TY - JOUR
T1 - Fixed low-order controller design and H∞ optimization for large-scale dynamical systems
AU - Mitchell, Tim
AU - Overton, Michael L.
N1 - Funding Information:
★The work of T. Mitchell and M.L. Overton was supported by ★The work of T. Mitchell and M.L. Overton was supported by NaTtihoenawloSrckienocfeTF.ouMnidtcahtieollnagnradntMD.LM.SO-1v3e1r7to2n05.was supported by NationalThe woSciencerk of T.FouMnidtcahtieollnandgrantMDM.L.S-1317205.Overton was supported by National Science Foundation grant DMS-1317205. National Science Foundation grant DMS-1317205.
Publisher Copyright:
© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
PY - 2015/7/1
Y1 - 2015/7/1
N2 - Large-scale linear time-invariant dynamical systems with inputs and outputs present major challenges for controller design. Model-order reduction has become popular in recent years, but controllers designed for reduced-order models may result in unstable closed-loop plants when applied to the larger-scale system. We investigate the practicality of fixed low-order controller design applied directly to large-scale continuous-time sparse systems. We assume that it is practical to compute the eigenvalues with largest real part of such systems using Matlab's eigs, which requires only matrix-vector products, but that it is not possible to compute the H,x norm using Matlab's getPeakGain or SLlCOT's slinorm, which use the Boyd-Balakrishnan-Bruinsma-Steinbuch algorithm, requiring both Hamiltonian eigenvalue decompositions and singular value decompositions. Instead, we employ a recently developed efficient algorithm called Hybrid-Expansion-Contraction (HEC), which while not guaranteed to correctly compute the H∞ norm, finds, under certain assumptions, at least a local maximizer of the associated transfer function. Our controller design code uses nonsmooth optimization techniques first to attempt to stabilize the closed-loop system and then to minimize its H∞ norm proxy as computed by HEC. It is implemented in a new experimental MATLAB code HIFOOS, based on the public-domain HIFOO toolbox first presented in ROCOND 2006, and will be made available for public use after further investigation and development.
AB - Large-scale linear time-invariant dynamical systems with inputs and outputs present major challenges for controller design. Model-order reduction has become popular in recent years, but controllers designed for reduced-order models may result in unstable closed-loop plants when applied to the larger-scale system. We investigate the practicality of fixed low-order controller design applied directly to large-scale continuous-time sparse systems. We assume that it is practical to compute the eigenvalues with largest real part of such systems using Matlab's eigs, which requires only matrix-vector products, but that it is not possible to compute the H,x norm using Matlab's getPeakGain or SLlCOT's slinorm, which use the Boyd-Balakrishnan-Bruinsma-Steinbuch algorithm, requiring both Hamiltonian eigenvalue decompositions and singular value decompositions. Instead, we employ a recently developed efficient algorithm called Hybrid-Expansion-Contraction (HEC), which while not guaranteed to correctly compute the H∞ norm, finds, under certain assumptions, at least a local maximizer of the associated transfer function. Our controller design code uses nonsmooth optimization techniques first to attempt to stabilize the closed-loop system and then to minimize its H∞ norm proxy as computed by HEC. It is implemented in a new experimental MATLAB code HIFOOS, based on the public-domain HIFOO toolbox first presented in ROCOND 2006, and will be made available for public use after further investigation and development.
KW - H control
KW - HIFOO
KW - Low-order controller design
KW - Robust stabilization
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U2 - 10.1016/j.ifacol.2015.09.428
DO - 10.1016/j.ifacol.2015.09.428
M3 - Conference article
AN - SCOPUS:84992530883
SN - 2405-8963
VL - 28
SP - 25
EP - 30
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
IS - 14
T2 - 8th IFAC Symposium on Robust Control Design, ROCOND 2015
Y2 - 8 July 2015 through 11 July 2015
ER -