Reduced-order greedy controllability of finite dimensional linear systems

Giulia Fabrini, Laura Iapichino, Stefan Volkwein

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)

Abstract

Often a dynamical system is characterized by one or more parameters describing physical features of the problem or geometrical configurations of the computational domain. As a consequence, by assuming that the system is controllable, a range of optimal controls exists corresponding to different parameter values. The goal of the proposed approach is to avoid the computation of a control function for any instance of the parameters. The greedy controllability consists in the selection of the most representative values of the parameter set that allows a rapid approximation of the control function for any desired new parameter value, ensuring that the system is steered to the target within a certain accuracy. By proposing the reduced basis (RB) method in this framework, we are able to consider linear parametrized partial differential equations (PDEs) in our setting. The computational costs are drastically reduced and the efficiency of the greedy controllability approach is significantly improved. As a numerical example a heat equation with convection is studied to illustrate our proposed RB greedy controllability strategy.

Original languageEnglish
Pages (from-to)296-301
Number of pages6
JournalIFAC-PapersOnLine
Volume51
Issue number2
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • controllability
  • greedy algorithm
  • Optimal control
  • parametrized linear systems
  • parametrized parabolic equations
  • reduced basis method

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