Structured H∞-control of infinite-dimensional systems
Structured H∞-control of infinite-dimensional systems
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DOI：
10.1002/rnc.4073
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发表时间：
2018-06-01
影响因子：
3.9
通讯作者：
Noll, D.
中科院分区：
文献类型：
--
作者：
Apkarian, P.;Noll, D.
我们为一大类传递函数形式的无限维线性时不变系统开发了一种新颖的基于频率的 H 无穷大控制方法。我们的方法的一个主要好处是不需要减少或识别技术，这避免了典型的扭曲。我们的方法允许利用状态空间或传递函数模型以及输入/输出频率响应数据（当只有这些数据可用时）。我们的目标是设计任何方便的结构和尺寸的实用 H-infinity 控制器。我们使用非平滑信任域捆绑方法来计算任意结构的局部最优 H 无穷控制器，以实现底层无限维 H 无穷问题的频率采样近似，从而 (i) 保证闭环中的指数稳定性，并且 (ii) 近似的最佳 H 无穷值与真实无限维值的区别仅在于先前用户指定的容差。我们证明了我们的方法在各种无限维 H-无穷综合问题上的多功能性和实用性，包括偏微分方程的分布式和边界控制、死区时间和延迟系统的控制以及使用丰富的测试集。
We develop a novel frequency-based H-infinity-control method for a large class of infinite-dimensional linear time-invariant systems in transfer function form. A major benefit of our approach is that reduction or identification techniques are not needed, which avoids typical distortions. Our method allows to exploit both state-space or transfer function models and input/output frequency response data when only such are available. We aim for the design of practically useful H-infinity-controllers of any convenient structure and size. We use a nonsmooth trust-region bundle method to compute arbitrarily structured locally optimal H-infinity-controllers for a frequency-sampled approximation of the underlying infinite-dimensional H-infinity-problem in such a way that (i) exponential stability in closed loop is guaranteed and that (ii) the optimal H-infinity-value of the approximation differs from the true infinite-dimensional value only by a prior user-specified tolerance. We demonstrate the versatility and practicality of our method on a variety of infinite-dimensional H-infinity-synthesis problems, including distributed and boundary control of partial differential equations, control of dead-time and delay systems, and using a rich testing set.