Optimal State-Feedback Regulation of the Hydrogen Evolution Reactions

Abstract

A control strategy is developed in order to keep processes based on the hydrogen evolution reactions (HER) near operational steady states. The problem is treated in the context of Optimal Control for nonlinear systems subject to quadratic cost objectives. The original dynamics is shown to be accurately approximated by a bilinear model without increasing the dimension, so the state variables retain their physical meaning. Finite and infinite horizon optimal control strategies are developed, based on the Hamiltonian formalism, and introducing a novel approach for working on-line with generalized Riccati differential equations and the associated costate dynamics. When there exists a final penalty on the state deviation, then a first order quasi-linear partial differential equation is discovered and solved for the Riccati matrix. The observability problem is also treated, since the natural state (electrode surface coverage) can not be measured continuously. The output variable (current density) is fed into a high-gain nonlinear observer based on Lyapunov´s stability considerations. The whole approach allows for (in general time-dependent) state-feedback control.