures. Usage of linked data structures provides an increase in speed of insertion and deletion of elements compared with linear arrays of data. Among the most common effective simple data structures organized as linked data structures, we can select lists, stacks and queues that are the subject of this chapter. In the chapter is given a detailed realization of a linked list using the object-oriented programming language C++. In this chapter also is proposed a modified linked data structure – a multilevel linked data structure which is represented in a form of a set of recursively embedded each to other linear linked lists. The efficiency of a practical application of this data structure is shown on an example of solving of the NP-completed orthogonal packing problem.

Using Pyatnitskiy’s theorem on the transition from a system of two matrix inequalities to one equivalent to it, it turns out to re-prove some classical results and obtain new results. The results obtained are illustrated by examples in which the existence question of a quadratic Lyapunov function is solved for systems with switchings between four linear subsystems.