Adaptive polyhedral meshing for approximate dynamic programming in control

This work proposes a new criterion for adaptive meshing in polyhedral partitions which interpolate a value function in Approximate Dynamic Programming (ADP) in optimal control problems. The criterion adds new points to a simplicial mesh, based on: a user-defined initial condition probability density function which determines 'influential' regions of the state space, uncertainty (variance) propagation, and temporal-difference error. A collection of lemmas justifies the algorithmic proposal. Comparative analysis with other options in literature highlights the advantages of our proposal. The developed methods are applied to simulation examples and an experimental robotic setup.