Dr. Kartik Ariyur

Honeywell AES GN&C COE

 

Extremum Seeking Control: Theory and Applications

 

Abstract

 

Extremum seeking consists in maximizing or minimizing (extremizing) online (i.e., via feedback) the output of a plant with respect to its control inputs.  It is applicable to systems with a stable reference-to-output map, where this reference-to-output map has an extremum.  There are several methods to solve this problem-all of them different online (feedback) implementations of gradient descent.  Our talk will focus on the method of estimating local gradient using a sinusoidal perturbation into the plant dynamics, the most popularly used method, and the only one capable so far of converging as fast as the plant dynamics.  The first use of sinusoidal perturbation based extremum seeking was reported in 1922, making extremum seeking possibly the first method of adaptive control.  We will overview extremum seeking on a static map, its generalization to maps embedded amidst dynamics, with dynamic parameter variations, and to multiparameter systems.  Rigorous design guidelines for achieving stable extremum seeking feedback will be presented.  We will then present the application of extremum seeking to minimum power demand formation flight.  If time permits, we will also present near-optimal compressor operation via slope-seeking, a generalization of extremum seeking.