H/sub infinity /-control by state-feedback and fast algorithms for the computation of optimal H/sub infinity /-norms

Scherer C.

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H/sub infinity /-control by state-feedback and fast algorithms for the computation of optimal H/sub infinity /-norms

机译：通过状态反馈和快速算法控制H / sub无限/-，以计算最佳H / sub无限/-范数

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The suboptimality of some parameter for H/sub infinity /-optimization by dynamic state-feedback is characterized in terms of the solvability of Riccati inequalities. This is done without restricting the finite zero structure of the plant. If there are no system zeros on the imaginary axis, the H/sub infinity /-problem can be treated in a complete and satisfactory way. Explicit characterizations optimum to be achieved are provided, and a closed formula for the optimal value is derived in terms of the H/sub infinity /-norm of some fixed transfer matrix. If the optimum is not attained, any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high-gain. A globally and quadratically convergent algorithm to compute the optimal value is proposed. This algorithm is generalized to the H/sub infinity /-optimization problem by measurement feedback.

机译：通过Riccati不等式的可解性来表征通过动态状态反馈进行H / sub无限大/优化的某些参数的次优性。这样做不会限制工厂的有限零结构。如果虚轴上没有系统零，则可以完全令人满意的方式处理H / sub无限大/问题。提供了最佳的明确表征，并根据某些固定传递矩阵的H / sub无限大/范数，得出了最佳值的封闭式。如果没有达到最佳，那么构造成接近最小范数的有界控制器的任何序列都必须是高增益的。提出了一种全局和二次收敛的最优值计算算法。通过测量反馈将该算法推广到H / sub无穷大/最优化问题。

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《IEEE Transactions on Automatic Control》 |1990年第10期|P.1090-1099|共10页
作者
Scherer C.;
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1. Fast iterative computation of optimal two-block H/sup infinity /-norm [J] . Chang B., Banda S.S. IEEE Transactions on Automatic Control . 1989,第7期

机译：最优两块H / sup无限/范数的快速迭代计算
2. On the computation of the optimal H_( infinity) norms for two feedback control problems [J] . Lin Wen-Wei, Xu Quan-Fu, Wang Chern-Shuh Linear Algebra and its Applications . 1999,第1a3期

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3. FASTER AND MORE ACCURATE COMPUTATION OF THE H-infinity NORM VIA OPTIMIZATION [J] . Benner Peter, Mitchell Tim SIAM Journal on Scientific Computing . 2018,第5期

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4. Design and performance analysis of optimal reduced order H-infinity controller: L1 norm based genetic algorithm technique [C] . Nafees Ahamad, Gagan Singh, Shahala Khan, International Conference on Power and Embedded Drive Control . 2017

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7. On the computation of the optimal H-infinity norms for two feedback control problems [O] . Lin, WW 2010

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8. Digital State-Feedback H infinity Control of Pritchard-Salamon Systems. A PopovFunction Approach [R] . Dan Barb, F., Ionescu, V., de Koning, W. 1993

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H/sub infinity /-control by state-feedback and fast algorithms for the computation of optimal H/sub infinity /-norms

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