Stability analysis of non-vector space control via compressive feedbacks

Abstract

A new non-vector space control method with compressive feedback is presented in this paper. Two problems are discussed. The first is the development of the non-vector space control method. It formulates the control problem in the space of sets instead of the vector space, and it provides a convenient way to model physical phenomenon such as shapes and images. For the non-vector space dynamical systems, the issues related to stability analysis and design of controllers are discussed in the paper. The second problem is to design controllers for non-vector space dynamic systems using compressive feedback, which is a new concept proposed in this paper. Compressive feedback, obtained from the original feedback, reduces the amount of data for the original feedback but retains the essential information to ensure the stability and other key performance measures for a control system. The design methods for controllers based on compressive feedback are developed in this paper. Furthermore, the non-vector space control system with compressive feedback has been successfully applied to visual servoing, and simulations results have clearly demonstrated the superb performance and advantages. © 2012 IEEE.