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Analysis of instrumental methods for modeling stochastic processes in the economy

In this paper, the authors conduct a comparative analysis of instrumental methods used in modeling stochastic processes, namely, component analysis of time series, fractal modeling and modeling using p-adic mathematics. As an object of study, the authors chose the dynamics of the MICEX index. At the first step of the work, the authors carry out a detailed component analysis of the time series, which made it possible to identify the main development trend in the form of a quadratic function; periodic fluctuations with a period of six levels and a cyclical component describing fluctuations in the world economy with a period of fifty-five levels. At the second step of the work, the authors simulate the dynamics of the MICEX index using a fractal theory based on the self-similarity of the development of the economic process, which showed the ergodicity of the series under study with a stable influence of only the last twenty-four levels. The third step of the work was the p-adic modeling of the patterns existing in the series under study, which allowed the authors to reduce the model error to 6.8%. As a result of the work, a forecast of the dynamics of the MICEX exchange rate at four levels is presented, presented in three scenarios: optimistic, realistic and pessimistic. As conclusions of the work, an analysis was made of the possibility of using the considered methods for multiple, medium and long-term forecasts; the complexity of the methods and the need to use special software products are evaluated. Read more...

A method for solving the inverse kinematics problem based on reinforcement learning for controlling robotic manipulators

A method for solving the inverse kinematics problem for a three-link robotic manipulator is proposed based on one of the types of machine learning - reinforcement learning. In the general case, this task consists of finding the laws of change in the generalized coordinates of the manipulator’s gripping device that provide the specified kinematic parameters. When solving the problem analytically, the basis for calculating inverse kinematics is the Denavit – Hartenberg parameters with further implementation of numerical matrix calculations. However, taking into account the kinematic redundancy of multi-link manipulators, this approach is labor-intensive and does not allow automated consideration of changes in the external environment in real time, as well as the features of the robot’s field of application. Therefore, an urgent research task is to develop a solution whose structure contains a self-learning block that provides a solution to the inverse kinematics problem under conditions of a changing external environment, the behavior of which is unknown in advance. The proposed method is based on simulating the process of achieving the goal of robot control (positioning the gripping device of the manipulator) at a given point in space using the trial and error method. For approaching the goal at each learning step, a reward function is calculated, which is used when controlling the robot. In the proposed method, the agent is a recurrent artificial neural network, and the environment, the state of which is observed and assessed, is a robotic manipulator. The use of a recurrent neural network made it possible to take into account the history of the movement of the manipulator and overcome the difficulties associated with the fact that different combinations of angles between links can lead to the same point in the workspace. Testing of the proposed method was carried out on a virtual model of the robot, made using the MatLAB Robotics System Toolbox and the Simscape environment, which showed high efficiency in terms of the “time – accuracy” criterion of the proposed method for solving the inverse kinematics problem. Read more...