Planar Cooperative Extremum Seeking with Guaranteed Convergence Using A Three-Robot Formation

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at maximizer, and is assumed to be locally concave around maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighborhood disk around maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.Comment: Presented at the 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, US

Delayed Newton-based multivariable extremum seeking with sequential predictors

We provide a new method for Newton-based multivariable extremum seeking which allows different delays in each of the input channels. We allow arbitrarily long input delays. Our sequential predictor delay compensation method eliminates the need for the distributed terms that were required in earlier methods. We illustrate our method in a source seeking example

Extremum Seeking for Stefan PDE with Moving Boundary

This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is governed by an ordinary differential equation (ODE). This is the first effort to pursue an extension of extremum seeking from the heat PDE to the Stefan PDE. We compensate the average-based actuation dynamics by a controller via backstepping transformation for the moving boundary, which is utilized to transform the original coupled PDE-ODE into a target system whose exponential stability of the average equilibrium of the average system is proved. The discussion for the delay-compensated extremum seeking control of the Stefan problem is also presented and illustrated with numerical simulations.Comment: 10 pages and 10 figure

Newton Nonholonomic Source Seeking for Distance-Dependent Maps

The topics of source seeking and Newton-based extremum seeking have flourished, independently, but never combined. We present the first Newton-based source seeking algorithm. The algorithm employs forward velocity tuning, as in the very first source seeker for the unicycle, and incorporates an additional Riccati filter for inverting the Hessian inverse and feeding it into the demodulation signal. Using second-order Lie bracket averaging, we prove convergence to the source at a rate that is independent of the unknown Hessian of the map. The result is semiglobal and practical, for a map that is quadratic in the distance from the source. The paper presents a theory and simulations, which show advantage of the Newton-based over the gradient-based source seeking