# BOUNDARY CONTROL OF A CHANNEL - Last Improvements

### Valérie Dos Santos, Christophe Prieur

#### Abstract

Different improvements have been developed in regards to the stability and the control of two-by-two non linear systems of conservation laws, and in particular for the Saint-Venant equations and the control of flow and water level on irrigation channel. One stability result based on the Riemann coordinates is presented here and sufficient conditions are given to insure the Cauchy convergence. Another result still based on the Riemann approach is presented too, in the linear case, to improve the feedback control based on the Riemann invariants.

#### References

- Coron, J. M., d'Andréa Novel, B., and Bastin, G. (2007). A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws. Automatic Control, IEEE Transactions on Automatic Control, 52(1):2-11.
- Coron, J.-M., de Halleux, J., Bastin, G., and d'Andréa Novel, B. (2002). On boundary control design for quasi-linear hyperbolic systems with entropies as Lyapunov functions. Proceedings 41-th IEEE Conference on Decision and Control, Las Vegas, USA,, pages 3010 - 3014.
- Dos Santos, V., Bastin, G., Coron, J.-M., and d'Andréa Novel, B. (2007). Boundary control with integral action for hyperbolic systems of conservation laws: Lyapunov stability analysis and experimental validation. submitted to Automatica.
- Dos Santos, V. and Prieur, C. (2007). Boundary control of a channel: practical and numerical studies. in preparation.
- Litrico, X., Fromion, V., Baume, J.-P., Arranja, C., and Rijo, M. (2005). Experimental validation of a methodology to control irrigation canals based on saint-venant equations. Control Engineering Practice, 13:1425- 1437.
- Prieur, C., Winkin, J., and Bastin, G. (2006). Boundary control of non-homogeneous systems of conservation laws. preprint.
- Renardy, M. and Rogers, R. (1993). An introduction to partial differential equations. Springer Verlag.

#### Paper Citation

#### in Harvard Style

Dos Santos V. and Prieur C. (2007). **BOUNDARY CONTROL OF A CHANNEL - Last Improvements** . In *Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-972-8865-82-5, pages 320-325. DOI: 10.5220/0001637903200325

#### in Bibtex Style

@conference{icinco07,

author={Valérie Dos Santos and Christophe Prieur},

title={BOUNDARY CONTROL OF A CHANNEL - Last Improvements},

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

year={2007},

pages={320-325},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001637903200325},

isbn={978-972-8865-82-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - BOUNDARY CONTROL OF A CHANNEL - Last Improvements

SN - 978-972-8865-82-5

AU - Dos Santos V.

AU - Prieur C.

PY - 2007

SP - 320

EP - 325

DO - 10.5220/0001637903200325