Abstract
Two frameworks are proposed for extremum seeking of general nonlinear plants based on a sampled-data control law, within which a broad class of nonlinear programming methods is accommodated. It is established that under some generic assumptions, semi-global practical convergence to a global extremum can be achieved. In the case where the extremum seeking algorithm satisfies a stronger asymptotic stability property, the converging sequence is also shown to be stable using a trajectory-based proof, as opposed to a Lyapunov-function- type approach. The former is more straightforward and insightful. This allows for more general optimisation algorithms than considered in existing literature, such as those which do not admit a state-update realisation and/or Lyapunov functions. Lying at the heart of the analysis throughout is robustness of the optimisation algorithms to additive perturbations of the objective function. Multi-unit extremum seeking is also investigated with the objective of accelerating the speed of convergence.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2720-2733 |
| Number of pages | 14 |
| Journal | Automatica |
| Volume | 49 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2013 |
| Externally published | Yes |
Bibliographical note
Funding Information:This work was supported by the Australian Research Council ( DP0985388 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Nathan Van De Wouw under the direction of Editor Andrew R. Teel.
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 BE degree in Mechanical Engineering from The University of Belgrade, Yugoslavia in 1990, and his Ph.D. 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.
Keywords
- Extremum seeking
- Multi-unit systems
- Nonconvex global optimisation
- Robustness
- Sampled-data control