Related papers: A Hopf-Lax Type Formula for Multi-Agent Path Plann…

This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous…

Hamilton-Jacobi (HJ) partial differential equations (PDEs) have diverse applications spanning physics, optimal control, game theory, and imaging sciences. This research introduces a first-order optimization-based technique for HJ PDEs,…

We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main result is well-posedness (existence, uniqueness, and…

Multi-agent path finding (MAPF) involves planning efficient paths for multiple agents to move simultaneously while avoiding collisions. In typical warehouse environments, agents are often sparsely distributed along aisles; however,…

We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…

Safe Multi-Agent Motion Planning (MAMP) is a significant challenge in robotics. Despite substantial advancements, existing methods often face a dilemma. Decentralized algorithms typically rely on predicting the behavior of other agents,…

We propose a novel neural network architecture (TSympOCNet) to address high--dimensional optimal control problems with linear and nonlinear dynamics. An important application of this method is to solve the path planning problem of…

In this paper we consider a family of optimal control problems for economic models whose state variables are driven by Delay Differential Equations (DDE's). We consider two main examples: an AK model with vintage capital and an advertising…

The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…

Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case.…

The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…

We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem…

Multi-Agent Path Finding (MAPF) poses a significant and challenging problem critical for applications in robotics and logistics, particularly due to its combinatorial complexity and the partial observability inherent in realistic…

Large Language Models have recently emerged as a promising paradigm for automated heuristic design for NP-hard combinatorial optimization problems. Despite this progress, existing LLM-based methods typically rely on monolithic workflows…

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…

In this paper, we consider a problem of contract theory in which several Principals hire a common Agent and we study the model in the continuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we…

We present a novel hybrid learning-assisted planning method, named HyPlan, for solving the collision-free navigation problem for self-driving cars in partially observable traffic environments. HyPlan combines methods for multi-agent…

In this paper we study a path planning problem from a variational approach to collision and obstacle avoidance for multi-agent systems evolving on a Riemannian manifold. The problem consists of finding non-intersecting trajectories between…

Multi-agent pathfinding (MAPF) remains a critical problem in robotics and autonomous systems, where agents must navigate shared spaces efficiently while avoiding conflicts. Traditional centralized algorithms with global information provide…

This paper presents a hybrid control framework for the motion planning of a multi-agent system including N robotic agents and M objects, under high level goals. In particular, we design control protocols that allow the transition of the…