160 citations · 309 across the 13 of their papers we have counts for
14 papers
LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers
Patricia Pauli, Ruigang Wang, Ian Manchester +1
We propose a novel layer-wise parameterization for convolutional neural networks (CNNs) that includes built-in robustness guarantees by enforcing a prescribed Lipschitz bound. Each…
Lipschitz constant estimation for general neural network architectures using control tools
Patricia Pauli, Dennis Gramlich, Frank Allgöwer
This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural netw…
State space representations of the Roesser type for convolutional layers
Patricia Pauli, Dennis Gramlich, Frank Allgöwer
From the perspective of control theory, convolutional layers (of neural networks) are 2-D (or N-D) linear time-invariant dynamical systems. The usual representation of convolutiona…
Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations
Patricia Pauli, Aaron Havens, Alexandre Araujo +4
Recently, semidefinite programming (SDP) techniques have shown great promise in providing accurate Lipschitz bounds for neural networks. Specifically, the LipSDP approach (Fazlyab…
Learning Soft Constrained MPC Value Functions: Efficient MPC Design and Implementation providing Stability and Safety Guarantees
Nicolas Chatzikiriakos, Kim P. Wabersich, Felix Berkel +2
Model Predictive Control (MPC) can be applied to safety-critical control problems, providing closed-loop safety and performance guarantees. Implementation of MPC controllers requir…
Convolutional Neural Networks as 2-D systems
Dennis Gramlich, Patricia Pauli, Carsten W. Scherer +2
This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers w…
Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian
Patricia Pauli, Ruigang Wang, Ian R. Manchester +1
We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees. In doing so, we use the Lipschitz constant of…
Lipschitz constant estimation for 1D convolutional neural networks
Patricia Pauli, Dennis Gramlich, Frank Allgöwer
In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity prop…
Bounding the difference between model predictive control and neural networks
Ross Drummond, Stephen R. Duncan, Matthew C. Turner +2
There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches. Each of these two approaches has their own…
Neural network training under semidefinite constraints
Patricia Pauli, Niklas Funcke, Dennis Gramlich +2
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particu…
Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multipliers
Patricia Pauli, Dennis Gramlich, Julian Berberich +1
In this paper, we analyze the stability of feedback interconnections of a linear time-invariant system with a neural network nonlinearity in discrete time. Our analysis is based on…
Offset-free setpoint tracking using neural network controllers
Patricia Pauli, Johannes Köhler, Julian Berberich +2
In this paper, we present a method to analyze local and global stability in offset-free setpoint tracking using neural network controllers and we provide ellipsoidal inner approxim…
Robust and optimal predictive control of the COVID-19 outbreak
Johannes Köhler, Lukas Schwenkel, Anne Koch +3
We investigate adaptive strategies to robustly and optimally control the COVID-19 pandemic via social distancing measures based on the example of Germany. Our goal is to minimize t…
Training robust neural networks using Lipschitz bounds
Patricia Pauli, Anne Koch, Julian Berberich +2
Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in…