A variational approach to the control of electrochemical hydrogen reactions

Optimal control problems for the hydrogen evolution reaction (HER) system are solved for different cost objectives and admissible control strategies. The solution for the set-point-change process is given in analytical terms when the admissible controls are continuous functions of time. For piecewise-continuous controls the problem admits a solution as a feedback law. In both cases the cost functional penalizes the electrochemical power spent in the process, which translates into a Lagrangian more involved than classical quadratic. The theoretical framework remains into the Calculus of Variations for infinite-horizon problems. The Hamiltonian control formalism is adapted to treat the problem when the final time is bounded.