Slope seeking: a generalization of extremum seeking

Abstract

This work introduces slope seeking, a new idea for non-model based adaptive control. It involves driving the output of a plant to a value corresponding to a commanded slope of its reference-to-output map. To achieve this objective, we introduce a slope reference input into a sinusoidal perturbation-based extremum seeking scheme; derive a stability test for single parameter slope seeking, and then develop a systematic design algorithm based on standard linear SISO control methods to satisfy the stability test. We then extend the results to the multivariable case of gradient seeking. Finally, we illustrate near-optimal compressor operation under slope seeking feedback through a simulation study upon the well-known Moore-Greitzer model of compressor instability.

A rapidly settled closed-loop control for airfoil aerodynamics based on plasma actuation

“…Several existing adaptive control methods only require the limited system information and can achieve the target performance with large parameter uncertainties in the system (Cho and Shyy 2011). Ariyur and Krstić (2004) proposed the non-model-based adaptive control method, viz. slope seeking, to extend the extremum seeking algorithm.…”

Stochastic Averaging and Stochastic Extremum Seeking

“…The extremum seeking (ES) method has seen significant theoretical advances during the past decade, including the proof of local convergence [6,27,119,140], PID tuning [61], slope seeking [7], performance improvement and limitations in ES control [70], extension to semi-global convergence [137], development of scalar Newton-like algorithms [101,102,108], inclusion of measurement noise [135], extremum seeking with partial modeling information [1,2,33,36,50], and learning in noncooperative games [40,136].…”

Extremum seeking via continuation techniques for optimizing biogas production in the chemostat

“…In the presence of random disturbances in the evaluation of F we gradually increase the accuracy of the evaluation of F during the iteration by using the mean of y over a longer time interval after the transients have settled. Note that, when using act-andwait and a discrete-time optimization algorithm one has removed two of the two slower time scales present in [4], replacing them with the algorithmic iteration (the Newton iteration converges super-exponentially).…”