发表机构
University of Illinois at Urbana-Champaign; University of Minnesota, Minneapolis（伊利诺伊大学厄巴纳-香槟分校; 明尼苏达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对实解析特征函数的线性参数化非线性系统，证明非主动探索可实现其有限样本辨识，给出反例说明非实解析系统需主动探索，并通过数值实验验证理论结果。
AI 中文摘要
本文研究线性参数化非线性（LPN）系统的辨识问题。尽管LPN系统与线性系统具有相同的线性参数化结构，但它们的辨识难度更大。此前研究通过基于分段仿射系统的反例表明，非主动探索通常不足以实现LPN系统的辨识。本文考虑具有实解析特征函数的LPN系统，通过建立最小二乘估计和集合Membership估计的非渐近收敛速率，证明非主动探索足以实现此类系统的辨识。此外，本文提供反例表明，即使系统是无穷可微的，非主动探索也可能不足以实现非实解析系统的辨识。本文还通过数值实验进一步支持和验证了理论结果。
英文摘要
This paper studies the identification of linearly parameterized nonlinear (LPN) systems. Although LPN systems share the same linear parameterization structure as linear systems, they are more challenging to identify. In particular, previous work has shown, through a counterexample based on a piecewise-affine system, that non-active exploration is generally insufficient for LPN system identification. In this paper, we consider LPN systems with real-analytic feature functions. We show that non-active exploration is sufficient for the identification of this class of systems by establishing non-asymptotic convergence rates of least-squares estimation and set-membership estimation. In addition, we provide counterexamples to show that non-active exploration may not be sufficient for system identification for non-real-analytic systems, even if those systems are infinitely differentiable. We present numerical experiments to further support and validate our theoretical results.
