  Over the past decades, engineering systems have developed as networks of
systems that deliver multiple services across multiple domains. This work aims
to develop an optimization program for a dynamic, hetero-functional graph
theory-based model of an engineering system. The manuscript first introduces a
general approach to define a dynamic system model by integrating the device
models in the hetero-functional graph theory structural model. To this end, the
work leverages Petri net dynamics and the hetero-functional incidence tensor.
The respective Petri net-based models are translated into the quadratic program
canonical form to finalize the optimization program. The optimization program
is demonstrated through the application of the program to a hydrogen-natural
gas infrastructure test case. Four distinct scenarios are optimized to
demonstrate potential synergies or cascading network effects of policy across
infrastructures.
  This work develops the first hetero-functional graph theory-based
optimization program and demonstrates that the program can be used to optimize
flows across a multi-operand network, transform the operands in the network,
store operands over time, analyze the behavior for a quadratic cost function,
and implement it for a generic, continuous, large flexible engineering systems
of arbitrary topology.
