Relaxation and Optimization of Impulsive Hybrid Systems - Inspired by Impact Mechanics

Elena Goncharova, Maxim Staritsyn

2017

Abstract

The paper compresses some results on modeling and optimization in a class of hybrid systems with control switches of dynamics. The study is motivated by widespread physical phenomena of impulsive nature, faced in contact dynamics, such as unilateral contacts of rigid bodies and impactively blockable degrees of freedom. The developed modeling approach is based on a representation of hybrid events as impulsive control actions produced by distributions or Borel measures under constraints on states before and after the action. Basically, such systems are described by measure differential equations with states of bounded variation, and the relations between the trajectory and the control measure are given by a specific mixed condition of a complementarity type. The main goal of the study is to describe the closure of the tube of solutions to the addressed system. For this, we design an approximation of the hybrid property, and develop a specific singular time-spatial transformation of the original system. A convexification of the transformed system then defines – after the inverse transform – the closed set of generalized, limit solutions. The main result concerns the asymptotic behavior of these generalized solutions, stating that the hybrid property is preserved after the relaxation.

Paper Citation

in Harvard Style

Goncharova E. and Staritsyn M. (2017). Relaxation and Optimization of Impulsive Hybrid Systems - Inspired by Impact Mechanics . In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-263-9, pages 474-485. DOI: 10.5220/0006426004740485

in Bibtex Style

@conference{icinco17,
author={Elena Goncharova and Maxim Staritsyn},
title={Relaxation and Optimization of Impulsive Hybrid Systems - Inspired by Impact Mechanics},
booktitle={Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2017},
pages={474-485},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006426004740485},
isbn={978-989-758-263-9},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Relaxation and Optimization of Impulsive Hybrid Systems - Inspired by Impact Mechanics
SN - 978-989-758-263-9
AU - Goncharova E.
AU - Staritsyn M.
PY - 2017
SP - 474
EP - 485
DO - 10.5220/0006426004740485