Abstract
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 language | English (US) |
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Pages (from-to) | 1970-1978 |
Number of pages | 9 |
Journal | Automatica |
Volume | 49 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2013 |
Bibliographical note
Funding Information:Dragan Nešić is a Professor in the Department of Electrical and Electronic Engineering (DEEE) at The University of Melbourne, Australia. He received his B.E. degree in Mechanical Engineering from The University of Belgrade, Yugoslavia, in 1990, and his Ph.D. degree from Systems Engineering, RSISE, Australian National University, Canberra, Australia, in 1997. Since February 1999 he has been with The University of Melbourne. His research interests include networked control systems, discrete-time, sampled-data and continuous-time nonlinear control systems, input-to-state stability, extremum seeking control, applications of symbolic computation in control theory, hybrid control systems, and so on. He was awarded a Humboldt Research Fellowship (2003) by the Alexander von Humboldt Foundation, an Australian Professorial Fellowship (2004–2009) and Future Fellowship (2010–2014) by the Australian Research Council. He is a Fellow of IEEE and a Fellow of IEAust. He is currently a Distinguished Lecturer of CSS, IEEE (2008–). He served as an Associate Editor for the journals Automatica, IEEE Transactions on Automatic Control, Systems and Control Letters and European Journal of Control.
Funding Information:
Ying Tan received her B.E. degree from Tianjin University, China, in 1995. In 1998, she joined the National University of Singapore and finished her Ph.D. study in 2002. She joined McMaster University in 2002 as a postdoctoral fellow in the Department of Chemical Engineering. She started her work in the Department of Electrical and Electronic Engineering, the University of Melbourne, in 2004. Currently Dr. Ying Tan is Future Fellow (2010–2013), which is a research position funded by the Australian Research Council. Her research interests are in intelligent systems, nonlinear control systems, real time optimisation, sampled-data distributed parameter systems and formation control.
Keywords
- DIRECT method
- Extremum seeking control
- Multidimensional global optimization
- Robustness analysis