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Several earlier studies have shown impressive control performance in complex robotic systems by designing the controller using a neural network and training it with model-free reinforcement learning. However, these outstanding controllers…

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 are increasingly applied to support decision making in safety-critical applications (like autonomous cars, unmanned aerial vehicles and face recognition based authentication). While many impressive static verification…

Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…

Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…

Over the last decade, Neural Networks (NNs) have been widely used in numerous applications including safety-critical ones such as autonomous systems. Despite their emerging adoption, it is well known that NNs are susceptible to Adversarial…

Reinforcement learning (RL) is capable of sophisticated motion planning and control for robots in uncertain environments. However, state-of-the-art deep RL approaches typically lack safety guarantees, especially when the robot and…

This paper investigates reinforcement learning with constraints, which are indispensable in safety-critical environments. To drive the constraint violation monotonically decrease, we take the constraints as Lyapunov functions and impose new…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…

It is well-known that neural networks are computationally hard to train. On the other hand, in practice, modern day neural networks are trained efficiently using SGD and a variety of tricks that include different activation functions (e.g.…

Safety is a fundamental requirement for autonomous systems operating in critical domains. Control barrier functions (CBFs) have been used to design safety filters that minimally alter nominal controls for such systems to maintain their…

Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded…

An increasing trend in the use of neural networks in control systems is being observed. The aim of this paper is to reveal that the straightforward application of learning neural network feedforward controllers with closed-loop data may…

We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more…

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…

Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…

This paper aims to enhance the computational efficiency of safety verification of neural network control systems by developing a guaranteed neural network model reduction method. First, a concept of model reduction precision is proposed to…

When autonomous vehicles encounter untrained scenarios, ensuring safety hinges on effective safety verification to prevent accidents stemming from unexpected model decisions. Reachability analysis, a method of safety verification, offers…