Application of stochastic model predictive control for building energy systems using latent force models - Wietzke, Thore; Landgraf, Daniel; Graichen, Knut (At-Automatisierungstechnik, 2025)
The model-based control of building energy systems (BES) is a hard task, since the system identification is very labor-intensive. This results in inexact models, which are subject to parameter uncertainties. Additionally, disturbances like solar radiation have a great impact on the system dynamics. In this paper we used stochastic model predictive control (SMPC) to account for parameter and disturbance uncertainties. The disturbances are modeled as time-dependent Gaussian Processes (GP), which are known as Latent-Force Models (LFM). The proposed approach is evaluated for two different BES using experimentally obtained data. The results show that the LFM-SMPC results in the lowest discomfort with a reasonable higher energy consumption compared to a constant disturbance predictio
Keywords: stochastic model predictive control; optimal control; building energy systems; stochastic optimization; temporal Gaussian process regression; latent force model

A software framework for stochastic model predictive control of nonlinear continuous-time systems (GRAMPC-S) - Landgraf, Daniel; Völz, Andreas; Graichen, Knut (Optimization and Engineering, 2025)
This paper presents the open-source stochastic model predictive control framework GRAMPC-S for nonlinear uncertain systems with chance constraints. It provides several uncertainty propagation methods to predict stochastic moments of the system state and can consider unknown parts of the system dynamics using Gaussian process regression. These methods are used to reformulate a stochastic MPC formulation as a deterministic one that is solved with GRAMPC. The performance of the presented framework is evaluated using examples from a wide range of technical areas. The experimental evaluation shows that GRAMPC-S can be used in practice for the control of nonlinear uncertain systems with sampling times in the millisecond rang
Keywords: Stochastic model predictive control; Nonlinear model predictive control; Stochastic nonlinear dynamics; Chance constraints; Real-time implementation

Distributed Stochastic Optimal Control of Nonlinear Systems based on ADMM - Pierer von Esch, Maximilian; Landgraf, Daniel; Steffel, Matthias; Völz, Andreas; Graichen, Knut (IEEE Control Systems Letters, 2024)
This paper presents an algorithm based on the alternating direction method of multipliers (ADMM) for the distributed solution of optimal control problems of stochastic multi-agent systems with nonlinear dynamics and state/input couplings as they arise, for instance, in distributed model predictive control of uncertain systems. The solution is based on a deterministic reformulation of the original stochastic problem in which certain covariances are exchanged between agents within the ADMM iterations resulting in a scalable algorithm. The algorithm is evaluated numerically for a nonlinear example system and for energy-optimal building automation control.<br
Keywords: Stochastic processes; Uncertainty; Covariance matrices; Optimal control; Couplings; Costs; Cost function

Hierarchical learning for model predictive collision avoidance - Landgraf, Daniel; Völz, Andreas; Kontes, Georgios; Graichen, Knut; Mutschler, Christopher (IFAC PapersOnLine, 2022)

Nonlinear model predictive control with latent force models - Landgraf, Daniel; Völz, Andreas; Graichen, Knut (Proceedings 2022 American Control Conference (ACC), 2022)

Probabilistic prediction methods for nonlinear systems with application to stochastic model predictive control - Landgraf, Daniel; Völz, Andreas; Berkel, Felix; Schmidt, Kevin; Specker, Thomas; Graichen, Knut (Annual Reviews in Control, 2023)
The performance of modern control methods, such as model predictive control, depends significantly on the accuracy of the system model. In practice, however, stochastic uncertainties are commonly present, resulting from inaccuracies in the modeling or external disturbances, which can have a negative impact on the control performance. This article reviews the literature on methods for predicting probabilistic uncertainties for nonlinear systems. Since a precise prediction of probability density functions comes along with a high computational effort in the nonlinear case, the focus of this article is on approximating methods, which are of particular relevance in control engineering practice. The methods are classified with respect to their approximation type and with respect to the assumptions about the input and output distribution. Furthermore, the application of these prediction methods to stochastic model predictive control is discussed including a literature review for nonlinear systems. Finally, the most important probabilistic prediction methods are evaluated numerically. For this purpose, the estimation accuracies of the methods are investigated first and the performance of a stochastic model predictive controller with different prediction methods is examined subsequently using multiple nonlinear systems, including the dynamics of an autonomous vehicle.<br
Keywords: Probabilistic prediction; Stochastic control; Nonlinear predictive control; Stochastic system model; Uncertainty approximation; Chance constraints; Stochastic model predictive control

Stochastic model predictive control with switched latent force models - Landgraf, Daniel; Wietzke, Thore; Graichen, Knut (European Journal of Control, 2025)
Switched latent force models (LFMs) are combinations of a first-principles physical model and a Gaussian process prior, where the driving force of the LFM may switch at certain time points. This allows to use expert knowledge to create an analytical state space model that describes large parts of the system behavior, while deviating parts are modeled using data-based methods. This paper proposes the combination of stochastic model predictive control and switched LFMs by reformulating the Gaussian process priors as linear state space models with additive white Gaussian noise. For this purpose, a stochastic optimization problem is formulated that can be solved by a deterministic approximation of the uncertainty propagation and the chance constraints. The switching points of the LFM introduce further uncertainty to the system that must be considered for the prediction of the state trajectories. Therefore, Gaussian mixture models are used to describe the probability density functions of the predicted states. The computation cost of the approach can be reduced by using a separate disturbance predictor, which allows to formulate the optimization problem of the model predictive controller independently of the internal disturbance states. The performance of the proposed method is illustrated for the control of a building energy syste
Keywords: Stochastic model predictive control; Gaussian processes; Stochastic system; Uncertainty propagation; Optimal control