不确定线性微分-代数方程的集员状态估计框架
Set-membership state estimation framework for uncertain linear differential-algebraic equations
摘要：
研究了希尔伯特空间中由不确定线性算子方程描述的动力系统的状态估计问题。不确定性应该承认一个集合成员的描述。我们提出了显式表达式的线性Minimax估计和误差提供的任何一对不确定参数属于二次边界集。我们引入了一个新的概念，极小极大方向可观性和指标的非因果线性非因果DAE。应用这些概念的线性不确定非因果DAE的状态估计问题，可以得到新的极小极大递归估计连续和离散时间。我们说明了非因果关系的植物应用我们的方法标量非线性集员状态估计问题的好处。给出了数值算例。
英文摘要：
We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for linear minimax estimation and error provided that any pair of uncertain parameters belongs to the quadratic bounding set. We introduce a new notion of minimax directional observability and index of non-causality for linear noncausal DAEs. Application of these notions to the state estimation problem for linear uncertain noncausal DAEs allows to derive new minimax recursive estimator for both continuous and discrete time. We illustrate the benefits of non-causality of the plant applying our approach to scalar nonlinear set-membership state estimation problem. Numerical example is presented.
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