A new two-step approach for solving a control system synthesis problem by symbolic regression methods

Abstract

The problem of synthesizing a control system using symbolic regression methods is considered. A new approach suggested in this work considers the control system synthesis problem as the set of optimal control problems and suggests a two-step algorithm to solve it. At the first step evolutionary algorithms are used to solve the optimal control problem numerically for each initial state from a given domain. As a result of the first step a set of optimal trajectories is obtained. At the second step symbolic regression methods are considered to solve the problem of approximating the found in the first step set of trajectories optimally. The result of the second step is a solution of the control system synthesis problem as a multidimensional control function of object’s state vector. Compared to the known approach to solve the control system synthesis problem using symbolic regression methods, the suggested approach provides betters results since the search of control function is carried out based on the set of optimal trajectories. Computational experiment presents the solution of the applied problem of synthesizing the optimal control system for the spacecraft landing on the Moon. It is experimentally demonstrated that the synthesized control system provides a close to optimal landing trajectory for any initial state from a given domain.