BECS: Collaborative Research: Characterization and Control of Emergent Behavior in Complex Systems

University Of Cincinnati Main Campus, Cincinnati OH

Investigators

Abstract

The current state of knowledge in the area of complex networked systems lacks formal theories that can accurately predict, and hence help control the behavior of such systems. The scientific objective of this project is to develop a theoretical basis to understand, analyze, and control emergent behavior in complex systems operating in uncertain environments. In order to validate the theoretical ideas, the project specifically considers complex swarm robotic systems and aims to apply the proposed analytical framework to such systems. The central approach uses the mathematical framework of stochastic differential equations wherein the swarm is treated as a dissipative Hamiltonian system coupled by nonlinear interacting potentials. In this framework, the influence of uncertainties (noise) is treated mathematically using both the discrete and continuum formulations to be obtained from a Fokker-Planck approach. The focus of this research is the development of a theoretical basis for modeling of complex systems and their analysis based upon given control inputs and inherent system uncertainty. This framework facilitates modeling the complex interactions, higher-dimensionality, nonlinearity, and uncertainty in complex systems as well as the control of desirable emergent behavior. Potential future applications of this research include power grids and communication networks. Furthermore, this project has broader impacts that include promoting teaching, training, and learning; broad dissemination to enhance understanding; and involvement of the underrepresented groups. Undergraduate and graduate students are mentored and trained via courses and involvement in research and outreach activities. Broad dissemination is achieved through special sessions, workshops, and tutorials at conferences that target both the dynamic systems and control as well as mathematics communities. Participation of undergraduates and students from underrepresented groups is facilitated via summer projects, summer camps, and other programs such as Women in Science and Engineering and Emerging Ethnic Engineers.