Discrete time extremum seeking by autonomous vehicles in a stochastic environment

In this paper, discrete time extremum seeking algorithms with sinusoidal perturbations have been developed for three different problems involving autonomous vehicle planar control: a) control of velocity actuated vehicles; b) control of force actuated vehicles; c) control of nonholonomic vehicles (unicycles). The algorithms assume time varying gains and are able to cope with stochastic perturbations. Convergence to the extremal point, with probability one, has been demonstrated for all three cases. It is also shown how the proposed algorithms can be applied to mobile sensors as a tool for achieving optimal observation positions. The proposed algorithms have been illustrated with several simulations.