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
Robust Invariant Sets Computation for Discrete-Time Perturbed Nonlinear Systems
In this paper we study the maximal robust invariant set estimation problem for discrete-time perturbed nonlinear systems within the optimal control framework. The maximal robust invariant set ofExpand

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