A bundle method for solving the fixed order control problem
Authors:
- M. RotunnoMRM. Rotunno
- R.A. de CallafonRCR.A. de Callafon
- 27 August 2003
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3, 3156-3161
Abstract
Recently bundle methods have been proposed for solv- ing Semi-Definite Programming (SDP) problems which consist of minimizing a linear objective subject to Lin- ear Matrix Inequality (LMI) constraints. These meth- ods are appealing especially for large scale problems. Many control problems can be cast as SDPs. In con- trast fixed order control problems in the LMI frame- work require an additional rank constraint on the LMIs which makes the problem insolvable with traditional SDP methods. One way of imposing the rank con- straint is to formulate the fixed order control problem in terms of the eigenvalues of the LMIs. This makes the problem nondifferentiable, but amenable to bundle methods.Keywords
This publication has 8 references indexed in Scilit:
- Solving large structured semidefinite programs using an inexact spectral bundle method2002
- A Spectral Bundle Method for Semidefinite ProgrammingSIAM Journal on Optimization, 2000
- A bundle method for efficiently solving large structured linear matrix inequalities2000
- A cone complementarity linearization algorithm for static output-feedback and related problemsIEEE Transactions on Automatic Control, 1997
- Low-order control design for LMI problems using alternating projection methodsAutomatica, 1996
- A linear matrix inequality approach toH∞controlInternational Journal of Robust and Nonlinear Control, 1994
- Proximity control in bundle methods for convex nondifferentiable minimizationMathematical Programming, 1990
- A constraint linearization method for nondifferentiable convex minimizationNumerische Mathematik, 1987