Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Terence Bayen (), Olivier Cots () and Pedro Gajardo ()
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Terence Bayen: Univ Montpellier, CNRS
Olivier Cots: INP-ENSEEIHT, IRIT and CNRS
Pedro Gajardo: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 2, No 15, 627-659

Abstract: Abstract Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type optimal control problem, we propose a slightly different optimal control approach in this paper: We study the minimal time control problem to reach a target point, which is chosen in such a way that it maximizes the biogas production at steady state. Thanks to the Pontryagin maximum principle and the geometric control theory, we provide an optimal feedback control for the minimal time control problem, when the initial conditions are taken within the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut locus.

Keywords: Geometric control; Pontryagin maximum principle; Optimal feedback; Chemostat model; 49J15; 49M30; 93A30 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1292-7

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