Model Predictive Control and Dynamic Programming

Model Predictive Control (MPC) and Dynamic Programming (DP) are two different methods to obtain an optimal feedback control law. The former uses on-line optimization to solve an open-loop optimal control problem cast over a finite size time window at each sample time. A feedback control law is defined implicitly by repeating the optimization calculation after a feedback update of the state at each sample time. In contrast, the latter attempts to derive an explicit feedback law off-line by deriving and solving so called Bellman´s optimality equation. Both have been used successfully to solve optimal control problems, the former for constrained control problems and the latter for unconstrained linear quadratic optimal control problem. In this paper, we examine the differences and similarities as well as their relative merits and demerits. We also propose ways to integrate the two methods to alleviate each other´s shortcomings.