Vol 56, No 1 (2017)

Control systems with a small parameter on the time scale, as well as optimal control problems with terminal and vector quality criteria, are considered. The justification of the averaging method on the asymptotically large period of time and the matching algorithm of the controls of the original and averaged systems are presented for these systems. The numerical-asymptotic method for solving problems of the optimal control of systems on time scales is given.

Issues concerning the implementation of temporal reasoning (inference) for models based on branching time logic as applied to intelligent decision support systems are considered. The focus is on the construction of a qualitative (interval) and quantitative (metric) branching time model. The inference is reduced to solving the temporal constraint satisfaction problem, and the corresponding procedures (algorithms) are proposed. An example of the practical application of the proposed techniques in a prototype of a real-time intelligent decision support system is described.

We consider the dynamics of the rotational motion of a satellite moving in the central Newtonian force field in a circular orbit due to gravity and constant torques. We propose a method for determining all positions of equilibrium (equilibrium orientations) of a satellite in the orbital coordinate system given the values of the vector of constant torque and the major central moments of inertia; we obtained the conditions for the existence of these positions. We classify the domains with an equal number of equilibrium positions using algebraic methods for the construction of discriminant hypersurfaces. The results obtained in this study can be used to construct gravitational control systems for the orientation of artificial Earth satellites.

An approach to forming analytical solutions of the discrete and continuous Sylvester and Lyapunov linear algebraic matrix equations is described. The approach is based on reducing the square matrix to the Jordan normal form. Examples, algorithms, and implementations in Matlab are presented.

A statistical description of the sampling and reconstruction procedure for the realizations of a random field with jumps and four possible states is given. A realization of such a field is formed by two realizations of binary Markov stochastic processes defined on two coordinate axes. The analysis of the sampling and reconstruction procedure of this field consists of two parts. In the first part, the sampling intervals are chosen based on the given probability of missing a state. In the second part, the points of state change in the realization being reconstructed are estimated, and the variances of these estimates are calculated. These variances characterize the quality of reconstruction. An example illustrating the proposed method is discussed.

This work considers algorithms of optimal control of nonlinear continuous determinate systems with feedback by the output variables with incomplete information about its parameters. It is proposed to determine optimal in average control in the form of decomposition by basis functions. Metaheuristic interval optimization methods (adaptive interval algorithm, interval explosion search and interval genetic algorithm) are used to find decomposition coefficients. Proposed algorithms are implemented in a form of software complex which was used to solve the interception problem.

Using the control problem of a two-state Markov process in discrete time as an example, we consider the basic stages concerning the application of theory of conditional Markov processes to synthesize optimal algorithms of the control of stochastic systems. It is assumed that the control changes the statistical properties of the states of a controlled plant. The numerical method for solving the problem and the results of solving particular example are presented. The special features of the solution of this problem compared to the well-known problem in continuous time are discussed.

Structural models of finite-state machines (FSMs) that make it possible to use the values of the output variables for encoding the internal states are studied. To minimize the area (the parameter area is used to denote cost in the context of this paper) of FSM implementation, it is proposed to use the structural model of the class D FSM. A method for the design of the class D FSM in FPGA is proposed. This method involves two phases—splitting the internal states of the FSM (to satisfy the necessary conditions for the construction of the class D FSM) and encoding the internal states (to ensure that the codes are mutually orthogonal). It is shown that the proposed method reduces the area of FSM implementation for all families of FPGAs of various manufacturers by a factor of 1.41–1.72 on average and by a factor of two for certain families. Practical issues concerning the method and the specific features of its use are discussed, and possible directions of the elaboration of this approach are proposed.

Estimates of the maneuvers of active space objects are considered. We propose analytical and numerical-analytical algorithms to estimate short-term and long-term one-impulse maneuvers for the case where the initial and final orbits are determined with errors. Both coplanar and noncoplanar maneuvers are considered. Special attention is given to the velocity and reliability of the solution of the problem. The process to find the solution has a geometrical interpretation. We provide examples of estimates for maneuvers of spacecraft located at geosynchronous orbits. The results obtained by the proposed method are compared with the results obtained by the traditional approach, excluding errors of orbit determination.

A method for controlling the angular orientation with respect to the horizon plane of the platform of a uniaxial wheeled module moving without slippage over the underlying surface is considered. For a module involving a one-axis gyroscope, a compensating flywheel, and a stabilizing weight, equations of motion are derived, which describe the module as a nonholonomic system due to the absence of slippage of its wheels over the underlying surface. The conditions for the “force of undisturbability” of the platform by the inertial forces upon its arbitrary translational-rotational motion and the conditions for “informational undisturbability” by the inertial forces of the accelometric sensor of the deviation of the platform from the horizon plane are determined. The analytical relationships determining the conditions for the absence of slippage of the wheels are found. By numerical simulation, rational values of the coefficient in the laws governing the moments of forces developed by the control elements of the structure are obtained. The effectiveness of these laws is confirmed by the results of simulating the control processes over the angular motion of the platform of the module along a typical trajectory of its motion over the underlying surface.

This paper presents a method for configuring the motion planning system of an omniwheeled mobile robot with a differential drive. A simulation program that models the horizontal movement of the robot is described. This simulation program is used to select the optimal parameters for the differential drive control algorithm. Then, the motion planning system is tested on a real robot, which is called RB-2, to adjust the parameters selected. This approach allows the control algorithm to be tuned efficiently and effectively, minimizing the number of its test runs on the physical robot.