Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality

TL;DR

This paper analyzes the stability and suboptimality of MPC and infinite-horizon control with plant-model mismatch using a unified quadratic cost framework, providing robustness guarantees and bounds.

Contribution

It introduces a unified analysis framework for discounted and undiscounted problems, establishing stability and suboptimality bounds under plant-model mismatch.

Findings

Exponential stability is guaranteed under certain conditions.

A suboptimality bound relates the surrogate and true costs.

Robustness is uniform over horizon length, independent of mismatch size.

Abstract

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.