非线性离散时间鲁棒自适应最优切换跟踪控制
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东北大学流程工业综合自动化国家重点实验室

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TP13

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国家自然科学基金项目(面上项目,重点项目,重大项目)


Nonlinear discrete-time robust adaptive optimal switching tracking control
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The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    针对具有未知动态特性的离散时间非线性系统, 提出了一种鲁棒自适应最优切换跟踪控制方法, 旨在解决实际工业过程中因系统工作点变化导致难以实现最优跟踪控制的难题. 首先, 在非线性系统的多个工作点附近, 建立多个近似线性化模型, 并通过递推最小二乘辨识算法在线估计模型未知参数, 从而得到控制器设计模型及其估计模型. 然后, 基于嵌入转换、极小值原理和二次规划技术, 推导出最优切换函数及自适应最优跟踪控制器, 并设计鲁棒补偿器以提升控制系统性能. 最后, 进行了数值仿真实验和电熔镁砂熔炼过程电极电流控制的应用, 实验结果均验证了本文所提方法的有效性及实际可应用性.

    Abstract:

    A robust adaptive optimal switching tracking control method is proposed for discrete-time nonlinear systems with unknown dynamic characteristics, aiming to address the challenge of achieving optimal tracking control in practical industrial processes where system operating points vary. First, multiple approximate linearized models are established around different operating points of the nonlinear system. An online recursive least squares identification algorithm is employed to estimate the unknown parameters of each model. Consequence both controller design model and its corresponding estimation model are yielded. Then, based on the embedding transformation, minimum principle, and quadratic programming technique, the optimal switching function and adaptive optimal tracking controller are derived. Additionally, a robust compensator is designed to enhance the performance of the control system. Finally, a numerical simulation and an application to electrode current control in the smelting process of fused magnesia are conducted. The results verify the effectiveness and practical applicability of the proposed method.

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  • 收稿日期:2025-11-21
  • 最后修改日期:2026-06-01
  • 录用日期:2026-06-03
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