2014/03/21 by Jieqiang Wei, Arjan van der Schaft, Wei, Jieqiang +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC
paper · pdf · doi:10.48550/arxiv.1403.5447
published in proceeding of 52nd IEEE Conference on Decision and Control (CDC 2013). arXiv admin note: text overlap with arXiv:1403.5198, arXiv:1403.5203
arxiv created 2014/03/21 · openalex publication_date 2014/03/21 · arxiv updated 2014/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. We analyze the dynamics of the system in closed-loop with a distributed proportional-integral controller structure, where the flow inputs are constrained to take value in closed intervals. Results from our previous work are extended to general flow constraint intervals, and conditions for asymptotic load balancing are derived that rely on the structure of the graph and its flow constraints.