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.
A review of safe reinforcement learning: Methods, theories, and applications.IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(12):11216–11235
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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.