对偶关系与不确定系统的状态估计
Duality Relation and State Estimation in Systems with Uncertainty
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摘要: 本文讨论如下系统状态估计问题, x=A(t)x+B1(t)u(t)+B2(t)w y=C(t)X+D1(t)u(t)+D2(t)w 其中u(t)为已知输入向量,w为不确定向量.假定w为时间t 的函数,对它只知道其可能的变化范围,不知道其具体实现.问题是根据量测y(t),0tT,如何去估计状态变量 x(T)?我们用[1]中所建立的对偶关系式解决了状态的min-max估计问题.在二次型限制之下的min-max状态估计与卡尔曼滤波完全一致.这里所用的方法比起[4]中的方法简单得多.Abstract: The present paper discusses the problem of state estimation for the following system x= A (t) x + B1(t) +B2 (t) w y= C (t) x+D1(t) u (t) + D2(t) w where u (t) is the known input vector and W the uncertain vector. Assume that W is a function of t, for which we know its range of variation only, but we do not know its concrete realization. The problem is that how to estimate the state variables x (T) on the base of observation values y (t), 0 t T. The duality relation establised, in [I] is used to solve the problem of the min-max estimation. The rain-max state estimation under the limitation of quadratic constraints coincides exactly with the Kalman filter. The method used here is much simples than that of [4].
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