Multidimensional global extremum seeking via the DIRECT optimisation algorithm

Sei Zhen Khong, Dragan Nešić, Chris Manzie, Ying Tan

Research output: Contribution to journalArticle

33 Scopus citations


DIRECT is a sample-based global optimisation method for Lipschitz continuous functions defined over compact multidimensional domains. This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants. Finite-time semi-global practical convergence is established based on a periodic sampled-data control law, whose sampling period is a parameter which determines the region and accuracy of convergence. A crucial part of the development is dedicated to a robustness analysis of the DIRECT method against bounded additive perturbations on the objective function. Extremum seeking involving multiple units is also considered within the same context as a means to increase the speed of convergence. Numerical examples of global extremum seeking based on DIRECT are presented at the end.

Original languageEnglish (US)
Pages (from-to)1970-1978
Number of pages9
Issue number7
StatePublished - Jul 1 2013


  • DIRECT method
  • Extremum seeking control
  • Multidimensional global optimization
  • Robustness analysis

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