通过聚类和基于核的Lipschitz回归学习经济模型预测控制

IF 4.2 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS
Weiliang Xiong , Defeng He , Haiping Du
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引用次数: 0

摘要

针对具有输入、状态约束和未知动力学的不确定非线性系统,提出了一种新的学习经济模型预测控制方案。利用输入输出数据,结合聚类和核回归,设计了一种快速准确的Lipschitz回归方法来学习未知动态。在每个聚类中,通过求解并行凸优化问题来估计核权值并减小预测器的Lipschitz常数,从而限制误差在预测层中的传播。我们导出了确定性和概率两种不同的学习误差边界,并为不连续预测器定制了一种新的鲁棒约束收紧策略。然后,通过引入稳定优化问题构造Lyapunov函数,建立了学习经济模型预测控制算法。导出了闭环系统递归可行性和输入状态稳定性的充分条件。通过数值算例和连续搅拌槽式反应器的仿真验证了该算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Learning economic model predictive control via clustering and kernel-based Lipschitz regression
This paper presents a novel learning economic model predictive control scheme for uncertain nonlinear systems subject to input and state constraints and unknown dynamics. We design a fast and accurate Lipschitz regression method using input and output data that combines clustering and kernel regression to learn the unknown dynamics. In each cluster, the parallel convex optimization problems are solved to estimate the kernel weights and reduce the Lipschitz constant of the predictor, hence limiting the error propagation in the prediction horizon. We derive two different bounds of learning errors in deterministic and probabilistic forms and customize a new robust constraint-tightening strategy for the discontinuous predictor. Then, the learning economic model predictive control algorithm is formulated by introducing a stabilized optimization problem to construct a Lyapunov function. Sufficient conditions are derived to ensure the recursive feasibility and input-to-state stability of the closed-loop system. The effectiveness of the proposed algorithm is verified by simulations of a numerical example and a continuously stirred tank reactor.
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来源期刊
CiteScore
7.30
自引率
14.60%
发文量
586
审稿时长
6.9 months
期刊介绍: The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.
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