2013/11/23 by Zak Costello, Costello, Zak, Magnus Egerstedt +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Advanced Control Systems Optimization #Distributed Control Multi-Agent Systems #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1311.5959
openalex publication_date 2013/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A network of locally interacting agents can be thought of as performing a distributed computation. But not all computations can be faithfully distributed. This paper investigates which global, linear transformations can be computed using local rules, i.e., rules which rely solely on information from adjacent nodes in a network. The main result states that a linear transformation is computable in finite time using local rules if and only if the transformation has positive determinant. An optimal control problem is solved for finding the local interaction rules, and simulations are performed to elucidate how optimal solutions can be obtained.