A J-spectral factorization approach to control
A J-spectral factorization approach to control
复制标题
J 谱分解方法进行控制
DOI：
10.1137/0328071
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发表时间：
1990
影响因子：
2.2
通讯作者：
J. Doyle
中科院分区：
文献类型：
--
作者：
M. Green;K. Glover;D. Limebeer;J. Doyle
利用J-谱分解理论，给出了与$\mathcal{H}_\infty $控制，J控制相关的标准模型匹配问题存在次优解的充要条件.模型匹配问题的解的存在性被证明是等价于两个耦合的J-谱分解问题的解的存在性，第二个因子提供了模型匹配问题的所有解的参数化。的J-谱因子的存在，然后被证明是等价于存在的非负定，稳定的解决方案，两个不定代数Riccati方程，允许一个状态空间公式的线性分数表示的所有控制器。该方法的优点是，可以在概念上简单的框架内处理非常一般的一类问题，并且不需要额外的辅助Riccati方程。
Necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with $\mathcal{H}_\infty $ control, J control are derived using J-spectral factorization theory. The existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled J-spectral factorization problems, with the second factor providing a parametrization of all solutions to the model matching problem. The existence of the J-spectral factors is then shown to be equivalent to the existence of nonnegative definite, stabilizing solutions to two indefinite algebraic Riccati equations, allowing a state-space formula for a linear fractional representation of all controllers to be given. A virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework, and no additional auxiliary Riccati equations are required.