Refined Optimal Control Problem and Its Solution Using Symbolic Regression

Abstract

The new refined setting of the optimal control problem is presented. Now a solution of the new problem can be realized in control object directly. Previously, the solution of the classical statement of the optimal control problem could not be realized on the object directly because this led to an open control system. The new refined setting of the problem includes additional conditions. The optimal trajectory in the state space must have an attraction property in some neighborhood. To solve the new refined problem the synthesized control method is proposed. According to the method initially the control synthesis problem is solved. The control object becomes a stable in some equilibrium point in the state space. Secondly the optimal control problem is solved by moving positions of stable equilibrium point. An example of solving the new optimal control problem with complex phase constraints for mobile robot is presented. For comparison this problem was solved by directly method without new additional conditions. Both solutions are simulated with perturbations of the model. Experiments shows that the solution of the new problem is less sensitivity to perturbations than the solution of the classical one.