Traditionally
the optimization of processing systems has relied on the availability
of an explicit model together with the corresponding gradient information.
However, there are some practical scenarios such as (a) nondifferentiable
systems, (b) physical experimental systems, (c) simulation environments,
and (d) reduced order systems where such a model and its gradient
are not available. Under these scenarios the deployment of derivative-free
optimization strategies provides an alternative manner to cope with
the optimization of such systems. In particular, in this work we deploy
a derivative-free optimization trust region approach to deal with
the product dynamic optimization problem of processing systems. To
this aim, we use a closed-loop model predictive control strategy where
the system to be optimized is embedded in a black-box dynamic simulation
environment. The results demonstrate that black-box dynamic models
can be dynamically optimized assuming that the number of decision
variables is not large. The first-principles dynamic model of a binary
distillation column embedded in the ASPEN dynamic simulation environment
was deployed as our black-box dynamic model, to demonstrate the advantages
of solving product dynamic transition problems when an explicit model
of the dynamic model and/or its gradient information are not available.
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