Related papers: DeepReach: A Deep Learning Approach to High-Dimens…
We propose a novel, mesh-free, and gradient-free fixed-point approach for computing viscosity solutions of high-dimensional Hamilton-Jacobi (HJ) equations. By leveraging the Hopf-Lax formula, our approach iteratively solves the associated…
Accurate and robust trajectory prediction of neighboring agents is critical for autonomous vehicles traversing in complex scenes. Most methods proposed in recent years are deep learning-based due to their strength in encoding complex…
Objective: In a companion paper, we propose a parametric hybrid automaton model and an algorithm for the online synthesis of robustly correct and near-optimal controllers for cyber-physical system with reach-avoid guarantees. A key part of…
We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience…
In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
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…
We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically,…
The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close as possible to a collection of target points. The problem does not verify the dynamic programming principle, and it needs a specific…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
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…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical…
A key challenge in contact-rich dexterous manipulation is the need to jointly reason over geometry, kinematic constraints, and intricate, nonsmooth contact dynamics. End-to-end visuomotor policies bypass this structure, but often require…
Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs,…
Interaction-aware planning for autonomous driving requires an exploration of a combinatorial solution space when using conventional search- or optimization-based motion planners. With Deep Reinforcement Learning, optimal driving strategies…
The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the…
Risk assessment is a crucial component of collision warning and avoidance systems in intelligent vehicles. To accurately detect potential vehicle collisions, reachability-based formal approaches have been developed to ensure driving safety,…
Autonomous highway driving involves high-speed safety risks due to limited reaction time, where rare but dangerous events may lead to severe consequences. This places stringent requirements on trajectory planning in terms of both…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…