A linear programming approach to routing control in networks of constrained nonlinear positive systems with concave flow rates

• Heather Arneson ^[1] ; Nicolas Dousse ^[2] ; Cédric Langbort ^[3]
  1. [1] NASA Ames Research Center;USA
  2. [2] Ecole Polytechnique Fédérale de Lausanne;Switzerland
  3. [3] University of Illinois at Urbana–Champaign;USA

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 68, 2016, págs. 357-368
• Idioma: inglés
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• Resumen

  • 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.