A linear programming approach to routing control in networks of constrained nonlinear positive systems with concave flow rates. (June 2016)

• Record Type: Journal Article
• Authors: Arneson, Heather; Dousse, Nicolas; Langbort, Cédric
• Is Part Of: Automatica. Volume 68(2016)
• Page Start: 357
• Page End: 368
• Publication Date: 2016-06
• Subjects: Linear programming -- Control of networks -- Positive systems -- Controller constraints and structure; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.01.067
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment. We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem.