  In response to the continuously changing feedstock supply and market demand
for products with different specifications, the processes need to be operated
at time-varying operating conditions and targets (e.g., setpoints) to improve
the process economy, in contrast to traditional process operations around
predetermined equilibriums. In this paper, a contraction theory-based control
approach using neural networks is developed for nonlinear chemical processes to
achieve time-varying reference tracking. This approach leverages the universal
approximation characteristics of neural networks with discrete-time contraction
analysis and control. It involves training a neural network to learn a
contraction metric and differential feedback gain, that is embedded in a
contraction-based controller. A second, separate neural network is also
incorporated into the control-loop to perform online learning of uncertain
system model parameters. The resulting control scheme is capable of achieving
efficient offset-free tracking of time-varying references, with a full range of
model uncertainty, without the need for controller structure redesign as the
reference changes. This is a robust approach that can deal with bounded
parametric uncertainties in the process model, which are commonly encountered
in industrial (chemical) processes. This approach also ensures the process
stability during online simultaneous learning and control. Simulation examples
are provided to illustrate the above approach.
