Related papers: Backward Reachability Analysis of Neural Feedback …
As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped…
Deep neural networks have been widely applied as an effective approach to handle complex and practical problems. However, one of the most fundamental open problems is the lack of formal methods to analyze the safety of their behaviors. To…
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
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…
This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of…
In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit…
We present a method for computing exact reachable sets for deep neural networks with rectified linear unit (ReLU) activation. Our method is well-suited for use in rigorous safety analysis of robotic perception and control systems with deep…
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 output behaviors of neural networks will be crucial for…
This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid…
Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is…
In this paper, we propose reachability analysis using constrained polynomial logical zonotopes. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently introduced set…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…
We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable states. When considering dynamical systems and neural networks in…
Inner-approximate reachability analysis involves calculating subsets of reachable sets, known as inner-approximations. This analysis is crucial in the fields of dynamic systems analysis and control theory as it provides a reliable…
This paper integrates prior knowledge into direct learning of safe controllers for linear uncertain systems under disturbances. To this end, we characterize the set of all closed-loop systems that can be explained by available prior…