Lars Grüne

Ruchuan Ou, Learta Januzi, Jonas Schießl et al.

The consideration of stochastic uncertainty in optimal and predictive control is a well-explored topic. Recently Polynomial Chaos Expansions (PCE) have received considerable attention for problems involving stochastically uncertain system parameters and also for problems with additive stochastic i.i.d. disturbances. While there exist a number of open-source PCE toolboxes, tailored open-source codes for the solution of OCPs involving additive stochastic i.i.d. disturbances in julia are not available. Hence, this paper introduces the toolbox PolyOCP$.$jl which enables to efficiently solve stochastic OCPs for linear systems subject to a large class of disturbance distributions. We explain the main mathematical concepts between the PCE transcription of stochastic OCPs and how they are provided in the toolbox. We draw upon two examples to illustrate the functionalities of PolyOCP$.$jl.

Christopher M. Kellett, Steven R. Weller, Timm Faulwasser et al.

For his work in the economics of climate change, Professor William Nordhaus was a co-recipient of the 2018 Nobel Memorial Prize for Economic Sciences. A core component of the work undertaken by Nordhaus is the Dynamic Integrated model of Climate and Economy, known as the DICE model. The DICE model is a discrete-time model with two control inputs and is primarily used in conjunction with a particular optimal control problem in order to estimate optimal pathways for reducing greenhouse gas emissions. In this paper, we provide a tutorial introduction to the DICE model and we indicate challenges and open problems of potential interest for the systems and control community.

Rolf Findeisen, Lars Grüne, Jürgen Pannek et al.

Control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting problems is the use of prediction based compensation schemes. Instead of a single input, a sequence of (predicted) future controls is submitted and implemented at the actuator. If suitable, so-called prediction consistent compensation and control schemes, such as certain predictive control approaches, are used, stability of the closed loop in the presence of delays and packet losses can be guaranteed. In this paper, we show that control schemes employing prediction based delay compensation approaches do posses inherent robustness properties. Specifically, if the nominal closed loop system without delay compensation is ISS with respect to perturbation and measurement errors, then the closed loop system employing prediction based delay compensation techniques is robustly stable. We analyze the influence of the prediction horizon on the robustness gains and illustrate the results in simulation.

Lars Grüne, Jürgen Pannek, Karl Worthmann

For networked systems, the control law is typically subject to network flaws such as delays and packet dropouts. Hence, the time in between updates of the control law varies unexpectedly. Here, we present a stability theorem for nonlinear model predictive control with varying control horizon in a continuous time setting without stabilizing terminal constraints or costs. It turns out that stability can be concluded under the same conditions as for a (short) fixed control horizon.

Shreyas Gururaj, Lars Grüne, Wojciech Samek et al.

Overfitting is a well-known issue extending even to state-of-the-art (SOTA) Machine Learning (ML) models, resulting in reduced generalization, and a significant train-test performance gap. Mitigation measures include a combination of dropout, data augmentation, weight decay, and other regularization techniques. Among the various data augmentation strategies, occlusion is a prominent technique that typically focuses on randomly masking regions of the input during training. Most of the existing literature emphasizes randomness in selecting and modifying the input features instead of regions that strongly influence model decisions. We propose Relevance-driven Input Dropout (RelDrop), a novel data augmentation method which selectively occludes the most relevant regions of the input, nudging the model to use other important features in the prediction process, thus improving model generalization through informed regularization. We further conduct qualitative and quantitative analyses to study how Relevance-driven Input Dropout (RelDrop) affects model decision-making. Through a series of experiments on benchmark datasets, we demonstrate that our approach improves robustness towards occlusion, results in models utilizing more features within the region of interest, and boosts inference time generalization performance. Our code is available at https://github.com/Shreyas-Gururaj/LRP_Relevance_Dropout.