Vol 57, No 1 (2018)

This paper considers the problem of constructing an inverse system for a given linear timeinvariant dynamical discrete-time system. We suggest a method to obtain the matrices of the inverse system based on calculating a finite-dimensional state space realization of the input-output map represented by a sequence of matrices.

The principal concepts, models and methods for software quality evaluation are presented. Since the definitions of functionality in the existing standards for software quality evaluation are inconsistent, this concept here is defined as a particular case of the concept of quality in qualimetry as applied to software quality evaluation. A generalized model for software functionality evaluation is proposed. A functionality evaluation model for machine translation systems that was developed based on it and can be a prototype for more detailed models is given. Some ways to use such models to evaluate the functionality of machine translation systems numerically are considered.

The planar problem of controlling the motion of a free-floating space robot is investigated. The robot consists of a body and a telescopic manipulator arm. The motion of the manipulator arm changes the body’s center of mass and causes the body to rotate. It is assumed that the length of the manipulator arm and the angle of its turn relative to the body are restricted. It is shown that the workspace of such a robot is significantly larger than the workspace of a robot with a fixed body. Due to the special motions of the manipulator arm, the robot’s body can be turned and the gripper can be moved from an arbitrary position to another arbitrary position if they are within the workspace, which is a ring centered at the robot’s center of mass. In addition, the prescribed angle between the manipulator arm and the body in the terminal position can be ensured.

A dynamic problem of a spacecraft (SC) turning from an arbitrary initial angular position to the required final angular position is considered and solved. The termination time of the maneuver is known. To optimize the turn control program, the quadratic criterion of quality is used; the minimized functional characterizes the energy consumption. The construction of the optimal control of the turn is based on quaternion variables and Pontryagin’s maximum principle. It is shown that during the optimal turn, the moment of forces is parallel to a straight line immobile in space and the angular momentum direction in the rotation process of the SC is constant relative to the inertial coordinate system. The formalized equations and calculation expressions to determine the optimal turn program are obtained. For a dynamically symmetric SC, a complete solution to the reorientation problem in the closed form is given. An example and results of the mathematical simulation of the dynamics of the SC’s motion under the optimal control are presented, which demonstrate the practical feasibility of the developed method to control the SC’s attitude.

This paper develops simple LMI-based criteria of controllability and observability for a linear time-invariant descriptor (differential-algebraic) multiple-input multiple-output (MIMO) system. Several examples illustrate the efficiency of the developed criteria. A restriction of these criteria is that the number of inputs (outputs, respectively) must not be smaller than half the states of the space dimension.

The problem of the simple pursuit of a single evader by a group of pursuers subject to phase constraints is considered. It is assumed that the pursuers receive information about the evader’s control and affect the control system with a time delay. Sufficient conditions for the solvability of the pursuit problem are obtained.

In recent decades, the theory of hypergraphs has been applied to real-life problems. The tools of hypergraph theory can be used for modeling networks, biological networks, data structures, scheduling processes and computations, and many other systems with complex relationships between the entities. From the theoretical point of view, hypergraphs make it possible to generalize certain theorems in graph theory or even replace a number of theorems on graphs by one theorem on hypergraphs. However, the majority of the potentials in the development of hypergraph theory are blocked due to inconsistencies in the basic terms. It is proposed to make up a list of basic terms related to hypergraph theory, which can help standardize this theory.

An algorithm that determines the winner in a cyclic game in polynomial time is proposed. The two-person game occurs continuously on the edges of a directed graph until a vertex visited earlier is reached. If the weight of the resulting cycle is nonnegative, then the maximizing player wins; if this cycle has a negative weight, then the minimizing player wins. A polynomial estimate of the expected algorithm execution time is obtained under the condition that the weights of the game’s graph edges are distributed uniformly. A brief justification of the time estimate of the algorithm is given. Such games have applications in the validating the correctness of parallel-distributed computer systems, including problems of making up a feasible schedule with logical precedence conditions and preprocessing possibilities.

We consider the problem of the optimal shock isolation of an object whose mechanical model is described by two masses with a linear elastic connection between them. The object is situated on a base whose movement is considered as a shock load. The base acceleration law (shock action) is given. For the sake of safety, the object is fastened to the base by a special device—an shock isolator. The isolator is characterized by the force of the action on the object. We pose the problem of constructing the force law of the isolator such that the stroke of the isolator (the maximum change in the distance between the fastening points of the isolator on the object and on the base) is minimal under the condition that the force of the elastic connection between the masses of the object does not exceed the given admissible value. We obtain approximate solutions of the problem, as well as exact solutions for various classes of shock actions. We provide examples. We show that the solutions include the summands that are the impulse functions. The results can be used to create highly effective devices to protect against shock of technical systems and humans in industry and in transport.

A problem of best estimation of the current values of part of the state variables of a discrete stochastic Markovian plant using measurement results is considered. To ensure that these measurements are sufficiently simply processed, it is proposed to synthesize a finite-dimensional filter that stores only the last few measurements in its state vector. The filter’s memory size is arbitrary and can be chosen as a compromise between the attained estimation accuracy and complexity of the hardware implementation of the filter. The root-mean-squarely optimal structure of the filter is represented via the respective probability distribution, a recurrent way to find this distribution is found, and the algorithm for the numerical construction of the filter by the Monte Carlo method is given. Since it is cumbersome, analytical Gaussian and linearized approximations to the proposed filter are considered. A comprehensive example to compare the accuracies of these approximations with their known analogues is shown.