Distributed sourcing seeking via stochastic approximation algorithm with expanding truncations

We investigate the problem of distributed source seeking with velocity actuated and force actuated vehicles by developing distributed Kiefer-Wolfowitz algorithm. First, based on stochastic approximation algorithm with expanding truncations, we present the distributed Kiefer-Wolfowitz algorithm, in which two noisy observations of each agent's objective function is used to estimate its gradient and for each agent, a new iterative estimation is produced by its and its neighbors' measurements. Then, we present source seeking algorithms for velocity actuated and force actuated vehicles without no exact form of objective function. The convergence of the algorithm is proven and compared with the existing similar work, boundedness condition for convergence is eliminate and more kinds of measurement noise can be allowed. Finally, numerical simulations are given to illustrate the effectiveness of the proposed algorithm.