Equivalence of Optimality Criteria for Markov Decision Process and Model Predictive Control

This paper shows that the optimal policy and value functions of a Markov Decision Process (MDP), either discounted or not, can be captured by finite-horizon undiscounted Optimal Control Problem (OCP), even if based on an inexact model. achieved selecting proper stage cost terminal for OCP. A very useful particular case OCP is Model Predictive (MPC) scheme where deterministic (possibly nonlinear) model used to reduce computational complexity. observation leads us parameterize MPC fully, including function. In practice, Reinforcement Learning algorithms then tune parameterized scheme. We verify developed theorems analytically in LQR we investigate some other nonlinear examples simulations.