D. Veldman, E. Zuazua (2025) Local Stability and Convergence of Unconstrained Model Predictive Control
Abstract. The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based on a linear time-invariant plant model is studied. Based on the long-time behavior of the solution of the Riccati Differential Equation (RDE), explicit error estimates are derived that clearly demonstrate the influence of the two critical parameters in MPC: the prediction horizon T and the control horizon \tau. In particular, if the MPC-controller has access to an exact (linear) plant model, the MPC-controls and the corresponding optimal state trajectories converge exponentially to the solution of an infinite-horizon optimal control problem when T-\tau \rightarrow \infty. When the difference between the linear model and the nonlinear plant is sufficiently small in a neighborhood of the origin, the MPC strategy is locally stabilizing and the influence of modeling errors can be reduced by choosing the control horizon $\tau$ smaller. The obtained convergence rates are validated in numerical simulations.
arxiv: 2206.01097