About minimal-time impulse control of sequential batch reactors with one or more species.
Event details
| Date | 20.11.2009 |
| Hour | 10:15 |
| Speaker | Prof. A. Rapaport, INRA & INRIA Montpellier. |
| Location |
MEC2405
|
| Category | Conferences - Seminars |
We consider the minimal-time optimal control problem of feeding a tank, where several
species compete for a single resource, with the objective to reach a given level of the
resource. We allow controls to be bounded measurable functions of time as well as impulses.
For the one species case, we show that the immediate one impulse strategy (filling the whole
reactor with one single impulse at initial time) is optimal when the growth function is
monotonic. For non-monotonic growth functions with one maximum, we show that the
singular arc strategy (making the resource reach this maximum as fast as possible and
maintain it at this level until the fill is complete) is optimal. These results extend former ones
obtained by J. Moreno for the class of measurable controls. For the two species case with
monotonic growth functions, we first give conditions under which immediate one impulse
strategy is optimal. We also give optimality conditions for the singular arc strategy (at a level
that depends on the initial condition) to be optimal. The possibility for the immediate one
impulse strategy to be non-optimal, although both growth functions are monotonic, is a
surprising result, illustrated with the help of numerical simulations. This is a joined work
with P. Gajardo and H. Ramirez, from Univ. of Chile.
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