Optimality of affine control system of several species in competition on a Sequential Batch Reactor

Abstract : In this paper we analyze the optimalty of affine control system of several species in competition for a single substrate on a Sequential Batch Reactors (SBR), with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which we apply different optimality conditions de-rived from Pontryagin principle and the Hamilton-Jacobi-Bellman equation. We thus characterize the singular trajectories of our problem as the extremal trajecto-ries keeping the substrate at a constant level. We also establish conditions for which a Immediate One impulse (IOI) strategy is optimal. Some numerical experiences are then included in order to illustrate our study and show that those conditions are also necessary to ensure the optimality of the IOI strategy.
Document type :
Journal articles
Complete list of metadatas

Cited literature [12 references]  Display  Hide  Download

https://hal.inria.fr/hal-01088224
Contributor : Pablo Koch <>
Submitted on : Thursday, November 27, 2014 - 4:43:06 PM
Last modification on : Tuesday, August 13, 2019 - 2:30:11 PM
Long-term archiving on : Monday, March 2, 2015 - 9:25:15 AM

File

Optimality of affine control s...
Files produced by the author(s)

Identifiers

Collections

Citation

J.C. Rodriguez, Hector Ramirez, Pedro Gajardo, Alain Rapaport. Optimality of affine control system of several species in competition on a Sequential Batch Reactor. International Journal of Control, Taylor & Francis, 2014, 87 (9), pp.1877-1885. ⟨10.1080/00207179.2014.891360⟩. ⟨hal-01088224⟩

Share

Metrics

Record views

671

Files downloads

343