Abstract

We study the minimum time control problem of a series of two interconnected chemostats under the input constraint $u_{2}\leq u_{1}$, where $u_{i}$ are the respective dilution rates in the tanks. This constraint brings controllability issues in the study of the optimal strategies. We overcome this difficulty by splitting the state domain into two subdomains, one with no lack of controllability of the target, and its complement where any optimal trajectory satisfies $u_{1}=u_{2}$. We explicitly compute the complete optimal synthesis that depends on the position of the target with respect to a semipermeable curve that passes through a steady-state singular point.

Keywords

  1. optimal control
  2. minimal time problem
  3. Pontryagin's maximum principle
  4. optimal synthesis
  5. chemostat model
  6. gradostat model
  7. nonlinear controllability
  8. semipermeability

MSC codes

  1. 49J15
  2. 49K15
  3. 49N25

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 2568 - 2594
ISSN (online): 1095-7138

History

Submitted: 23 December 2013
Accepted: 28 May 2014
Published online: 28 August 2014

Keywords

  1. optimal control
  2. minimal time problem
  3. Pontryagin's maximum principle
  4. optimal synthesis
  5. chemostat model
  6. gradostat model
  7. nonlinear controllability
  8. semipermeability

MSC codes

  1. 49J15
  2. 49K15
  3. 49N25

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