Synthesized Control for Optimal Control Problem of Motion Along the Program Trajectory

The optimal control problem of object motion along the program trajectory is considered. The problem is stated as the optimal control problem with phase constraints in the form of equalities. Initial and terminal states are constrained. The numerical solution to the problem is proposed. Some points are defined on the program trajectory. The quality criterion includes time and hitting accuracy to the terminal state, integral error of motion along the program trajectory and sum of minimal distances to defined points on the program trajectory. To solve the problem direct approach on the base of control approximation by piecewise linear function and synthesized control are used. For synthesized control a method of machine learning control by symbolic regression is applied. In computational experiment the optimal control problem is solved for mobile robot moving along a program trajectory. Solutions obtained by both methods are compared in the presence of perturbations of the mathematical model of control object.