Emergent Dynamics and Consensus-Based Algorithms
Abstract
The overall goal of this proposal is to continue our ongoing investigation of emergent phenomena in two complementary lanes: (i) add ressing open mathematical questions which arise with emergent dynamics, and (ii) their interplay in new algorithms driven by self-or ganization, the so-called consensus-based algorithms, with applications to synchronization, control, optimization and prediction of large crowd dynamics.Specifically, our research will address the following fundamental and largely open problems in our current und erstanding of emergent dynamics.(i) We propose a new paradigm for repulsion based of communication in topological neighborhoods. The key issue is that repulsion is not measures solely by metric distance but, as known from the biological world, agents repulsion is inversely proportional to how crowded their immediate neighborhood is.(ii) A second line of interest is to address alignment dynami cs based on short-range communication kernels. Long-range kernels are at the heart of much of the current emergence analysis. We pro pose to study the discrete Cucker-Smale dynamics using the topologically-based short-range communication.(iii) We propose to continu e our investigation of multi-species alignment. In this case, different species either compete of cooperate with other species, whi ch leads to different and more interesting phenomena.(iv) We propose a different approach for Consensus-Based Optimization (CBO) whi ch consists of crowd of agents with evolving masses, each is taking into account both local gradient descent and global communicatio n with dynamically evolving global minimizer. The agents represent distribution of probabilities of reaching the global minimizer(v ) We propose to investigate the ``Wanderlust algorithm which was introduced as an ad-hoc algorithm in computational biology litera ture. Our approach recast the Wanderlust as a repulsion/attraction dynamic and we will study its optimal time protocol for reaching its large time "consensus .(vi) We propose to study the anticipation-based alignment based on orientation of positions, a bearing-o nly dynamic, rather their relative distances. The anticipation-based is an adjustment to orientation of anticipated (positions/veloc ities), and as such should yield the finite-time "consensus which is currently available only in first-order dynamics of positions . In summary, our research plan is to investigate new models, analyze their large time behavior and complement our study with accura te and "faithful" numerical simulations to gain insight into these new paradigms of emergent phenomena in collective dynamics.Approv ed for Public Release.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 20, 2021
- Source ID
- N000142112773
Entities
People
- Eitan Tadmor
Organizations
- Office of Naval Research
- United States Navy
- University of Maryland