Editing Model predictive control (section)

== MPC vs. LQR ==
Model predictive control and linear-quadratic regulators are both expressions of optimal control, with different schemes of setting up optimisation costs.

While a model predictive controller often looks at fixed length, often graduatingly weighted sets of error functions, the linear-quadratic regulator looks at all linear system inputs and provides the transfer function that will reduce the total error across the frequency spectrum, trading off state error against input frequency.

Due to these fundamental differences, LQR has better global stability properties, but MPC often has more locally optimal[?] and complex performance.

The main differences between MPC and [[Linear–quadratic regulator|LQR]] are that LQR optimizes across the entire time window (horizon) whereas MPC optimizes in a receding time window,<ref name="wang">{{cite book|pages=xii|title=Model Predictive Control System Design and Implementation Using MATLAB®|last=Wang|first=Liuping|publisher=Springer Science & Business Media|year=2009}}</ref> and that with MPC a new solution is computed often whereas LQR uses the same single (optimal) solution for the whole time horizon. Therefore, MPC typically solves the optimization problem in a smaller time window than the whole horizon and hence may obtain a suboptimal solution. However, because MPC makes no assumptions about linearity, it can handle hard constraints as well as migration of a nonlinear system away from its linearized operating point, both of which are major drawbacks to LQR.

This means that LQR can become weak when operating away from stable fixed points. MPC can chart a path between these fixed points, but convergence of a solution is not guaranteed, especially if thought as to the convexity and complexity of the problem space has been neglected.