Optimal control separating two microalgae species competing in a chemostat

Djema, Walid; Bernard, Olivier; Bayen, Térence

doi:10.1109/cdc42340.2020.9304115

Cited by 2 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the competition described by the Droop model turns out to be significantly more complicated than for the Monod model in dimension 2 [17]. We have improved the preliminary results about this problem to be found in [22,29] in order to provide an optimal synthesis depending on the initial condition. In particular, we applied the PMP, we discussed the structure of the optimal control, and we identified the singular arc steering optimal paths to the desired target set in a minimal amount of time.…”

Section: Discussionmentioning

confidence: 89%

See 1 more Smart Citation

Optimal Darwinian Selection of Microorganisms with Internal Storage

2022

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate the problem of species separation in minimal time. Droop model is considered to describe the evolution of two distinct populations of microorganisms that are in competition for the same resource in a photobioreactor. We focus on an optimal control problem (OCP) subject to a five-dimensional controlled system in which the control represents the dilution rate of the chemostat. The objective is to select the desired species in minimal-time and to synthesize an optimal feedback control. This is a very challenging issue, since we are are dealing with a ten-dimensional optimality system. We provide properties of optimal controls allowing the strain of interest to dominate the population. Our analysis is based on the Pontryagin Maximum Principle (PMP), along with a thorough study of singular arcs that is crucial in the synthesis of optimal controls. These theoretical results are also extensively illustrated and validated using a direct method in optimal control (via the Bocop software for numerically solving optimal control problems). The approach is illustrated with numerical examples with microalgae, reflecting the complexity of the optimal control structure and the richness of the dynamical behavior.

show abstract

Section: Discussionmentioning

confidence: 89%

“…We start this section by generalizing previously obtained results [22,29] characterizing optimal solutions of (6). For that, we apply the PMP which allows for obtaining necessary conditions satisfied by optimal controls of (6).…”

Section: Necessary Conditions On Optimal Controlsmentioning

confidence: 84%

Optimal Darwinian Selection of Microorganisms with Internal Storage

2022

Self Cite

View full text Add to dashboard Cite

show abstract

Turnpike features in optimal selection of species represented by quota models

et al. 2021

Self Cite

View full text Add to dashboard Cite

The paper focuses on a generic optimal control problem (OCP) deriving from the competition between two microbial populations in continuous cultures. The competition for nutrients is reduced to a two-dimensional dynamical nonlinear-system that can be derived from classical quota models. We investigate an OCP that achieves species separation over a fixed time-window, suitable for a large class of empirical growth functions commonly used in quota models. Using Pontryagin's Maximum Principle (PMP), the optimal control strategy steering the model trajectories is fully characterized. Then, we provide sufficient conditions for the existence of a turnpike property associated with the optimal control and state-trajectories, as well as their respective costate trajectories. Indeed, we prove that for a sufficiently large time, the optimal strategy achieving strain separation remains most of the time exponentially close to an optimal steady-state defined from an associated simpler static-OCP. This turnpike feature is based on the hyperbolicity of the linearized Hamiltonian-system around the solution of the static-OCP. The obtained theoretical results are then illustrated on microalgae, described by the Droop model in dimension 5. The optimal strategy is numerically computed in Bocop (open source toolbox for optimal control ) with direct optimization methods.

show abstract

Optimal control separating two microalgae species competing in a chemostat

Cited by 2 publications

References 19 publications

Optimal Darwinian Selection of Microorganisms with Internal Storage

Optimal Darwinian Selection of Microorganisms with Internal Storage

Turnpike features in optimal selection of species represented by quota models

Contact Info

Product

Resources

About