Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation

Morin, Pascal and Murray, Richard M. and Praly, L. (1997) Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:1997.014]

Full text available as:

PDF - Requires Adobe Acrobat Reader or other PDF viewer.

Abstract

Motivated by some recent results on the stabilization of homogeneous systems, we present a gain-scheduling approach for the stabilization of non-linear systems. Given a one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show how the parameter can be rescaled as a function of the state to give a new stabilizing controller. In the case of homogeneous systems, we obtain generalizations of some existing results. We show that this approach can also be applied to nonhomogeneous systems. In particular, the main application considered in this paper is to the problem of stabilization with magnitude limitations. For this problem, we develop a design method for single-input controllable systems with eigenvalues in the left closed plane.

EPrint Type:	Monograph (Technical Report)
Additional Information:	P. Morin contributed to this work while he was with the CDS Dept. at Caltech as a Post-doctoral fellow.
Uncontrolled Keywords:	gain scheduling, global stabilization, bounded control, nonlinear feedback
Subjects:	All Records
ID Code:	160
Deposited By:	Arun Sannuti
Deposited On:	19 December 2007
Unique Identifier:	CaltechCDSTR:1997.014
Official Persistent URL:	http://resolver.caltech.edu/CaltechCDSTR:1997.014
Official Citation:	Morin, Pascal, Murray, Richard M. and Praly, L. (1997) Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation. Technical Report. California Institute of Technology, Pasadena, CA. [http://resolved.caltech.edu/CaltechCDSTR:1997.014]
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

Archive Staff Only: edit this record