An extended approach to solving the optimal control problem in the class of implemented control functions

Abstract

The article discusses the actual problem of implementing solutions to the classical optimal control problem used in automated real-time systems. It is well known that the direct application of the time-dependent control function obtained within the framework of the classical approach is ineffective for real objects due to the open nature of the control loop and sensitivity to disturbances. An innovative method based on the concept of an extended management object model is proposed. The key idea of the method is the initial synthesis of a universal object motion stabilization system capable of accurately following any given trajectory in a wide class of states. This system is then integrated into the management facility. For the effective and automatic synthesis of a universal motion stabilization system, a machine learning method is used – symbolic regression, which makes it possible to obtain compact and analytical expressions for control actions. The paper describes in detail the application of the proposed approach to the complex problem of optimal control of a quadcopter, demonstrating not only the theoretical possibility, but also the practical feasibility of the solution found, as well as its high robustness with respect to various initial disturbances. The results of computational experiments confirming the effectiveness of the approach are presented.