Optimal Control Problem and Its Solution in Class of Feasible Control Functions by Advanced Model of Control Object

Askhat Diveev and Elena Sofronova ()
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Askhat Diveev: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova Str., 44, Build. 2, 119333 Moscow, Russia
Elena Sofronova: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova Str., 44, Build. 2, 119333 Moscow, Russia

Mathematics, 2025, vol. 13, issue 4, 1-17

Abstract: This paper is devoted to the solution of the optimal control problem. The obtained control should be optimal in terms of quality criteria and, at the same time, feasible when implemented in the control object. To solve the optimal control problem in the class of feasible control functions, an advanced mathematical model of the control object is used. Firstly, the universal stabilisation system of the motion along any trajectory from some class is developed via symbolic regression. Then, the obtained stabilisation system is inserted into the right part of the control object model instead of the control vector. A reference model with a free control vector in the right part is added to the model; thus, the advanced mathematical model of the control object is obtained. After this, the optimal control problem is solved with the advanced mathematical model of the control object. The optimal control problem is stated in the classical form when the control is a time function. Here, the control function is searched for the reference model. The preliminary design of the universal stabilisation system for some class of trajectories allows the solution of the optimal control problem via the control object in a reasonable time frame. The proposed methodology is computationally tested for a model of the spatial motion of a quadcopter and a group of two-wheeled mobile robots with a differential drive. The results of the experiments show that the universal stabilisation system ensures the stabilisation of the motion of the objects along optimal trajectories, which are not known beforehand but obtained as a result of solving the problem with an advanced model.

Keywords: stabilisation; trajectory tracking; optimal control; stabilisation system; machine learning; symbolic regression; mobile robot; quadcopter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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