Nonlinear Controlled Port-Hamiltonian Systems: Existence of (Optimal) Solutions

We investigate the existence of solutions of reversible and irreversible port-Hamiltonian systems. To this end, we utilize the associated exergy, a function that is composed of the system’s Hamiltonian and entropy, to prove global existence in time for bounded control functions. Then, we rigorously verify our existence conditions for two examples, the gas-piston system and a network of heat exchangers. Last, we explore model predictive control tailored to irreversible port-Hamiltonian systems by means of a numerical case study with a heat exchanger network.