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A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

https://doi.org/10.1109/tac.2005.851439
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Reachability Analysis of Nonlinear Systems Using Conservative Approximation
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Validating a Hamilton-Jacobi Approximation to Hybrid System Reachable Sets
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Reachability Analysis Using Polygonal Projections
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Reachability Analysis of a Class of Switched Continuous Systems by Integrating Rectangular Approximation and Rectangular Analysis
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Algorithmic analysis of nonlinear hybrid systems
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Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
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Viability Theory
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Numerical Methods for Pursuit-Evasion Games via Viscosity Solutions
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Set-Valued Numerical Analysis for Optimal Control and Differential Games
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Some properties of viscosity solutions of Hamilton-Jacobi equations
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Algorithmic analysis of nonlinear hybrid systems
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Computation of piecewise quadratic Lyapunov functions for hybrid systems
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Analysis of linear systems with saturation using convex optimization
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Computational techniques for hybrid system verification
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A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games
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Graph-Based Algorithms for Boolean Function Manipulation
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High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
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Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
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Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations
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A Differential Game with Two Players and One Target
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A Differential Game Formulation of Alert Levels in ETMS Data for High Altitude Traffic

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Algorithm of uniform filling of nonlinear dynamic system reachable set based on maximin problem solution
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Model predictive control: past, present, and future
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Determination of Inner and Outer Bounds of Reachable Sets Through Subpavings
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Understanding Human Avoidance Behavior: Interaction-Aware Decision Making Based on Game Theory
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Human-Like Motion Planning Based on Game Theoretic Decision Making
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Backward Reachability Analysis for Nonlinear Dynamical Systems via Pseudospectral Method
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Safety-Enhanced Berthing Control Strategy for Surface Ships Using Backward and Forward Reachability Analysis
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On the Suicidal Pedestrian Differential Game
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Differential Games in $$L^{\infty }$$
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Aircraft Control During Cruise Flight in Windshear Conditions: Viability Approach
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Reach-Avoid Differential Games with Targets and Obstacles Depending on Controls
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A review of model extensions and solution methods for space orbital games
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Data-Driven Safe Learning and Control with Safety Certificates
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Control Barrier Functions and Safety Nonlinear Filters
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Safe landing area determination for a Moon lander by reachability analysis
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An approximate analytical method for solving the coplanar spacecraft pursuit-evasion game barrier
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Coordination and collision avoidance for Lagrangian systems with disturbances
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Robust pursuit of a hybrid evader
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On backwards and forwards reachable sets bounding for perturbed time-delay systems
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Probabilistic reach-Avoid problems in nondeterministic systems with time-Varying targets and obstacles
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A dimensionality reduction method for computing reachable tubes based on piecewise pseudo-time dependent Hamilton–Jacobi equation
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On flight operational issues management: Past, present and future
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Safety-critical control for autonomous systems: Control barrier functions via reduced-order models
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Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control
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A stochastic approximation method for probability prediction of docking success for aerial refueling
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A diffusion reinforcement learning framework for air traffic conflict detection and resolution
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Rapid assessment of feasible flight domain for stratospheric airships under multi-physics constraints
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UAV collision avoidance exploitation for noncooperative trajectory modification
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Reachability analysis on optimal trim state for aerial docking
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Potential hop reachable domain over surfaces of small bodies
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Effects of landing gear layout on the safe rollout envelope of equipped–skid aircraft
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Longitudinal dynamic envelope solution and transition path optimization based on reachability analysis for fixed-wing VTOL UAVs
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Interceptability analysis under line-of-sight constraints for a class of hybrid UAVs
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Convex pursuit–evasion games for spacecraft proximity operations on circular and elliptical orbits
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On reachability and minimum cost optimal control
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Bounds on the reachable sets of nonlinear control systems
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Provably safe and robust learning-based model predictive control
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Lagrangian methods for approximating the viability kernel in high-dimensional systems
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Computational techniques for reachability analysis of Max-Plus-Linear systems
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Distributed robust adaptive equilibrium computation for generalized convex games
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Cooperative pursuit with Voronoi partitions
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Barriers and potentially safe sets in hybrid systems: Pendulum with non-rigid cable
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A dynamic game approach to distributionally robust safety specifications for stochastic systems
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Linear functional state bounding for positive systems with disturbances varying within a bounded set
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On maximal robust positively invariant sets in constrained nonlinear systems
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Flexible performance-based robust control for a class of nonlinear systems with input saturation
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Least-violating symbolic controller synthesis for safety, reachability and attractivity specifications
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Tight reachability bounds for constrained nonlinear systems using mean value differential inequalities
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Small-gain theorem for safety verification of interconnected systems
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Matching-based capture strategies for 3D heterogeneous multiplayer reach-avoid differential games
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Reachable set computation of linear systems with nonconvex constraints via convex optimization
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Justification of the geometric solution of a target defense game with faster defenders and a convex target area using the HJI equation
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Solving viability problems in dynamic games using individual strategies derived from guaranteed viability kernels: Application to an agricultural cooperative model
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Multiplayer Homicidal Chauffeur reach-avoid games: A pursuit enclosure function approach
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Soft-minimum and soft-maximum barrier functions for safety with actuation constraints
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Dominance regions of pursuit-evasion games in non-anticipative information patterns
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Multi-defender capture-the-flag game with convex target regions
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Fixed-time learning for safe time-critical verification using reachability analysis
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Safe fixed-time reinforcement learning for nonlinear zero-sum games with obstacle avoidance awareness
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Approximation of reachable sets using optimal control and support vector machines
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Interval enclosures for reachable sets of chemical kinetic flow systems. Part 2: Direct-bounding method
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Interval enclosures for reachable sets of chemical kinetic flow systems. Part 3: Indirect-bounding method
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Flight safety measurements of UAVs in congested airspace
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Tube-based robust reinforcement learning for autonomous maneuver decision for UCAVs
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Improving flight performance of UAVs by ice shape modulation
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Safe reinforcement learning for high-speed autonomous racing
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Maximal safe set computation for pressure swing adsorption processes
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Computing robust control invariant sets of constrained nonlinear systems: A graph algorithm approach
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Thermal runaway avoidance using Hamilton–Jacobi reachability and model predictive control
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An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems
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Computing control invariant sets of cascade nonlinear systems: Decomposition and distributed computing
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Computing control invariant set using reinforcement learning by leveraging default value function
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Guaranteeing safety for heavy duty vehicle platooning: Safe set computations and experimental evaluations
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Safety enforcement in closed-loop anesthesia—A comparison study
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Multi-agent interaction and enhanced safety in autonomous overtaking with backward reachability analysis
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CASL-HJX: A comprehensive guide to solving deterministic and stochastic hamilton-Jacobi equations
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A Markov model for assessing ecological stability properties
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Multi-objective low-thrust spacecraft trajectory design using reachability analysis
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One superior pursuer and multiple-evader differential games with two lifelines
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Robust reachability within deep reinforcement learning framework
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Safety Analysis of Stochastic Dynamical Systems
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Determination of reachable flight regions: a zonotopic approach
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Control Design with Guaranteed Transient Performance via Reachable Set Estimates
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