The Structure-preserving Doubling Numerical Algorithm of the Continuous Coupled Algebraic Riccati Equation
The Structure-preserving Doubling Numerical Algorithm of the Continuous Coupled Algebraic Riccati Equation
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DOI：
10.1007/s12555-019-0368-y
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Juan Zhang;Shifeng Li
中科院分区：
文献类型：
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作者：
Juan Zhang;Shifeng Li
本文应用保结构加倍算法求解连续耦合代数Riccati方程（CCARE）。利用CCARE的存在唯一性，证明了CCARE的迭代解是正半定的、对称的和唯一的。进一步讨论了保结构加倍算法的收敛性分析。此外，我们还提出了两种改进的保结构加倍算法。最后，给出了相应的数值算例来说明所推导的数值算法的有效性。
In the paper, we apply a structure-preserving doubling algorithm to solve the continuous coupled algebraic Riccati equation (CCARE). Using the existence and uniqueness of the CCARE, we show that the iteration solution of the CCARE are positive semi-definite, symmetric, and unique. Further, we discuss the convergent analysis of the structure-preserving doubling algorithm. Moreover, we present two modified structure-preserving doubling algorithms. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived numerical algorithms.