Related papers: Efficient Reachability Analysis for Convolutional …

As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability…

The zonotope containment problem, i.e., whether one zonotope is contained in another, is a central problem in control theory. Applications include detecting faults and robustifying controllers by computing invariant sets, and obtain fixed…

Neural networks are ubiquitous. However, they are often sensitive to small input changes. Hence, to prevent unexpected behavior in safety-critical applications, their formal verification -- a notoriously hard problem -- is necessary. Many…

This paper presents optimizations to improve the scalability of reachability analysis on a subclass of hybrid automata extended with stochasticity. The optimizations target different components of the analysis, such as quantifier…

A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this…

This doctoral thesis develops new methods for set-based state estimation and active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii) discrete-time nonlinear systems whose trajectories satisfy nonlinear equality constraints…

The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify their behavior and guarantee safety. This paper presents a backward reachability approach for safety verification of neural…

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer…

Performing real-time receding horizon motion planning for autonomous vehicles while providing safety guarantees remains difficult. This is because existing methods to accurately predict ego vehicle behavior under a chosen controller use…

Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…

This paper presents a new reachability analysis approach to compute interval over-approximations of the output set of feedforward neural networks with input uncertainty. We adapt to neural networks an existing mixed-monotonicity method for…

This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…

Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the behaviors of neural network systems will be crucial for…

Seed phenotyping is the idea of analyzing the morphometric characteristics of a seed to predict the behavior of the seed in terms of development, tolerance and yield in various environmental conditions. The focus of the work is the…

We propose a matrix zonotope perturbation framework that leverages matrix perturbation theory to characterize how noise-induced distortions alter the dynamics within sets of models. The framework derives interpretable Cai-Zhang bounds for…

Scalable safety verification of continuous state dynamic systems has been demonstrated through both reachability and viability analyses using parametric set representations; however, these two analyses are not interchangable in practice for…

Reachability analysis has been a prominent way to provide safety guarantees for neurally controlled autonomous systems, but its direct application to neural perception components is infeasible due to imperfect or intractable perception…

Deep neural networks have achieved impressive experimental results in image classification, but can surprisingly be unstable with respect to adversarial perturbations, that is, minimal changes to the input image that cause the network to…

Deep neural networks can be trained to be efficient and effective controllers for dynamical systems; however, the mechanics of deep neural networks are complex and difficult to guarantee. This work presents a general approach for providing…

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…