ESDIRK-based nonlinear model predictive control for stochastic differential-algebraic equations

This paper presents 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 method uses iterated internal numerical differentiation to compute precise integrator sensitivities, which are used to provide accurate gradient and constraint Jacobian information of the OCPs, as well as to efficiently compute the estimation covariance 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.