Monitoring function based extremum seeking control for uncertain relative degrees with light source seeking experiments

In this paper, we consider the problem of seeking a light source with a cart-track linear positioning servomechanism. The cart does not have the capability of sensing its position/velocity or the position of the source but is capable of sensing the light signal generated by a light bulb. The light field created by the light source decays away from the position of the light bulb but the servo does not have the knowledge of the functional form of this field. We employ an extremum seeking control strategy based on monitoring functions recently proposed by the authors. First, we briefly introduce the theoretical results of the monitoring function based extremum seeking controller for one-dimensional (1D) optimization. The class of systems previously considered was restricted to the relative degree one case. Here, as a theoretical contribution, generalization is achieved to include more general dynamics with arbitrary and uncertain relative degrees. In lieu of using differentiators to compensate the relative degree, a time-scaling procedure is developed. Then, we present the design for a light-seeking servomechanism and obtain experimental results of such a mounted device performing localizing and tracking of the level-sets of the light source.