2 research outputs found
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
Prescribed-Time Seeking of a Repulsive Source by Unicycle Angular Velocity Tuning
All the existing source seeking algorithms for unicycle models in GPS-denied
settings guarantee at best an exponential rate of convergence over an infinite
interval. Using the recently introduced time-varying feedback tools for
prescribed-time stabilization, we achieve source seeking in prescribed time,
i.e., the convergence to the source, without the measurements of the position
and velocity of the unicycle, in as short a time as the user desires, starting
from an arbitrary distance from the source. The convergence is established
using a singularly perturbed version of the Lie bracket averaging method,
combined with time dilation and time contraction operations. The algorithm is
robust, provably, even to an arbitrarily strong gradient-dependent repulsive
velocity drift emanating from the source