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Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing…
Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very…
We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained…
This paper proposes a cooperative integrated estimation-guidance framework for simultaneous interception of a non-maneuvering target using a team of unmanned autonomous vehicles, assuming only a subset of vehicles are equipped with…
This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust…
This paper presents experiments for embedded cooperative distributed model predictive control applied to a team of hovercraft floating on an air hockey table. The hovercraft collectively solve a centralized optimal control problem in each…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
This paper first introduces a method to approximate the value function of high-dimensional optimal control by neural networks. Based on the established relationship between Pontryagin's maximum principle (PMP) and the value function of the…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By leveraging the method of characteristics, we derive…
Due to the intricate of real-world road topologies and the inherent complexity of autonomous vehicles, cooperative decision-making for multiple connected autonomous vehicles (CAVs) remains a significant challenge. Currently, most methods…
Motivated by the scalability limitations of Eulerian methods for variational Hamilton-Jacobi-Isaacs (HJI) formulations that provide a least restrictive controller in problems that involve state or input constraints under a worst-possible…
This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
Aiming at the problem of driver's perception lag and low utilization efficiency of space-time resources in expressway ramp confluence area, based on the preemptive spatiotemporal trajectory Adjustment system, from the perspective of…
We unify Hamilton-Jacobi (HJ) reachability and Reinforcement Learning (RL) through a proposed running cost formulation. We prove that the resultant travel-cost value function is the unique bounded viscosity solution of a time-dependent…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal…