Related papers: Reachable Set Estimation and Safety Verification f…
In this paper, we consider the problem of training neural network (NN) controllers for nonlinear dynamical systems that are guaranteed to satisfy safety and liveness (e.g., reach-avoid) properties. Our approach is to combine model-based…
Neural networks can be used as approximations of several complex control schemes such as model predictive control. We show in this paper which properties deep neural networks with rectifier linear units as activation functions need to…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
We present a novel technique for online safety verification of autonomous systems, which performs reachability analysis efficiently for both bounded and unbounded horizons by employing neural barrier certificates. Our approach uses barrier…
The decision logic for the ACAS X family of aircraft collision avoidance systems is represented as a large numeric table. Due to storage constraints of certified avionics hardware, neural networks have been suggested as a way to…
A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We…
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…
Control Barrier Functions (CBFs) are a popular approach for safe control of nonlinear systems. In CBF-based control, the desired safety properties of the system are mapped to nonnegativity of a CBF, and the control input is chosen to ensure…
The proliferation of neural networks in safety-critical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural…
In this work, we address the problem of formal safety verification for stochastic cyber-physical systems (CPS) equipped with ReLU neural network (NN) controllers. Our goal is to find the set of initial states from where, with a…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
The design of tracking controllers that closely follow a reference trajectory while ensuring safety and robustness against disturbances is a challenging problem in the control of autonomous systems. In this work, we propose a neural…
We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…
This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and…
This paper presents a novel approach to ensure the safety of continuous-time linear dynamical systems controlled by a neural network (NN) based state-feedback. Our method capitalizes on the use of continuous piece-wise affine (PWA)…
In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such as: Given symbolic specifications of allowed inputs and outputs in form of Linear…
We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative…
Neural networks achieved high performance over different tasks, i.e. image identification, voice recognition and other applications. Despite their success, these models are still vulnerable regarding small perturbations, which can be used…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…