Introduction

This manual describes the structure and the application of GRAMPC-S, a framework for stochastic model predictive control of nonlinear continuous-time systems subject to nonlinear probabilistic constraints. It is based on the toolbox GRAMPC [1], which solves an optimization problem using the augmented Lagrangian approach and a tailored gradient method. GRAMPC-S is implemented as C++ code which allows implementation on embedded hardware and can be used in Simulink and dSPACE.

The documentation is outlined as follows. Installation describes the installation of GRAMPC-S for Windows and Linux. System class describes the class of optimal control problems (OCP) that are considered. Implementation of the problem description shows the implementation of an OCP as C++ code. Several methods are implemented in GRAMPC-S in order to solve the OCP and propagate uncertainties, whose application is described in Approximation of the stochastic OCP. For a more detailed explanation of these methods, please refer to [2] and [3]. Simulation and Visualization describes the realization of closed-loop simulations and the plotting of results in Matlab. Example: Continuous stirred tank reactor concludes with an example of the application and parameterization of GRAMPC-S.

[1]

T. Englert, A. Völz, F. Mesmer, S. Rhein, and K. Graichen. A software framework for embedded nonlinear model predictive control using a gradient-based augmented Lagrangian approach (GRAMPC). Optimization and Engineering, 20(3):769–809, 2019.

[2]

Daniel Landgraf, Andreas Völz, Felix Berkel, Kevin Schmidt, Thomas Specker, and Knut Graichen. Probabilistic prediction methods for nonlinear systems with application to stochastic model predictive control. Annual Reviews in Control, 56:100905, 2023.

[3]

Daniel Landgraf, Andreas Völz, and Knut Graichen. A software framework for stochastic model predictive control of nonlinear systems (GRAMPC-S). 2025.