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H∞ Control of Nonlinear Systems: A Class of Controllers

Lu, Wei-Min and Doyle, John C. (1993) H∞ Control of Nonlinear Systems: A Class of Controllers. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1993.008

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Abstract

The standard state space solutions to the H∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H∞-controllers are parameterized as nonlinear fractional transformations on contractive, stable free nonlinear parameters. As in the linear case, the H∞ control problem is solved by its reduction to four simpler special state space problems, together with a separation argument. Another byproduct of this approach is that the sufficient conditions for H∞ control problem to be solved are also derived with this machinery. The solvability for nonlinear H∞-control problem requires positive definite solutions to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy an additional coupling condition. An illustrative example, which deals with a passive plant, is given at the end.


Item Type:Report or Paper (Technical Report)
Additional Information:The authors would like to thank Prof. R. Murray at Caltech for extensive discussion during this work. They also gratefully acknowledge helpful discussion with Prof. K. Astrom (Lund Inst Tech), Prof. M. Dahleh (MIT), M. Newlin (Caltech) and P. Young (Caltech). Support for this work was provided by NSF, AFOSR, and ONR.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:H infinity control
Record Number:CaltechCDSTR:1993.008
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1993.008
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28060
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:01 Sep 2006
Last Modified:26 Dec 2012 14:29

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