AI 中文总结
研究一维扩散反应系统在干扰和参考信号由不稳定外系统生成时的输出调节问题，提出基于有限维跟踪误差的调节器设计方法，通过推导组合装置转化问题，利用模态分解法刻画可观测性，证明观测器增益性质并给出LMI条件，分析了含未知时变测量延迟的情况。
AI 中文摘要
本文研究一维扩散反应系统的输出调节问题，其中干扰和参考信号由不稳定外系统生成。针对这类可能不稳定的系统，我们提出一种基于有限维跟踪误差的调节器设计方法。基于调节器方程推导组合装置，将输出调节问题转化为组合系统的部分稳定问题。用模态分解法在适当传输零点和可观测性条件下刻画截断模态的可观测性。控制器设计中，由于外系统引入的耦合，观测器增益具有满秩。证明观测器增益可设计为其范数相对于观测器维数保持一致有界。提供基于LMI的条件确定观测器维数，表明对于足够大的维数LMI是可行的。最后分析了存在未知时变测量延迟时的输出调节问题，并给出数值例子验证理论结果。
英文摘要
This paper addresses the output regulation problem for 1-D diffusion-reaction system, where both the disturbance and reference signals are generated by an unstable exosystem. We propose a constructive approach to the design of a finite-dimensional tracking error-based regulator for this class of possibly unstable systems. Based on the regulator equations, a combined plant is derived, converting the output regulation problem into a partial stabilization problem for the combined system. Using the modal decomposition method, the observability of the truncated modes is characterized under appropriate transmission zeros and observability conditions. For the controller design, unlike in the standard stabilization case, where the observer gain is dependent on the unstable modes only, the observer gain here has full order due to the coupling introduced by the exosystem. We prove that the observer gain can be designed such that its norm remains uniformly bounded with respect to the dimension of the observer. LMI-based conditions are provided for determining the observer dimension, and it is shown that the LMI is feasible for a sufficiently large dimension. Finally, the output regulation problem in the presence of unknown time-varying measurement delays is analyzed. Numerical examples are provided to validate the theoretical results.
Comments16 pages, 3 figures
