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) |
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Pages (from-to) | 2720-2733 |
Number of pages | 14 |
Journal | Automatica |
Volume | 49 |
Issue number | 9 |
DOIs | |
State | Published - Sep 1 2013 |
Keywords
- Extremum seeking
- Multi-unit systems
- Nonconvex global optimisation
- Robustness
- Sampled-data control