The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the local algebraic observability problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant.
We present a probabilistic seminumerical algorithm that proposes a solution to this problem in polynomial time. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the complexity of evaluation of the model and in the number of variables. Furthermore, we show that the size of the integers involved in the computations is polynomial in the number of variables and in the degree of the system. Last, we estimate the probability of success of our algorithm.
在系统和控制理论中经常遇到以下问题。给定物理过程的代数模型,理论上可以从实验的输入输出行为推导出哪些变量?为了确定所有其他变量,我们应该假设知道剩余多少个变量?这些问题是局部代数可观察性 I>问题的一部分,该问题与模型对称性的非平凡Lie子代数的存在有关,从而使输入和输出不变。 P>
我们提出了一种概率半数值 I>算法,该算法在多项式时间内 I>提出了该问题的解决方案。给出了有理数域上必要数量的算术运算的界限。此边界是模型的评估复杂度 I>和变量数量的多项式。此外,我们表明,在计算中涉及的整数的大小 I>在变量数和系统度上是多项式。最后,我们估计算法成功的可能性。 P>
机译:在多项式时间内测试局部代数可观性的概率算法
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机译:一种概率算法,用于测试多项式时间的局部代数观测
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机译:多项式时间内测试局部代数可观性的概率算法