Global output-feedback extremum seeking for a class of nonlinear dynamic systems with arbitrary relative degree

ABSTRACT

An output-feedback sliding-mode-based extremum-seeking controller was recently introduced for linear uncertain systems by using periodic switching functions. Nonlinear systems were also considered but restricted to relative degree one plants as well as the former linear case. Here, generalisation is achieved to include more general dynamics with arbitrary relative degree, thanks to the introduction of a high-gain adaptive observer with updated gain. Global stability properties of the closed-loop system with convergence to a controlled neighbourhood of the desired maximum point are also rigorously proved. Simulation and experimental results illustrate the performance of the proposed extremum-seeking control algorithm.

KEYWORDS:

• Nonlinear systems
• arbitrary relative degree
• sliding mode control
• extremum seeking
• output-feedback
• adaptive observers
• global stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Without loss of generality, we only address the maximum-seeking problem.

2. In fact, $t_{y^{*}}$ can be chosen large enough to assure that the HGO estimation error is small (t_y^* > t_μ) and that the exponential term in (29(29) $$|d_e(x,\xi )|+\delta \le \bar{\varrho }(\omega ,t)+{\pi }_2,$$(29) ) has decreased to an arbitrarily small value so that the modulation function ϱ overcomes the disturbance d_e.

Additional information

Funding

The study is funded by CAPES, FAPERJ and CNPq from Brazil.