Time-Optimal Motions of Mechanical System with Viscous Friction

Dmitrii Kamzolkin; Vladimir Ternovski

doi:10.20944/preprints202404.1144.v2

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preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202404.1144.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Time-Optimal Motions of Mechanical System with Viscous Friction

Dmitrii Kamzolkin

and

Vladimir Ternovski

Version 1 : Received: 17 April 2024 / Approved: 17 April 2024 / Online: 18 April 2024 (07:09:14 CEST)
Version 2 : Received: 3 May 2024 / Approved: 3 May 2024 / Online: 3 May 2024 (10:28:32 CEST)

A peer-reviewed article of this Preprint also exists.

Kamzolkin, D.; Ternovski, V. Time-Optimal Motions of a Mechanical System with Viscous Friction. Mathematics 2024, 12, 1485. Kamzolkin, D.; Ternovski, V. Time-Optimal Motions of a Mechanical System with Viscous Friction. Mathematics 2024, 12, 1485.

Abstract

Optimal control is a critical tool for mechanical robotic systems, facilitating precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin's Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Keywords

inverse problems; optimal control; maximum principle; viscous friction; reachibility set

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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