# A generalization of Bellman's equation with application to path planning, obstacle avoidance and invariant set estimation

@article{Jones2021AGO, title={A generalization of Bellman's equation with application to path planning, obstacle avoidance and invariant set estimation}, author={Morgan Jones and Matthew M. Peet}, journal={Autom.}, year={2021}, volume={127}, pages={109510} }

The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP's) with additively separable objective functions. In this paper we consider a larger class of MSOP's with monotonically backward separable objective functions; additively separable functions being a special case of monotonically backward separable functions. We propose a necessary and sufficient condition, utilizing a generalization of Bellman's equation, for a solution of a MSOP, with… Expand

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