Related papers: Time-Optimal Collaborative Guidance Using the Gene…
This work presents a sequential convex program method to compute fuel-optimal collision avoidance maneuvers for long-term encounters. The low-thrust acceleration model is used to account for the control, but the method can compute…
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form…
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…
Optimal control problems are crucial in various domains, including path planning, robotics, and humanoid control, demonstrating their broad applicability. The connection between optimal control and Hamilton-Jacobi (HJ) partial differential…
Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that…
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical…
A method to compute optimal collision avoidance maneuvers for short-term encounters is presented. The maneuvers are modeled as multiple-impulses to handle impulsive cases and to approximate finite burn arcs associated either with short…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
In this paper, we present a game-theoretic feedback terminal guidance law for an autonomous, unpowered hypersonic pursuit vehicle that seeks to intercept an evading ground target whose motion is constrained in a one-dimensional space. We…
Multi-object tracking (MOT) is critical in numerous real-world applications, including surveillance, autonomous driving, and robotics. Accurately predicting object motion is fundamental to MOT, but current methods struggle with the…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
We present an algorithm for a multi-agent path planning problem with pattern coordination based on dynamic programming and a Hamilton-Jacobi-Bellman equation. This falls broadly into the class of partial differential equation (PDE) based…
The pursuit-evasion game in Smart City brings a profound impact on the Multi-vehicle Pursuit (MVP) problem, when police cars cooperatively pursue suspected vehicles. Existing studies on the MVP problems tend to set evading vehicles to move…
Pursuit-evasion is a multi-agent sequential decision problem wherein a group of agents known as pursuers coordinate their traversal of a spatial domain to locate an agent trying to evade them. Pursuit evasion problems arise in a number of…
Optimization-based approaches such as Model Predictive Control (MPC) are promising approaches in proactive control for safety-critical applications with changing environments such as automated driving systems. However, the computational…
Provably safe and scalable multi-vehicle trajectory planning is an important and urgent problem. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several…
This paper presents a global trajectory optimization framework for minimizing lap time in autonomous racing under uncertain vehicle dynamics. Optimizing the trajectory over the full racing horizon is computationally expensive, and tracking…
This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the…
In this paper, we propose a hybrid MPC local planner that uses a learning-based approximation of a time-varying safe set, derived from local observations and applied as the MPC terminal constraint. This set can be represented as a…