# SETTLING-TIME IMPROVEMENT IN GLOBAL CONVERGENCE LAGRANGIAN NETWORKS

### Acho L.

#### Abstract

In this brief, a modification of Lagrangian networks given in (Xia Y., 2003) is presented. This modification improves the settling time of the convergence of Lagrangian networks to a stationary point; which is the optimal solution to the nonlinear convex programming problem with linear equality constraints. This is important because, in many real-time applications where Lagrangian networks are used to find an optimal solution, such as in signal and image processing, this settling time is interpreted as the processing time. Simulation results applied to a quadratic optimization problem show that settling time is improved from about to 2000 to 20 seconds. Lyapunov theory was used to obtain our main result.

#### References

- M. Krstic, I. Kanellakopoulos, and P. Kokotovic, 1995. Non-linear and Adaptive Control Design, John Wiley and Sons. New York.
- Y. Xia, 2003. Global Convergence Analysis of Lagrangian Networks, In IEEE Transaction on Circuits and Systems I, 50 (6), 818-822, 2003.

#### Paper Citation

#### in Harvard Style

L. A. (2005). **SETTLING-TIME IMPROVEMENT IN GLOBAL CONVERGENCE LAGRANGIAN NETWORKS** . In *Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 972-8865-29-5, pages 315-318. DOI: 10.5220/0001152903150318

#### in Bibtex Style

@conference{icinco05,

author={Acho L.},

title={SETTLING-TIME IMPROVEMENT IN GLOBAL CONVERGENCE LAGRANGIAN NETWORKS},

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

year={2005},

pages={315-318},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001152903150318},

isbn={972-8865-29-5},

}

#### in EndNote Style

TY - CONF

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

TI - SETTLING-TIME IMPROVEMENT IN GLOBAL CONVERGENCE LAGRANGIAN NETWORKS

SN - 972-8865-29-5

AU - L. A.

PY - 2005

SP - 315

EP - 318

DO - 10.5220/0001152903150318