Vol 55, No 1 (2016)

The problem of optimal control of automatic deterministic discrete systems in conditions of parametric uncertainty is considered. The state change (switchover) of a system is described by a recurrent equation in which instant multiple switchovers are admitted. The times and the number of switchovers are not specified in advance—they are found as a result of optimization of a functional. The initial state of the system is not known exactly, but the set of possible initial states is known; therefore, problems of average optimal control and guaranteed optimal control of bunches of trajectories are formulated. For solving these problems, it is suggested to use the principle of separation: namely, to control the bunch of trajectories by applying a control optimal for one specially chosen trajectory of the bunch. The resulting control of the bunch is suboptimal, but it may be satisfactory in practice. On the basis of sufficient conditions for optimality of a full-feedback control, an algorithm for constructing a suboptimal control in conditions of uncertainty is developed. Counterexamples of linear–quadratic problems of control of automaton-type systems in which the principle of separation fails are presented.

The problem of the most accurate estimation of the current state of a multimode nonlinear dynamic observation system with discrete time based on indirect measurements of this state is considered. The general case when a mode indicator is available and the measurement errors depend on the plant disturbances is investigated. A comparative analysis of two known approaches is performed—the conventional absolutely optimal one based on the use of the posterior probability distribution, which requires the use of an unimplementable infinite-dimensional estimation algorithm, and a finitedimensional optimal approach, which produces the best structure of the difference equation of a low-order filter. More practical equations for the Gaussian approximations of these two optimal filters are obtained and compared. In the case of the absolutely optimal case, such an approximation is finitedimensional, but it differs from the approximation of the finite-dimensional optimal version in terms of its considerably larger dimension and the absence of parameters. The presence of parameters, which can be preliminarily calculated using the Monte-Carlo method, allows the Gaussian finite-dimensional optimal filter to produce more accurate estimates.

An optimal control of the MM1N queue is considered on the basis of the minimum criterion for the expected service time if constraints on the average number of rejected demands and average energy expenditure are present. Two variants of an input flow are studied: with the separation of demands according to priorities and without such a separation. A dual optimization method and a Lagrange multiplier rule are used to synthesize a constrained optimal control. Two iteration procedures, the effectiveness of which is analyzed on the basis of the numerical simulation results, are presented in order to solve numerically a dual problem.

This paper reviews the possibility of upgrading the conventional “bag-of-words” model to reflect the structural features of text documents and take them into account in the process of categorization by means of machine learning theory methods. It is suggested to use these features to characterize the relationships within a set of tokens. It is also proposed to use the names of such relationships as features, along with the names of tokens. The proposed models differ from the traditional approach, which only reflects unary relations. The efficiency of the upgraded methods of machine learning is tested by means of computer experiments run for the Reuters-21578 set classes by using eight common classifiers. The relevance of applying such a modernized approach to categorize text documents with the help of simple classifiers is demonstrated.

Improvement of the classification quality for the generalization problem is considered. In order to improve the classification models produced by generalization algorithms, it is proposed to use argumentation methods based on defeasible reasoning with justification degrees. New methods and algorithms are proposed, and experimental results on various test data sets are described, including instances with noisy initial data.

The paper considers electric generator network control under conditions of parametric uncertainty and disturbing actions caused by the mechanical power nonstationarity and possible changes in transmission-line admittance. A decentralized control algorithm that maintains operator generation stability and network phase synchronization with the required accuracy is synthesized. Numerical examples and computational simulation results are presented illustrating the operation capability of the proposed control scheme.

The influence of the position of the center of mass of a multilegged robot that moves along the surface of a freely rolling ball on the direction of rolling of this ball over a horizontal plane is studied. The case when the center of mass of this robot is shifted (in the plane that is perpendicular to the velocity vector) from the vertical axis that goes through the ball center is analyzed. Approximation formulas that allow one to estimate the radius of curvature of the trajectory of the center of a ball during turn are obtained under certain simplifying assumptions. It is found that a shift of the center of mass from the vertical axis that goes through the ball center inevitably produces a certain spin of the ball about this axis, complicating the task of maneuvering on this ball. The problem of insectomorphic robot maneuvering with two freely rolling balls on a horizontal plane is solved in the model formulation. The problem consists in moving a robot from a horizontal plane over to a movable ball, rolling this ball close to another free ball, and making the robot climb from the first ball to the second one and then back to the horizontal plane. The difficulty is that the mechanical system under consideration is highly unstable and is thus strongly influenced by execution errors. It is demonstrated constructively that the problem of the indicated interaction between a robot and two balls is fundamentally solvable, and a model robot is able to perform this task, although it is forced to shift its center of mass from the vertical axis in the process.

Algorithms for calculating an aircraft’s orientation angles based on the results of the numerical integration of Poisson’s and quaternion equations are proposed. The algorithms in the presence of random errors of the matrix elements of direction cosines and quaternions are characterized by a significantly higher accuracy in comparison to the formulas for solving the formulated problem. The results of testing the mathematical modeling data under random errors, which confirm the increased accuracy of the calculation of the orientation angles, are given.