# Solution of a Singular H¥ Control Problem: A Regularization Approach

### Valery Y. Glizer, Oleg Kelis

#### Abstract

We consider an infinite horizon H¥ control problem for linear systems with additive uncertainties (disturbances). The case of a singular weight matrix for the control cost in the cost functional is treated. In such a case, a part of the control coordinates is singular, meaning that the H¥ control problem itself is singular. We solve this problem by a regularization. Namely, we associate the original singular problem with a new H¥ control problem for the same equation of dynamics. The cost functional in the new problem is the sum of the original cost functional and an infinite horizon integral of the squares of the singular control coordinates with a small positive weight. This new H¥ control problem is regular, and it is a partial cheap control problem. Based on an asymptotic analysis of this H¥ partial cheap control problem, a controller solving the original singular H¥ control problem is designed. Illustrative example is presented.

Download#### Paper Citation

#### in Harvard Style

Glizer V. and Kelis O. (2017). **Solution of a Singular H¥ Control Problem: A Regularization Approach** . In *Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-263-9, pages 25-36. DOI: 10.5220/0006397600250036

#### in Bibtex Style

@conference{icinco17,

author={Valery Y. Glizer and Oleg Kelis},

title={Solution of a Singular H¥ Control Problem: A Regularization Approach},

booktitle={Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2017},

pages={25-36},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006397600250036},

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 - Solution of a Singular H¥ Control Problem: A Regularization Approach

SN - 978-989-758-263-9

AU - Glizer V.

AU - Kelis O.

PY - 2017

SP - 25

EP - 36

DO - 10.5220/0006397600250036