Related papers: Hamilton-Jacobi formulation for reach-avoid differ…
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the…
Hamilton-Jacobi Reachability (HJR) analysis has been successfully used in many robotics and control tasks, and is especially effective in computing reach-avoid sets and control laws that enable an agent to reach a goal while satisfying…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but solving high-dimensional HJ partial differential equations limits its use in real-time planning. This paper presents a contingency-aware…
This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ…
This paper extends the considerations of the works [1, 2] regarding curse-of-dimensionality-free numerical approaches to solve certain types of Hamilton-Jacobi equations arising in optimal control problems, differential games and elsewhere.…
We study a time-optimal control problem of a two-peakon collision. First, we state the controllability. Next, we find the time-optimal strategy. This is done via the HamiltonJacobi-Bellman equation and the dynamic programming method. We…
Provably safe and scalable multi-vehicle path planning is an important and urgent problem due to the expected increase of automation in civilian airspace in the near future. Although this problem has been studied in the past, there has not…
As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have recently been proposed throughout industry and academia. Yet, achieving consensus on an…
In continuous-time optimal control, evaluating the Hamiltonian requires solving a constrained optimization problem using the system's dynamics model. Hamilton-Jacobi reachability analysis for safety verification has demonstrated practical…
The aim of this work is to deal with a discontinuous Hamilton-Jacobi equation in the whole euclidian N-dimensional space, associated to a possibly unbounded optimal control problem. Here, the discontinuities are located on a hyperplane and…
Road safety continues to be a pressing global issue, with vehicle collisions imposing significant human, societal, and economic burdens. Human-machine shared collision avoidance in critical collision scenarios aims to aid drivers' accident…
This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the…
This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the…
The purpose of this paper is to address a class of hybrid optimal control problems constrained with hyperelasticity and constant global volume. This type of problems can intervene for example in the mechanical aspects of cardiac activity.…
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical control systems. Its advantages include compatibility with general nonlinear system…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
Hamilton-Jacobi (HJ) reachability analysis is a fundamental tool for the safety verification and control synthesis of nonlinear control systems. Classical HJ reachability analysis methods compute value functions over grids which discretize…
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…