Stochastic extremum seeking with applications to mobile sensor networks

In this paper the extremum seeking algorithm with sinusoidal perturbation has been modified and extended in two ways: a) the amplitudes of the perturbation signals, as well as the gain of the integrator block, are time varying and tend to zero at a pre-specified rate; b) the output of the system is corrupted with measurement noise. Local convergence to the extremal point, with probability one and in the mean square sense, has been proved. Also, it has been shown how the proposed algorithm can be applied to mobile sensor networks as a tool for achieving the optimal observation positions. The proposed algorithms have been illustrated through several simulations.