Discrete-Time Stochastic Source Seeking via Tunning the Velocity Actuated Vehicle

We consider the problem of using the velocity actuated vehicle as search agent, and only use the noisy measurements of a scalar signal field to design a discrete-time stochastic extremum seeking controller to tune the vehicle towards the source of the signal field. Firstly, based on the definition of integral, we transform the model of continues-time vehicle to a discrete one. Secondly, only using noisy measurements of the signal field at vehicle's positions, an extremum seeking control law is designed to navigate the vehicle by using the discrete-time ergodic process as the probing signal. Thirdly, using the extended discrete-time stochastic averaging theory, we prove exponential convergence, both almost surely and in probability, to a small neighborhood near the source. Finally, numerical simulations are given to illustrate the efficiency of the algorithm.