Fixed low-order controller design and H optimization for large-scale dynamical systems

Tim Mitchell, Michael Overton

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)25-30
Number of pages6
JournalUnknown Journal
Volume28
Issue number14
DOIs
StatePublished - Jul 1 2015

Fingerprint

Controller Design
MATLAB
Dynamical systems
Dynamical system
Norm
Controllers
Optimization
Contraction
Eigenvalue Decomposition
Model Order Reduction
Nonsmooth Optimization
Reduced Order Model
Cross product
Matrix Product
Large-scale Systems
Singular value decomposition
Hamiltonians
Transfer Function
Optimization Techniques
Closed-loop

Keywords

  • H control
  • HIFOO
  • Low-order controller design
  • Robust stabilization

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Fixed low-order controller design and H optimization for large-scale dynamical systems. / Mitchell, Tim; Overton, Michael.

In: Unknown Journal, Vol. 28, No. 14, 01.07.2015, p. 25-30.

Research output: Contribution to journalArticle

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