基于结构化状态空间模型，实现非线性系统的数据驱动控制器设计。
Controller Design for Structured State-space Models via Contraction Theory
- 用收缩理论构建基于SSM的可控可观测性分析框架
- 通过线性矩阵不等式实现可扩展控制设计
- 建立分离原理，独立设计观测器与控制器并保持系统稳定
本文提出一种间接数据驱动的输出反馈控制器设计方法，利用结构化状态空间模型（SSMs）作为替代模型。SSMs在建模时间序列数据和动态系统方面展现出优势：能够捕捉长期依赖关系，同时计算复杂度为线性，相比Transformer的二次复杂度更具效率。本工作贡献有三：首次对SSMs的可控性与可观测性进行分析，从而基于收缩理论通过线性矩阵不等式（LMIs）实现可扩展控制设计；建立了适用于SSMs的分离原理，允许独立设计观测器与状态反馈控制器，同时保证闭环系统的指数稳定性；通过数值例子验证了该框架的有效性，展示了非线性系统辨识及输出反馈控制器的合成能力。
原文摘要 · Abstract (English)
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling time-series data and dynamical systems. They can capture long-term dependencies while maintaining linear computational complexity with respect to the sequence length, in comparison to the quadratic complexity of Transformer-based architectures. The contributions of this work are threefold. We provide the first analysis of controllability and observability of SSMs, which leads to scalable control design via Linear Matrix Inequalities (LMIs) that leverage contraction theory. Moreover, a separation principle for SSMs is established, enabling the independent design of observers and state-feedback controllers while preserving the exponential stability of the closed-loop system. The effectiveness of the proposed framework is demonstrated through a numerical example, showcasing nonlinear system identification and the synthesis of an output feedback controller.
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