Paul Frihauf

ABSTRACT We introduce an approach for stable deployment of agents into planar arc formations, including full circles and spirals. These deployments correspond to the equilibrium profiles of a nonlinear PDE model. The model incorporates the follower agents' control laws, which employ a spatial internal model principle, enabling them to achieve a family of arc deployments while utilizing only local information. Anchor agents are used to manipulate the geometry of the group, but are not required for stability. We obtain control laws for the discrete agents by spatially discretizing the PDE model with respect to the continuous agent index.

We consider the problem of deployment of a group of N autonomous fully actuated vehicles (agents) in a non-cooperative manner in a planar signal field using the recently introduced method of stochastic extremum seeking. The spatial distribution of the signal is unknown to the vehicles but known to be convex. The vehicles are not able to sense their own positions

ABSTRACT We consider a general, stable nonlinear dynamic system with N inputs and N outputs, where in the steady state, the output signals represent the non-quadratic payoff functions of a noncooperative game played by the values of the input signals. We introduce a non-model based approach for locally stable convergence to a steady-state Nash equilibrium. In classical game theory algorithms, each player employs the knowledge of the functional form of its payoff and of the other players' actions, whereas in the proposed algorithm, the players need to measure only their own payoff values. This strategy is based on the so-called "extremum seeking" approach, which has previously been developed for standard optimization problems and employs sinusoidal perturbations to estimate the gradient. Since non-quadratic payoffs create the possibility of multiple, isolated Nash equilibria, our convergence results are local. Specifically, the attainment of any particular Nash equilibrium is assured only for initial conditions in a set around that specific stable Nash equilibrium. Moreover, for non-quadratic payoffs, the convergence to a Nash equilibrium is biased in proportion to the perturbation amplitudes and the payoff functions' third derivatives. We quantify the size of these residual biases.

ABSTRACT Using the method of stochastic extremum seeking, we navigate an autonomous vehicle, modeled as a nonholonomic unicycle, towards the maximum of an unknown, spatially distributed signal field by measuring only the signal at the vehicle's position. The vehicle position is not measured. Keeping the angular velocity constant, we control the forward velocity by designing a stochastic source seeking control law, which employs excitation based on filtered white noise rather than sinusoidal perturbations used in previous works. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source and provide numerical simulations to illustrate the effectiveness of the algorithm.