Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Abstract

Engineers strive to realize the goal of control in the best possible way based on a given quality criterion when developing control system. The well-known optimal control problem requires finding a solution as a function of time. Such a function cannot be directly used to control a real object because its application corresponds to an open-loop control system and engineers usually complete it with a feedback stabilization system. Hence, there is an obvious need to reformulate the optimal control problem so that its solution can be directly applied to real objects. The paper presents a new extended statement of the optimal control problem. An additional requirement for the control function is introduced to give the system describing the control object properties that will ensure the stability of solutions. The desired control function must provide for the optimal trajectory given the properties of the attractor in the neighbourhood. The solution to the extended optimal control problem can be directly used to control a real object. The paper presents a computational machine learning approach to solving the extended problem of optimal control based on the application of a synthesized optimal control technique. Examples of the practical solution to the stated problem are given to illustrate the efficiency of the approach, where the solution to the conventional optimal control problem is compared with the proposed extended one in the presence of perturbations in models and initial conditions.