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Inexact methods for model predictive control (MPC), such as real-timeiterative schemes or time-distributed optimization, alleviate the computationalburden of exact MPC by providing suboptimal solutions. While the asymptoticstability of such algorithms is well studied, their finite-time performance hasnot received much attention. In this work, we quantify the performance ofsuboptimal linear model predictive control in terms of the additionalclosed-loop cost incurred due to performing only a finite number ofoptimization iterations. Leveraging this novel analysis framework, we propose anovel suboptimal MPC algorithm with a diminishing horizon length andfinite-time closed-loop performance guarantees. This analysis allows thedesigner to plan a limited computational power budget distribution to achieve adesired performance level. We provide numerical examples to illustrate thealgorithm's transient behavior and computational complexity.

On the Finite-Time Behavior of Suboptimal Linear Model Predictive Control