  This paper explores some variations of a hierarchical control framework that
has been recently proposed. The framework is dedicated to control a network of
interconnected subsystems such as the ones describing cryogenic processes or
power plants. Recent investigations showed that handling constraints and
nonlinearities might challenge the real-time feasibility of the approach. This
paper investigates and combine two successful directions, namely, the use of
truncated fast gradient and deep neural networks based controller modeling in
order to reduce the computation time of the most critical subsystem. It is also
shown that by doing so, the control updating period can be drastically reduced
and the closed-loop performances highly improved. The paper can therefore be
seen as a concrete implementation and validation of some key ideas in real-time
distributed NMPC design. All the concepts are validated using the realistic and
challenging example of real-life cryogenic refrigerator.
