Solving the Control Synthesis Problem Through Supervised Machine Learning of Symbolic Regression

This paper considers the control synthesis problem and its solution using symbolic regression. Symbolic regression methods, which were previously called genetic programming methods, allow one to use a computer to find not only the parameters of a given regression function but also its structure. Unlike other works on solving the control synthesis problem using symbolic regression, the novelty of this paper is that for the first time this work employs a training dataset to address the problem of general control synthesis. Initially, the optimal control problem is solved from each point in a given set of initial states, resulting in a collection of control functions expressed as functions of time. A reference model is then integrated into the control object model, which generates optimal motion trajectories using the derived optimal control functions. The control synthesis problem is framed as an approximation task for all optimal trajectories, where the control function is sought as a function of the deviation of the object from the specified terminal state. The optimization criterion for solving the synthesis problem is the accuracy of the object’s movement along the optimal trajectory. The paper includes an example of solving the control synthesis problem for a mobile robot using a supervised machine learning method. A relatively new method of symbolic regression, the method of variational complete binary genetic programming, is studied and proposed for the solution of the control synthesis problem.