Optimal control of port-Hamiltonian systems: energy, entropy, and exergy

TL;DR

This paper develops an optimal control framework for nonlinear port-Hamiltonian systems, linking energy, entropy, and exergy concepts to thermodynamic equilibria, with applications to heat exchangers and gas-piston systems.

Contribution

It introduces a novel optimal control approach that incorporates thermodynamic quantities and establishes the integral turnpike property for such systems.

Findings

Optimal control trajectories tend to thermodynamic equilibria over finite time.

The framework unifies energy, entropy, and exergy considerations in control design.

Applications demonstrate the effectiveness in heat exchanger and gas-piston systems.

Abstract

We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on finite-time horizons. We analyze a class of optimal control problems, where the performance functional can be interpreted as a linear combination of energy supply, entropy generation, or exergy supply. Our results establish the integral turnpike property towards the set of thermodynamic equilibria providing a rigorous connection of optimal system trajectories to optimal steady states. Throughout the paper, we illustrate our findings by means of two examples: a network of heat exchangers and a gas-piston system.