Input/state invariant LQ-optimal control: Application to competitive coexistence in a chemostat

Charlotte Beauthier; Joseph J. Winkin; Denis Dochain

doi:10.3934/eect.2015.4.143

Input/state invariant LQ-optimal control: Application to competitive coexistence in a chemostat

Charlotte Beauthier, Joseph J. Winkin, Denis Dochain

Namur Institute for Complex Systems

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to the application of the input/state-invariant linear quadratic (LQ) problem in order to solve the problem of coexistence of species in competition in a chemostat. The methodology that is used has for objective to guarantee the local positive input/state-invariance of the nonlinear system which describes the chemostat model by ensuring the input/stateinvariance of its linear approximation around an equilibrium. This is achieved by applying an appropriate LQ-optimal control to the system, following two different approaches, namely a receding horizon method and an inverse problem approach.

Original language	English
Pages (from-to)	143-158
Number of pages	16
Journal	Evolution Equations and Control Theory
Volume	4
Issue number	2
DOIs	https://doi.org/10.3934/eect.2015.4.143
Publication status	Published - 1 Jan 2015

Keywords

Chemostat model
Coexistence problem
Input constraints
Invariant systems
Linear quadratic (LQ) problem
Optimal control
State constraints

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10.3934/eect.2015.4.143

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abstract = "This paper is devoted to the application of the input/state-invariant linear quadratic (LQ) problem in order to solve the problem of coexistence of species in competition in a chemostat. The methodology that is used has for objective to guarantee the local positive input/state-invariance of the nonlinear system which describes the chemostat model by ensuring the input/stateinvariance of its linear approximation around an equilibrium. This is achieved by applying an appropriate LQ-optimal control to the system, following two different approaches, namely a receding horizon method and an inverse problem approach.",

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AB - This paper is devoted to the application of the input/state-invariant linear quadratic (LQ) problem in order to solve the problem of coexistence of species in competition in a chemostat. The methodology that is used has for objective to guarantee the local positive input/state-invariance of the nonlinear system which describes the chemostat model by ensuring the input/stateinvariance of its linear approximation around an equilibrium. This is achieved by applying an appropriate LQ-optimal control to the system, following two different approaches, namely a receding horizon method and an inverse problem approach.

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KW - Coexistence problem

KW - Input constraints

KW - Invariant systems

KW - Linear quadratic (LQ) problem

KW - Optimal control

KW - State constraints

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Input/state invariant LQ-optimal control: Application to competitive coexistence in a chemostat

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Keywords

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