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arXiv · 2305.10085

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

Aren Karapetyan·Efe C. Balta·Andrea Iannelli·John Lygeros
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Abstract

Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of such algorithms is well studied, their finite-time performance has not received much attention. In this work, we quantify the performance of suboptimal linear model predictive control in terms of the additional closed-loop cost incurred due to performing only a finite number of optimization iterations. Leveraging this novel analysis framework, we propose a novel suboptimal MPC algorithm with a diminishing horizon length and finite-time closed-loop performance guarantees. This analysis allows the designer to plan a limited computational power budget distribution to achieve a desired performance level. We provide numerical examples to illustrate the algorithm's transient behavior and computational complexity.

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Aren Karapetyan, Efe C. Balta, Andrea Iannelli, John Lygeros. 2023-05-17. On the Finite-Time Behavior of Suboptimal Linear Model Predictive Control. https://arxiv.org/abs/2305.10085

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