Using Novel Distance Metrics to Evaluate Statistical Robustness of Chaotic Control Systems

• Activity Number: 505
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Morris Morgan*+ and Carolyn Bradshaw Morgan
• Companies: Hampton University and Hampton University
• Keywords: statistical robustness ; fuzzy systems ; statistical synchronization ; control

Abstract

Evaluating the robustness of integrated controls systems with clusters of unmanned aerial vehicles (UAVs) flying in stable formation is of primary concern in the aerospace industry. This paper describes the use of traditional linearized robust statistical control metrics (covariance arising from white noise inputs or additive and multiplicative model uncertainties) to assess the level of synchronization existing between chaotic systems or networks comprised of small local chaotic sub-systems. New distance measures based on chordal and spherical displacements will be used to determine the distance between companion dynamical systems. The success of such metrics for a linear control system is well documented. The paper addresses the extension and statistical limitations of these metrics to highly nonlinear systems where robust statistical control is sensitive to both parameter and disturbance input noises.