On the finite time performance of model predictive control

This paper addresses the finite time performance of model predictive control (MPC) for linear-time-invariant (LTI) systems without constraints. The performance of MPC is compared with that of finite horizon optimal control to find out how well model predictive control can perform relative to the optimal performance with the same or different horizons. By exploring the properties of the Riccati difference equation (RDE), an upper and a lower bound of the ratio between the finite time performance of MPC and finite horizon optimal cost are obtained. It is possible to extend the obtained results to more complicated systems such as nonlinear dynamic systems with constraints with appropriate generalizations. Simulation example supports our results.