The work presented in this thesis studies the numerical performance of a class of new hybrid adaptive algorithms applied to autonomous navigation. Hybrid adaptive control is used to find the source of some signal which the vehicle can locally measure, while evading multiple obstacles at unknown positions. The source-seeking methods proposed achieve convergence to an neighborhood of the extremum values while evading multiple obstacles at unknown positions under the presence of arbitrary small perturbations, overcoming limitations imposed by the topological obstructions induced by the obstacles.

We explore the use of both point-mass and nonholonomic unicycle dynamics to model the vehicle or robot using hybrid adaptive feedback law based on a signal (localization) function. Furthermore, we explore the use of data-enabled source seeking based on concurrent learning. We also discuss convergence guarantees for these real-time optimization methods, even under the presence of arbitrary small perturbations.

Lastly, real-time optimization numerical studies are shown to demonstrate the use of both hybrid adaptive feedback law and data enabled extremum seeking controllers. Moreover, experimental results under the presence of adversarial signals are shown to numerically illustrate both controller's robustness.