A discounted reach-cost Bellman operator is contractive, has a unique fixed point identical to the HJ reachability value function, and can be approximated by sample-based RL.
Hamilton- jacobi reachability: A brief overview and recent advances
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For linear systems meeting specific dynamics assumptions, the optimal input matrix that warps the reachable set along a target direction is found by solving a finite number of linear optimization problems.
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Reachability-Preserving Bellman Operator for the Discounted Reach-Cost Value Function: Uniting Hamilton-Jacobi Reachability and Reinforcement Learning
A discounted reach-cost Bellman operator is contractive, has a unique fixed point identical to the HJ reachability value function, and can be approximated by sample-based RL.
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Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems
For linear systems meeting specific dynamics assumptions, the optimal input matrix that warps the reachable set along a target direction is found by solving a finite number of linear optimization problems.