First results of optimal control of average biogas production for the chemostat over an infinite horizon

Haddon, Antoine; Ramírez, Héctor; Rapaport, Alain

doi:10.1016/j.ifacol.2018.03.123

Cited by 3 publications

(11 citation statements)

References 4 publications

(5 reference statements)

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“…We study optimal strategies and compare their related optimal costs. This study extends the preliminary results presented in the conference paper [18] and considers a large class of growth functions, that can be in particular density-dependent (such as the Contois law) or not (such as the Monod or Haldane law). Our work for the finite horizon exploits and extends an approximation technique presented in [19].…”

Section: Introductionsupporting

confidence: 74%

“…Proposition 4. For any initial condition ξ ∈ D, any control u(·) ∈ U(0, ∞) that drives the system asymptotically to the state (s, 1) is optimal for problems (14), (15) and (18). We then have…”

Section: Solution Of Optimal Control Problemsmentioning

confidence: 99%

“…Note also that the feedback ψ S will drive the system asymptotically towards the state (s, z) = (s, 1) so that it is also optimal for the infinite horizon problems (14), (15) and (18).…”

Section: Application To Particular Growth Functionsmentioning

confidence: 99%

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Optimal and Sub-optimal Feedback Controls for Biogas Production

Haddon

Ramírez

Rapaport

2019

J Optim Theory Appl

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We revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the discount factor goes to 0 and we show that the value functions of both problems are equal. For the finite horizon problem, our approach relies on a framing of the value function by considering a different reward for which the optimal solution has an explicit optimal feedback that is timeindependent. In particular, we show that this technique allows us to provide explicit bounds on the sub-optimality of the proposed controllers. The various strategies are finally illustrated on Haldane and Contois growth functions.

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Section: Introductionsupporting

confidence: 74%

Section: Solution Of Optimal Control Problemsmentioning

confidence: 99%

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Optimal and Sub-optimal Feedback Controls for Biogas Production

Haddon

Ramírez

Rapaport

2019

J Optim Theory Appl

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“…A stable performance of the process and a continuous biofuels production can be achieved through complex dynamics estimation and control strategies implementation. In the work of Haddon et al, an optimal control problem of maximizing the average biogas production over an infinite horizon in a chemostat model is proposed. The proposed feedback is not optimal for a finite horizon and it requires the substrates and biomass measurements to calculate the adequate control.…”

Section: Introductionmentioning

confidence: 99%

Inverse optimal neural control via passivity approach for nonlinear anaerobic bioprocesses with biofuels production

Gurubel

Sánchez²,

Coronado-Mendoza

et al. 2019

Optim Control Appl Methods

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Summary This paper proposes an inverse optimal neural control method of a nonlinear anaerobic bioprocesses model for simultaneous hydrogen and methane production in presence of disturbances. Based on the fundamental properties of the system, a passivity approach is designed such that asymptotic stability is guaranteed. A recurrent high‐order neural network for unknown nonlinear systems in presence of unknown bounded disturbances and parameter uncertainties is proposed to identify nonmeasurable state variables of the system, which are directly related to biofuels production. Optimal control laws based on the neural model are proposed so that the passivation of the entire plant is preserved. The neural control strategy performance for trajectory tracking in presence of disturbances is proven. Results via simulation show the optimal control methodology efficiency to stabilize the H2 and CH4 productions along desired trajectories even in presence of disturbances.

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“…More recently, the general one-reaction model has been revisited to propose a sub-optimal control for which there is an estimation of sub-optimality [14]. Let us mention that the problem has also been considered in the infinite horizon case [15]. To the best of our knowledge, a complete synthesis for the problem of maximizing biogas production over a fixed finite horizon has not been addressed before, even for the single reaction model.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for Maximizing the Biogas Production in a Chemostat

Haddon

Hermosilla

2019

J Optim Theory Appl

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In this work, we deal with the optimal control problem of maximizing biogas production in a chemostat. The dilution rate is the controlled variable, and we study the problem over a fixed finite horizon, for positive initial conditions. We consider the single reaction model and work with a broad class of growth rate functions. With the Pontryagin maximum principle, we construct a one-parameter family of extremal controls of type bang-singular arc. The parameter of these extremal controls is the constant value of the Hamiltonian. Using the Hamilton-Jacobi-Bellman equation, we identify the optimal control as the extremal associated with the value of the Hamiltonian, which satisfies a fixed point equation. We then propose a numerical algorithm to compute the optimal control by solving this fixed point equation. We illustrate this method with the two major types of growth functions of Monod and Haldane.

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First results of optimal control of average biogas production for the chemostat over an infinite horizon

Cited by 3 publications

References 4 publications

Optimal and Sub-optimal Feedback Controls for Biogas Production

Optimal and Sub-optimal Feedback Controls for Biogas Production

Inverse optimal neural control via passivity approach for nonlinear anaerobic bioprocesses with biofuels production

An Algorithm for Maximizing the Biogas Production in a Chemostat

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