Minimal-power control of hydrogen evolution reactions

Abstract

An integral approach to solve finite-horizon optimal control problems posed by set-point changes in electrochemical hydrogen reactions is developed. The methodology extends to nonlinear problems with regular, convex Hamiltonians that cannot be explicitly minimized, i.e. where the functional dependence of the H-minimal control on the state and costate variables is not known. The Lagrangian functions determining trajectory costs will not have special restrictions other than positiveness, but for simplicity the final penalty will be assumed quadratic. The answer to the problem is constructed through the solution to a coupled system of three first-order quasi-linear partial differential equations (PDEs) for the missing boundary conditions x(T ), γ(0) of the Hamiltonian equations, and for the final value of the control variable u(T ). The independent variables of these PDEs are the time-duration T of the process and the characteristic parameter S of the final penalty. The solution provides information on the whole (T, S)-family of control problems, which can be used not only to construct the individual optimal control strategies online, but also for global design purposes.