Semi-supervised pattern synthesis in spatially distributed dynamical systems

Iman Haghighi, Kevin Leahy, Rachael Ivison, Calin Belta

Abstract: Pattern producing networks of dynamical systems are useful in a variety of applications ranging from formation control in multi-agent robotics to biological networks. We propose a formal methods framework with minimal user input to synthesize system parameters that result in the emergence of global steady state patterns in spatially distributed dynamical systems. Our framework consists of extensive exploration of steady state behaviors, dividing these behaviors into groups of patterns using a clustering algorithm, and determining system parameters for each pattern cluster using a recently developed formal methods approach for parameter synthesis. A case study illustrating the implementation of this framework on a network of locally interacting living cells is included.