No 1 (2023)

A range of issues related to the impulse transfer matrix of a system of linear differential-algebraic equations is considered. For systems with infinitely differentiable coefficients, it is shown that this matrix can be represented as the sum of the impulse transfer matrices of its differential and algebraic subsystems. A form of a nondegenerate change of variables is found, which does not affect the form of the impulse transfer matrix. It is proposed to search for realizations of this matrix in the class of differential-algebraic equations of index 1 with separated differential and algebraic components. Necessary and sufficient conditions for the realizability of an impulse transfer matrix in the class of algebraic systems are obtained. The problem of construction methods and the dimension of minimal realizations of such a matrix is discussed under various assumptions.

The problem of synthesizing optimal and quasi-optimal algorithms for complex information processing is solved using the methods of Markov theory for estimating random processes when maintaining a maneuvering object and two-channel vector observation with violations in statistically uncertain situations. The problem is solved in relation to a discrete-continuous Markov process for the case when its continuous part is a vector Markov sequence, and the discrete part is characterized by a three-component discrete Markov process, each component of which is described by a Markov chain to several positions. A block diagram of quasi-optimal complex information processing is given. Using a simple example, simulation modeling shows the performance of a quasi-optimal algorithm in statistically uncertain situations.

A method for solving the signal recovery problem based on a direct search for the optimal program control is considered. It is based on the parameterization of the desired signals and finding a solution by numerical optimization in a finite-dimensional space using any genetic or population algorithm. In order to check the efficiency of the method, the problem of finding the angular velocities and orientation angles of the aircraft from the data available onboard in the absence of direct measurements is given. Different variants of signal parameterization are compared based on Hermitian cubic splines.

A constructive method is proposed for solving a linear-quadratic problem of the robust optimization of spatiotemporal control actions in systems with distributed parabolic parameters under conditions of interval uncertainty of the time-invariant parametric characteristics of an object. In accordance with the control strategy according to the principle of the best guaranteed result, the assessment of achievable target sets of the controlled system is carried out according to the accuracy of uniform approximation to the required final state on an extended set of arguments, which includes, in addition to spatial variables, the entire admissible set of uncertain factors. The developed approach is based on the previously developed alternance method for constructing parameterizable program control algorithms, which extends the results of the theory of nonlinear Chebyshev approximations to a wide range of optimization problems and uses the fundamental laws of the subject area. It is shown that the proposed equations of optimal controllers, which are reduced to linear feedback laws on the measured state of the object with nonstationary transmission coefficients, lead to achievable values of the optimality criteria that do not exceed their upper bounds under the considered uncertainty conditions

The problem of the optimal arrangement of control modules in a real-time computing system is considered. This problem is formulated as a minimax problem. Various structures of the graph of the partial execution order of applied modules are studied: a sequential chain, several independent sequential chains, a tree oriented from the root to the leaves, a tree oriented from the leaves to the root, and an arbitrary graph without cycles. Algorithms for constructing the optimal arrangement of control modules are developed.

Decision-making problems with a large number of alternatives are considered. It is proposed to preliminarily narrow the initial set of alternatives, excluding the obviously worse options. For this purpose, the decomposition of the original problem into preference levels of the majority graph is carried out. Graph levels containing the least preferred alternatives are removed. An algorithm for constructing an aggregated full quasi-order for ordering the set of best alternatives is developed. Majority graph preference levels are used to rank alternatives using Hamiltonian paths in a digraph. An algorithm for finding Hamiltonian paths in a digraph is proposed by raising the adjacency matrix to a power. An applied problem of ordering drone models using an algorithm for constructing a complete quasi-order is presented.

The solution of the problem according to precedent is possible if the experience of solving similar problems (precedents) is accumulated. Subject-independent structures of the experimental knowledge matrix containing information on precedents and the procedural knowledge matrix used to solve the problem are presented. An example of a solution based on the precedent of a problem that arose onboard a passenger aircraft in the situation “Aircraft takeoff after an interrupted run on the runway—the task “Where to fly after takeoff?” is given.”

A method is proposed for coordinating the instrumental coordinate systems of different posts of the optical-electronic system of aircraft with each other and with the inertial navigation system. The method does not require preflight preparation and is based on processing video information streams generated by thermal imaging and television channels of the optoelectronic system and using information from inertial navigational and radar systems when performing special maneuvers. Theoretical analysis of the accuracy and modeling showed the potential benefits of the proposed method.

The movement of a vibrating robot, consisting of a body, two homogeneous flywheels, and an unbalance, is considered. A mathematical model of plane-parallel motion is constructed. The principal possibility of unbalance control, which results in the rotation of the robot in the horizontal plane, is shown. The dependences of the body’s rotation angle on the system’s parameters are described. The conditions for a complete stop of the body after rotation are determined. The displacement of the body from the initial position is analyzed.