Moritz Schulze Darup

Manuel Klädtke, Feiran Zhao, Florian Dörfler et al.

This paper proposes an explainability concept for direct data-driven linear quadratic regulation (LQR) with quadratic regularization. Our perspective follows the parametric effect of regularization, an analysis approach that translates regularization costs from auxiliary variables to system quantities, enabling intuitive interpretations. The framework further enables the elimination of auxiliary variables, thereby reducing computational complexity. We demonstrate the effectiveness of our approach and the identified effect of regularization via simulations.

Dieter Teichrib, Moritz Schulze Darup

Convex piecewise quadratic (PWQ) functions frequently appear in control and elsewhere. For instance, it is well-known that the optimal value function (OVF) as well as Q-functions for linear MPC are convex PWQ functions. Now, in learning-based control, these functions are often represented with the help of artificial neural networks (NN). In this context, a recurring question is how to choose the topology of the NN in terms of depth, width, and activations in order to enable efficient learning. An elegant answer to that question could be a topology that, in principle, allows to exactly describe the function to be learned. Such solutions are already available for related problems. In fact, suitable topologies are known for piecewise affine (PWA) functions that can, for example, reflect the optimal control law in linear MPC. Following this direction, we show in this paper that convex PWQ functions can be exactly described by max-out-NN with only one hidden layer and two neurons.

Janis Adamek, Moritz Schulze Darup

Federated learning (FL) schemes allow multiple participants to collaboratively train neural networks without the need to directly share the underlying data.However, in early schemes, all participants eventually obtain the same model. Moreover, the aggregation is typically carried out by a third party, who obtains combined gradients or weights, which may reveal the model. These downsides underscore the demand for fair and privacy-preserving FL schemes. Here, collaborative fairness asks for individual model quality depending on the individual data contribution. Privacy is demanded with respect to any kind of data outsourced to the third party. Now, there already exist some approaches aiming for either fair or privacy-preserving FL and a few works even address both features. In our paper, we build upon these seminal works and present a novel, fair and privacy-preserving FL scheme. Our approach, which mainly relies on homomorphic encryption, stands out for exclusively using local gradients. This increases the usability in comparison to state-of-the-art approaches and thereby opens the door to applications in control.

Dieter Teichrib, Moritz Schulze Darup

We present a method for representing the closed-loop dynamics of piecewise affine (PWA) systems with bounded additive disturbances and neural network-based controllers as mixed-integer (MI) linear constraints. We show that such representations enable the computation of robustly positively invariant (RPI) sets for the specified system class by solving MI linear programs. These RPI sets can subsequently be used to certify stability and constraint satisfaction. Furthermore, the approach allows to handle non-linear systems based on suitable PWA approximations and corresponding error bounds, which can be interpreted as the bounded disturbances from above.

Philipp Binfet, Janis Adamek, Moritz Schulze Darup

The security of networked control systems (NCS) is receiving increasing attention from both cyber-security and system-theoretic perspectives. The former focuses on classical IT security goals such as confidentiality, integrity, and availability of process data, while the latter investigates tailored attacks (and detection schemes), including covert and zero-dynamics attacks. Confidentiality in control systems can, for instance, be achieved by securely outsourcing the evaluation of the controller to third-party platforms, such as cloud services. The underlying technology enabling such secure computation often is homomorphic encryption (HE). Recent works in encrypted control have proposed modifications to underlying HE schemes to achieve not only confidentiality but also resilience to certain types of integrity attacks. While extensions in this direction are desirable in principle, we show that the integrity problem in encrypted control cannot be solved by public-key HE schemes alone due to their inherent malleability. In other words, the same homomorphisms that enable encrypted control % in the first place can be leveraged not only constructively but also destructively. More precisely, we demonstrate that NCS are vulnerable to covert attacks, even when encrypted control is employed. Remarkably, this remains possible without knowledge of an unencrypted model. Yet, resilience to such attacks can still be achieved through complementary techniques. We present an approach based on verifiable computation that integrates with modern homomorphic cryptosystems and is asymptotically secure while incurring no communication overhead.

Dieter Teichrib, Moritz Schulze Darup

Learning-based predictive control is a promising alternative to optimization-based MPC. However, efficiently learning the optimal control policy, the optimal value function, or the Q-function requires suitable function approximators. Often, artificial neural networks (ANN) are considered but choosing a suitable topology is also non-trivial. Against this background, it has recently been shown that tailored ANN allow, in principle, to exactly describe the optimal control policy in linear MPC by exploiting its piecewise affine structure. In this paper, we provide a similar result for representing the optimal value function and the Q-function that are both known to be piecewise quadratic for linear MPC.