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Found 13 papers, 5 papers with code
Lipschitz constant estimation for general neural network architectures using control tools
This paper is devoted to the estimation of the Lipschitz constant of neural networks using semidefinite programming.
State space representations of the Roesser type for convolutional layers
For this reason, we explicitly provide a state space representation of the Roesser type for 2-D convolutional layers with $c_\mathrm{in}r_1 + c_\mathrm{out}r_2$ states, where $c_\mathrm{in}$/$c_\mathrm{out}$ is the number of input/output channels of the layer and $r_1$/$r_2$ characterizes the width/length of the convolution kernel.
Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations
However, a direct application of LipSDP to the resultant residual ReLU networks is conservative and even fails in recovering the well-known fact that the MaxMin activation is 1-Lipschitz.
Learning Soft Constrained MPC Value Functions: Efficient MPC Design and Implementation providing Stability and Safety Guarantees
This combination enables us to obtain a corresponding optimal control law, which can be implemented efficiently on embedded platforms.
Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian
We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees.
Convolutional Neural Networks as 2-D systems
This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems.
Lipschitz constant estimation for 1D convolutional neural networks
In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs).
Bounding the difference between model predictive control and neural networks
There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches.
Neural network training under semidefinite constraints
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees.
Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multipliers
In this paper, we analyze the stability of feedback interconnections of a linear time-invariant system with a neural network nonlinearity in discrete time.
Offset-free setpoint tracking using neural network controllers
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 approximations of the corresponding region of attraction.
Robust and optimal predictive control of the COVID-19 outbreak
Our theoretical findings support various recent studies by showing that 1) adaptive feedback strategies are required to reliably contain the COVID-19 outbreak, 2) well-designed policies can significantly reduce the number of fatalities compared to simpler ones while keeping the amount of social distancing measures on the same level, and 3) imposing stronger social distancing measures early on is more effective and cheaper in the long run than opening up too soon and restoring stricter measures at a later time.
Training robust neural networks using Lipschitz bounds
More specifically, we design an optimization scheme based on the Alternating Direction Method of Multipliers that minimizes not only the training loss of an NN but also its Lipschitz constant resulting in a semidefinite programming based training procedure that promotes robustness.
