Universal Stabilisation System for Control Object Motion along the Optimal Trajectory

• Published in: Mathematics (Basel) Vol. 11; no. 16; p. 3556
• Main Authors: Diveev, Askhat, Sofronova, Elena
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-08-2023
• Subjects: Analysis; control synthesis; Control systems; Dynamic programming; Equilibrium; evolutionary algorithm; Evolutionary computation; Mathematical models; Mathematics; Numerical methods; Object motion; Optimal control; stabilisation system; Subsystems; symbolic regression; Synthesis; Trajectory optimization
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11163556

An attempt to construct a universal stabilisation system that ensures the object motion along specified trajectory from certain class is presented. If such a stabilisation system is constructed, then only the problem of optimal control is solved, but for a model of the object, which includes a stabilisation system and a subsystem with a reference model for generating a specified trajectory. In this case, the desired control is the control in the reference model. Statement of complete optimal control problem includes two problems, optimal control problem and stabilisation system synthesis problem for motion along given trajectory in the state space. Numerical methods for solving these problems based on evolutionary computation and symbolic regression are described. It is shown that when solving the stabilisation system synthesis problem, it is possible to obtain a universal system that provides stabilisation of the object motion relative to any trajectory from a certain class. Therefore, it is advisable to formulate an optimal control problem for an object with a motion stabilisation system. A computational example of solving the problem for the spatial motion of a quadrocopter is given.