AI 中文总结
研究从状态线性函数观测值重建非线性动力系统状态问题，提出可调观测器设计方法及相关定理，将其应用于化学反应网络模型，通过数值结果展示该观测器有效性，在小噪声下优于粒子滤波器。
AI 中文摘要
我们考虑从状态的线性函数观测值重建非线性动力系统状态的问题。提出了一种可调观测器的设计方法，并给出一个一般性定理，在某些条件下保证观测器无论初始误差如何都能指数收敛。还给出了将该定理应用于化学反应网络模型的其他结果，并通过化学反应网络质量作用形式的例子进行说明，其中观测部分物种浓度。提供了数值结果以展示所提观测器的有效性，还给出了有噪声观测情况下的结果，且在观测噪声较小时，所提观测器优于粒子滤波器。
英文摘要
We consider the problem of state reconstruction for a nonlinear dynamical system from observations of a linear function of the state. We present a design method for a tunable observer and provide a general theorem which under certain conditions guarantees exponential convergence of the observer regardless of initial error. Additional results are provided that apply this theorem to chemical reaction network models. Moreover, these results are illustrated via examples of mass action form of chemical reaction networks where a subset of the species concentrations are observed. Numerical results are provided to show the efficacy of our proposed observer. Numerical results are also shown for the case of noisy observations and our observer is compared favorably with the particle filter when the observation noise is small.
