Stochastic nonholonomic source seeking

We apply stochastic extremum seeking to navigate a nonholonomic unicycle towards the maximum of an unknown, spatially distributed signal field, using only the measurement of the signal at the vehicle´s position but without the measurement of the vehicle´s position. Keeping the forward velocity constant and controlling only the angular velocity, we design a stochastic source seeking control law which employs excitation based on filtered white noise, rather than sinusoidal perturbations used in the past work. We study stability using stochastic averaging theorems that we recently developed for general nonlinear continuous-time systems with stochastic perturbations. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. We characterize the convergence speed explicitly and provide design guidelines for maximizing it, as well as for minimizing the residual set near the source.