Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
SIAM Journal on Control and Optimization
On non-local stability properties of extremum seeking control
Automatica (Journal of IFAC)
Brief Stability of extremum seeking feedback for general nonlinear dynamic systems
Automatica (Journal of IFAC)
Brief Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties
Automatica (Journal of IFAC)
Multivariable Newton-based extremum seeking
Automatica (Journal of IFAC)
A non-gradient approach to global extremum seeking: An adaptation of the Shubert algorithm
Automatica (Journal of IFAC)
Extremum-seeking control for nonlinear systems with periodic steady-state outputs
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
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.