Spatially interconnected systems (SISs) are formed by a chain of subsystems or units with the same or similar structure, all of which directly interact with their neighbors. For robust tracking of SISs subject to both polytopic uncertainty and external disturbances, a PD-type iterative learning control (ILC) algorithm integrated with real-time output feedback is proposed in the absence of accurate state measurement. By lifting along the spatial variable, the SISs are first transformed into an equivalent one-dimensional (1D) state-space model. Then, the transformed 1D system, together with the learning law, is reformulated as an equivalent discrete repetitive process model. Based on the Lyapunov theory, sufficient conditions in terms of bilinear matrix inequalities (BMIs) are established to ensure the robust stability of the resulting ILC system along the trial. To circumvent computation problem of BMIs, a two-stage heuristic approach is developed to derive ILC gains iteratively. Finally, the validity of the proposed method is verified by the comparative simulation of temperature distribution model of the metal rod.

中文翻译：

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基于输出反馈的不确定空间互联系统的PD型鲁棒迭代学习控制

空间互连系统 (SIS) 由一系列具有相同或相似结构的子系统或单元组成，所有这些子系统或单元都直接与其邻居相互作用。为了对受多面体不确定性和外部干扰影响的 SIS 进行稳健跟踪，在缺乏准确状态测量的情况下，提出了一种与实时输出反馈集成的 PD 型迭代学习控制 (ILC) 算法。通过沿空间变量提升，SIS 首先转换为等效的一维 (1D) 状态空间模型。然后，转换后的一维系统与学习规律一起被重新表述为等效的离散重复过程模型。基于李雅普诺夫理论，建立了双线性矩阵不等式 (BMI) 方面的充分条件，以确保所得到的 ILC 系统在试验过程中具有稳健的稳定性。为了规避 BMI 的计算问题，开发了一种两阶段启发式方法来迭代地推导出 ILC 增益。最后通过金属棒温度分布模型的对比仿真验证了所提方法的有效性。