卷 56, 编号 1 (2017)
- 年: 2017
- 文章: 14
- URL: https://journals.rcsi.science/1064-2307/issue/view/13623
Control in Deterministic Systems
Averaging of multicriteria control problems of systems on time scales
摘要
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.
Systems Analysis and Operations Research
An implementation of inference in temporal branching time models
摘要
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.
Navigation Systems
Satellite dynamics due to gravity and constant torques
摘要
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.
Systems Theory and General Control Theory
General analytical forms for the solution of the Sylvester and Lyapunov equations for continuous and discrete dynamic systems
摘要
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.
Analysis of stability and stabilization of cascade systems with time delay in terms of linear matrix inequalities
摘要
The stability of nonlinear cascade systems with a time delay is studied. Conditions of the global asymptotic stability in terms of linear matrix inequalities for a finite set of matrices are obtained. The problem of stabilization of the controlled delay system is considered, which is solved based on the stability conditions. The proposed approach to the analysis of qualitative properties and to the solution of stabilization problems is based on the results concerning the asymptotic stability of the delay linear systems, the decomposition of the original system, and the representation of the delay nonlinear system by a Takagi–Sugeno system. Examples illustrating the simplification of the system analysis by reducing its size and decreasing the number of linear matrix inequalities are discussed.
Data Processing and Identification
Sampling of realizations of the random field formed by the sum of Markov binary processes
摘要
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.
Control in Stochastic Systems and Under Uncertainty Conditions
Meta-heuristic interval methods of search of optimal in average control of nonlinear determinate systems with incomplete information about its parameters
摘要
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.
System shape optimization and stabilization of controlled quasi-linear stochastic systems that operate on an infinite time interval
摘要
The necessary conditions in the stabilization and optimization problem for a stationary quasi-linear stochastic system in continuous time, with its matrices depending on a vector parameter to be chosen, i.e., the optimization problem for the system shape, are obtained. An equivalent deterministic problem is stated and a numerical method to solve it using the analytical formula obtained for the criterion gradient, which is the function of a finite number of variables, is proposed. The optimization problem for an output-controlled system is a particular case, sufficient optimality conditions are obtained for it in the case that the complete information of the state is available. Optimality conditions are found for the proportional–integral–derivative controller in the quasi-linear stochastic system. These optimality conditions are applied to the optimal control problem for a small unmanned aerial vehicle moving in a disturbed atmosphere.
Optimal control of the two-state Markov process in discrete time
摘要
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.
Discrete Systems
Minimization of mealy finite-state machines by using the values of the output variables for state assignment
摘要
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.
Control Systems of Moving Objects
Estimates of near-circular orbits after a single correction: a geometrical method
摘要
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.
Robotics
Control of the angular orientation of the platform of a uniaxial wheeled module moving without slippage over an underlying surface
摘要
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.
Robot motion control in zero-gravity conditions
摘要
We have considered the motion control of a space robot composed of a body and a telescopic manipulator arm. The robot is in the state of free passive flight. The vector of the number of movements and the kinetic moment of the robot relative to the center of mass are zero. The manipulator arm motion causes a corresponding motion of the robot body (change in the position of the center of mass of the body and its rotation). Unlike earlier results, we have revealed that the robot grip can be shifted from an arbitrary initial position to an arbitrary final position inside the operating area and, in addition, the required (most convenient for operations) angle between the manipulator arm and the robot body in the final position can be obtained.
Method for tuning the motion planning parameters of a mobile robot
摘要
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.