## Abstract

A new approach is presented for the study of H_{∞} optimal control of biochemical pathways. Starting with various linear models of single enzymatic reaction systems, a simple unbranched four-block enzyme system that contains a negative feedback loop is analyzed in the open- and the closed-loop configurations, where it is shown that the closed-loop configuration is one of the static output-feedback control systems. The original nonlinear four-block system is modeled as a polytopic-type uncertain linear system, where the extent of the nonlinearity can be “tuned” by a fictitious uncertainty interval, thus better capturing the nonlinear nature of the systems under study. The sensitivity of the latter enzymatic system to variations in certain variables is explored via the optimal H_{∞} control approach. Based on this approach, the threonine synthesis pathway that contains three negative feedback loops is analyzed and is shown to be optimal in the H_{∞} sense.

Original language | English |
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Title of host publication | Lecture Notes in Control and Information Sciences |

Publisher | Springer Verlag |

Pages | 231-278 |

Number of pages | 48 |

DOIs | |

State | Published - 2019 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 481 |

ISSN (Print) | 0170-8643 |

ISSN (Electronic) | 1610-7411 |

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