  In this paper, we present a nonlinear model predictive control (NMPC)
algorithm for systems modeled by semi-explicit stochastic
differential-algebraic equations (DAEs) of index 1. The NMPC combines a
continuous-discrete extended Kalman filter (CD-EKF) with an optimal control
problem (OCP) for setpoint tracking. We discretize the OCP using direct
multiple shooting. We apply an explicit singly diagonal implicit Runge-Kutta
(ESDIRK) integration scheme to solve systems of DAEs, both for the one-step
prediction in the CD-EKF and in each shooting interval of the discretized OCP.
The ESDIRK methods use an iterated internal numerical differentiation approach
for precise sensitivity computations. These sensitivities are used to provide
accurate gradient information in the OCP and to efficiently integrate the
covariance information in the CD-EKF. Subsequently, we present a simulation
case study where we apply the NMPC to a simple alkaline electrolyzer stack
model. We use the NMPC to track a time-varying setpoint for the stack
temperature subject to input bound constraints.
