A compressed-sensing approach for closed-loop optimal control of nonlinear systems

Lionel Mathelin*, Luc Pastur, Olivier Le Maitre

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We present a method that seeks to combine the properties of optimal controlwith the robust character of closed-loop control. The method relies on the availability of a reduced model of the system to be controlled, in order to express the control problem in a low-dimensional space where the system-state-dependent optimal control law is subsequently approximated in a preprocessing stage. A polynomial expansion is used for the approximation, enabling fast update of the optimal control law each time a new observation of the system state is made available. It results in a real-time compatible, efficient (optimal-like), and robust control strategy. A compressed-sensing approach is proposed to efficiently construct the approximate control law, exploiting the compressible character of the optimal control law in the retained approximation basis. The method is demonstrated for the control of the flow around a cylinder and is shown to perform as well as the much more costly receding-horizon optimal control approach, where the exact optimal control problem is actually recomputed, even in the presence of large aleatoric perturbations. Potential and remaining issues toward application to larger dimensional reduced systems are also discussed, and some directions for improvement are suggested.

Original languageEnglish (US)
Pages (from-to)319-337
Number of pages19
JournalTheoretical and Computational Fluid Dynamics
Volume26
Issue number1-4
DOIs
StatePublished - Jan 1 2012

Keywords

  • Closed-loop control
  • Compressed sensing
  • Model reduction
  • Nonlinear control

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Engineering(all)
  • Fluid Flow and Transfer Processes

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