Compressive feedback based non-vector space control

A non-vector space control method based on compressive feedback is presented in this paper. The non-vector space means the control is not performed in traditional vector space but in the space of sets. Consider an initial set and a goal set, a stabilizing controller is designed to make the set dynamics converge to the goal set. The compressive feedback means the controller works even when only partial elements of the feedback set are available; that is, the same controller can still stabilize the set dynamics around the goal set with the compressive feedback. The controller is applied to visual servoing by considering images as sets. In this way, image processing for feature extraction is not required, which is an essential process in conventional servo methods. Moreover, the compressive feedback can reduce the size of feedback image. It is important when the sampling is time consuming such as imaging using atomic force microscopy (AFM). The visual servoing formulation of the controller is further applied to the motion control in nanomanipulations. Simulation results suggest good performance of the controller. The framework proposed in this paper can be extended to other systems where the signals can be represented as sets.