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

TL;DR

This paper introduces an NMPC algorithm for stochastic DAE systems using ESDIRK methods, combining Kalman filtering and optimal control for accurate setpoint tracking in complex systems.

Contribution

It develops a novel NMPC framework that integrates ESDIRK integration with stochastic DAE modeling, enhancing prediction accuracy and computational efficiency.

Findings

Successful simulation on an electrolyzer model demonstrating effective setpoint tracking.

Accurate sensitivity computation improves control performance.

Efficient handling of stochastic DAE systems in NMPC.

Abstract

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.