ABSTRACT The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system, with nominal parameter values specified. Using spectral decomposition theorem, the power spectrum is written as . The matrix is expressed in terms of a truncated basis for , where is the cut-off frequency. The elements of the Fisher Information Matrix and the power constraints become homogeneous quadratics in basis coefficients. The optimality criterion used are -optimality, -optimality, -optimality and -optimality. This optimization problem is not known to be convex. A bi-linear formulation gives a lower bound on the optimum, while an upper bound is obtained through a convex relaxation. These bounds can be computed efficiently. The lower bound is used as a suboptimal solution, its sub-optimality determined by the difference between the bounds. Simulations reveal that the bounds match in many instances, implying global optimality.

中文翻译：

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使用谱分解进行系统识别的最优输入设计

摘要 本文的目的是设计一个带功率约束的带限最优输入，用于识别线性多输入多输出系统，并指定标称参数值。使用谱分解定理，功率谱写为 。矩阵用 的截断基表示，其中 是截止频率。Fisher 信息矩阵的元素和功率约束在基系数中变为齐次二次方程。使用的最优性标准是 -optimality、-optimality、-optimality 和 -optimality。这个优化问题不知道是凸的。双线性公式给出了最优值的下限，而上限是通过凸松弛获得的。可以有效地计算这些边界。下限用作次优解，它的次优性由边界之间的差异决定。模拟显示边界在许多情况下匹配，这意味着全局最优。