An adaptive compressed-sensing equation-free approach for closed-loop nonlinear control

Lionel Mathelin*, Luc Pastur, Olivier Le Maître

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a method which seeks to combine the efficiency of an optimal control command with the robustness of a closed-loop controller. While the performance of optimal control is excellent, it cannot account for perturbations to the system under control which make the resulting performance to drop. On the other hand, a closed-loop control makes use of the actual state of the system and is thus robust, at the price of limited performance. We here present a control method which is both robust (closed-loop) and achieves a near-optimal performance. The controller relies on an approximation of the optimal control command in the state space where the system lies upon reduction. The command can then be updated when a new observation of the system becomes available, hence achieving a closed-loop control. The approximation of the command in the state space is a computationally costly step but is achieved off-line and only once. To minimize its cost while achieving a good accuracy in the approximation, an adaptive multi-wavelets approach, combined with compressed-sensing acceleration exploiting compressibility, is here proposed. The control algorithm is demonstrated on the control of a cylinder wake in a 2-D flow.

Original languageEnglish (US)
Title of host publication6th AIAA Theoretical Fluid Mechanics Conference
StatePublished - 2011
Externally publishedYes
Event6th AIAA Theoretical Fluid Mechanics Conference - Honolulu, HI, United States
Duration: Jun 27 2011Jun 30 2011

Other

Other6th AIAA Theoretical Fluid Mechanics Conference
CountryUnited States
CityHonolulu, HI
Period06/27/1106/30/11

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

Fingerprint Dive into the research topics of 'An adaptive compressed-sensing equation-free approach for closed-loop nonlinear control'. Together they form a unique fingerprint.

Cite this