# What is the difference between moving-horizon DP and MPC?

What is the difference between moving-horizon DP (dynamic programming) and MPC (modelbased predictive control)? In both cases, the system input at time $t$ is determined by solving a finite-time optimization problem.

MHE are optimal observers that can be either linear or nonlinear. If you consider the MHE with unconstrained linear dynamics and quadratic cost its estimation of the current state $x_{t \mid t}$ is equivalent to the Kalman Filter.