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Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…

Machine Learning · Computer Science 2023-01-26 Brendon G. Anderson , Somayeh Sojoudi

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…

Systems and Control · Electrical Eng. & Systems 2022-02-24 Zain ul Abdeen , He Yin , Vassilis Kekatos , Ming Jin

This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…

Machine Learning · Computer Science 2022-08-09 Saber Jafarpour , Alexander Davydov , Matthew Abate , Francesco Bullo , Samuel Coogan

In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…

Machine Learning · Computer Science 2020-09-21 Brendon G. Anderson , Ziye Ma , Jingqi Li , Somayeh Sojoudi

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

Optimization and Control · Mathematics 2025-10-20 Simon Michalowsky , Carsten Scherer , Christian Ebenbauer

Practical application of H[infinity] robust control relies on system identification of a valid model-set, described by a linear system in feedback with a stable norm-bounded uncertainty, which must explains all possible (or at least all…

Optimization and Control · Mathematics 2019-01-07 Gray C. Thomas , Luis Sentis

The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network. We introduce a semidefinite programming hierarchy to…

Optimization and Control · Mathematics 2020-10-29 Tong Chen , Jean-Bernard Lasserre , Victor Magron , Edouard Pauwels

This paper presents a convex optimization-based framework for synthesizing time-varying controlled invariant funnels and associated feedback control around a given nominal trajectory for nonlinear systems subject to bounded disturbances.…

Optimization and Control · Mathematics 2025-11-13 Taewan Kim , Dayou Luo , Behçet Açıkmeşe

We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…

Optimization and Control · Mathematics 2025-05-14 Marta Fochesato , Han Wang , Antonis Papachristodoulou , Paul Goulart

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

Machine Learning · Statistics 2023-02-10 Calypso Herrera , Florian Krach , Josef Teichmann

Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…

Optimization and Control · Mathematics 2012-06-01 Didier Henrion , Jean Bernard Lasserre

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error…

Systems and Control · Electrical Eng. & Systems 2021-01-19 Lanlan Su

This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…

Optimization and Control · Mathematics 2021-05-27 Laurent Lessard , Benjamin Recht , Andrew Packard

The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…

Machine Learning · Computer Science 2024-10-30 Yuezhu Xu , S. Sivaranjani

Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified…

Machine Learning · Computer Science 2026-05-21 Elias Khalife , Mazen Farhood , Pierre-Loic Garoche

This paper addresses the problem of recursive set-membership identification for linear time varying (LTV) systems when both input and output measurements are affected by bounded additive noise. First we formulate the problem of online…

Optimization and Control · Mathematics 2021-07-06 Sophie M. Fosson , Diego Regruto , Talal Abdalla , Abdul Salam

The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by…

Optimization and Control · Mathematics 2023-10-10 Brendon G. Anderson , Samuel Pfrommer , Somayeh Sojoudi

Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial input uncertainty, but researchers…

Machine Learning · Computer Science 2023-01-26 Brendon G. Anderson , Somayeh Sojoudi

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification…

Machine Learning · Computer Science 2023-06-16 Hong-Ming Chiu , Richard Y. Zhang

We study finite-time horizon continuous-time linear-convex reinforcement learning problems in an episodic setting. In this problem, the unknown linear jump-diffusion process is controlled subject to nonsmooth convex costs. We show that the…

Optimization and Control · Mathematics 2022-03-03 Xin Guo , Anran Hu , Yufei Zhang