Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality
This work addresses stability and performance issues in control systems for applications where accurate modeling is challenging, offering theoretical guarantees that are incremental improvements over existing robust control methods.
The paper tackles the problem of ensuring stability and suboptimality in model predictive control (MPC) and infinite-horizon optimal control when there is a mismatch between the surrogate model and the real plant, providing guarantees of exponential stability and a suboptimality bound that recovers the optimal cost of the surrogate model.
We study closed-loop stability and suboptimality for MPC and infinite-horizon optimal control solved using a surrogate model that differs from the real plant. We employ a unified framework based on quadratic costs to analyze both finite- and infinite-horizon problems, encompassing discounted and undiscounted scenarios alike. Plant-model mismatch bounds proportional to states and controls are assumed, under which the origin remains an equilibrium. Under continuity of the model and cost-controllability, exponential stability of the closed loop can be guaranteed. Furthermore, we give a suboptimality bound for the closed-loop cost recovering the optimal cost of the surrogate. The results reveal a tradeoff between horizon length, discounting and plant-model mismatch. The robustness guarantees are uniform over the horizon length, meaning that larger horizons do not require successively smaller plant-model mismatch.