Thermodynamic framework for discrete optimal control in multiphase flow systems

Bellman's method of dynamic programming is used to synthesize diverse optimization approaches to active (work producing) and inactive (entropy generating) multiphase flow systems. Thermal machines, optimally controlled unit operations, nonlinear heat conduction, spontaneous relaxation processes, and self-propagating wave fronts are all shown to satisfy a discrete Hamilton-Jacobi-Bellman equation and a corresponding discrete optimization algorithm of Pontryagin's type, with the maximum principle for a Hamiltonian. The extremal structures are always canonical. A common unifying criterion is set for all considered systems, which is the criterion of a minimum generated entropy. It is shown that constraints can modify the entropy functionals in a different way for each group of the processes considered; thus the resulting structures of these functionals may differ significantly. Practical conclusions are formulated regarding the energy savings and energy policy in optimally controlled systems.