Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-07-12 DOI:10.1137/23m1551195

Thomas Berger, Dario Dennstädt, Lukas Lanza, Karl Worthmann

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2071-2097, August 2024.
Abstract. We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear multi-input multi-output systems of relative degree one with stable internal dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with a particular stage cost, and the model-free adaptive funnel controller. The new robust funnel MPC scheme guarantees output tracking of reference signals within prescribed performance bounds—even in the presence of unknown disturbances and a structural model-plant mismatch. We show initial and recursive feasibility of the proposed control scheme without imposing terminal conditions or any requirements on the prediction horizon. Moreover, we allow for model updates at runtime. To this end, we propose a proper initialization strategy, which ensures that recursive feasibility is preserved. Finally, we validate the performance of the proposed robust MPC scheme by simulations.

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鲁棒漏斗模型预测控制，实现具有规定性能的输出跟踪

SIAM 控制与优化期刊》，第 62 卷第 4 期，第 2071-2097 页，2024 年 8 月。摘要我们针对具有稳定内部动力学的相对度为 1 的非线性多输入多输出系统提出了一种新的鲁棒模型预测控制（MPC）方案。所提出的算法是漏斗 MPC（即具有特定阶段成本的 MPC）与无模型自适应漏斗控制器的结合。新的鲁棒漏斗 MPC 方案保证了在规定的性能范围内对参考信号进行输出跟踪，即使存在未知干扰和结构模型-设备不匹配的情况也是如此。我们展示了所提控制方案的初始和递归可行性，而无需强加终端条件或对预测范围有任何要求。此外，我们还允许在运行时更新模型。为此，我们提出了适当的初始化策略，确保递归可行性得以保留。最后，我们通过仿真验证了所提出的鲁棒 MPC 方案的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.