Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization
Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization
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DOI：
10.1145/1277548.1277578
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
M. Kanno;K. Yokoyama;H. Anai;S. Hara
中科院分区：
文献类型：
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作者：
M. Kanno;K. Yokoyama;H. Anai;S. Hara
本文提出了一种参数优化的代数方法，可用于信号处理和控制中的各种问题。该方法利用根和与多项式谱分解之间的关系，利用根和和Gröbner基理论来求解参数多项式谱分解。这使我们能够用参数和根之和来表达诸如最优成本之类的量。此外，还提出了一种参数优化方法，该方法利用参数多项式谱分解的结果，并采用量词消除。所提出的方法在特定控制问题的数值示例上进行了演示。
This paper proposes an algebraic approach for parametric optimization which can be utilized for various problems in signal processing and control.The approach exploits the relationship between the sum of roots and polynomial spectral factorization and solves parametric polynomial spectral factorization by means of the sum of roots and the theory of Gröbner basis. This enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots.Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs quantifier elimination.The proposed approach is demonstrated on a numerical example of a particular control problem.