Related papers: Neural Hamilton--Jacobi Characteristic Flows for O…
We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…
The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic processes have increasingly been applied to sample generation.…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
We prove that a directed last passage percolation model with discontinuous macroscopic (non-random) inhomogeneities has a continuum limit that corresponds to solving a Hamilton-Jacobi equation in the viscosity sense. This Hamilton-Jacobi…
A new algorithm for time dependent Hamilton Jacobi equations on networks, based on semi Lagrangian scheme, is proposed. It is based on the definition of viscosity solution for this kind of problems recently given in. A thorough convergence…
In this paper we study an approximation scheme for an Hamilton-Jacobi equation of Eikonal type defined on a network. We introduce an appropriate notion of viscosity solution for this class of equations (see \cite{sc}) and we prove that an…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain the control. In this work, instead of focusing on the value…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for…
In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…
The Hamilton-Jacobi formalism of constrained systems is used to study superstring. That obtained the equations of motion for a singular system as total differential equations in many variables. These equations of motion are in exact…
We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level…
This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum…
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its…
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after…