Local Stability and Convergence of Unconstrained Model Predictive Control

Daniel Veldman; Enrique Zuazua

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arXiv · 2206.01097

Local Stability and Convergence of Unconstrained Model Predictive Control

Daniel Veldman·Enrique Zuazua

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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.

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Daniel Veldman, Enrique Zuazua. 2022-06-02. Local Stability and Convergence of Unconstrained Model Predictive Control. https://arxiv.org/abs/2206.01097

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