A Stabilisation System Synthesis for Motion along a Preset Trajectory and Its Solution by Symbolic Regression

Askhat Diveev, Elena Sofronova and Nurbek Konyrbaev ()
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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
Nurbek Konyrbaev: Institute of Engineering and Technology, Korkyt Ata Kyzylorda University, Aiteke bi Str. 29A, Kyzylorda 120014, Kazakhstan

Mathematics, 2024, vol. 12, issue 5, 1-14

Abstract: The problem of a stabilisation system synthesis for the motion of a control object along a given spatial trajectory is considered. The complexity of the problem is that the preset trajectory is defined in the state subspace and not in time. This paper describes a stabilisation system synthesis for motion along a trajectory specified in time and along a trajectory specified in the form of a manifold in a state space. In order to construct a stabilisation system, it is necessary to determine a distance between an object and the given trajectory at each moment in time. For trajectories that are not given in time, the determination of this distance can be ambiguous. An object may be exactly on a trajectory but at a different time. This paper proposes some approaches to solve the problem. One of the approaches is to transform a given trajectory in a state subspace into a trajectory given in time. A description of a universal method to perform this transformation is presented. In order to solve the synthesis problem automatically, without having to analyse the mathematical model of the control object, it is suggested that machine learning control by symbolic regression is used. In computational experiments, examples of stabilisation system syntheses for quadcopter motion along a given spatial trajectory are presented.

Keywords: machine learning control; optimal control; control synthesis; stabilisation system; symbolic regression; quadcopter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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