Extremum seeking control for time-varying scalar signal

This paper considers the problem of designing controllers to steer a mobile robot, modeled as a nonholonomic unicycle, to the maximum of a signal field, assuming that the field is completely unknown to the robot and the robot has no knowledge of its own position. Only measurements of the signal field at the vehicle´s position are used. This paper proposes the extremum seeking algorithm which controls the forward velocity and keeps the angular velocity constant. Most extremum seeking control methods consider time-independent input-to-output mappings, however, time-varying scalar signal is considered in this paper. We prove local exponential convergence to a small neighborhood near the maximum of the signal. The theoretical results are verified with simulations.