$L_1$ Optimal Controller Synthesis for Sampled-Data Systems via Piecewise Linear Kernel Approximation
$L_1$ Optimal Controller Synthesis for Sampled-Data Systems via Piecewise Linear Kernel Approximation
复制标题
通过分段线性核逼近的采样数据系统的 $L_1$ 最优控制器综合
DOI：
10.1002/rnc.5513
复制
发表时间：
2021
影响因子：
3.9
通讯作者：
J. H. Kim and T. Hagiwara
中科院分区：
文献类型：
--
作者：
本岡駿人;蛯原義雄;J. H. Kim and T. Hagiwara
本文为采样数据系统的l∞最优控制问题提供了一个新的框架，即对于给定的连续时间对象，离散时间最优控制器使闭环系统的连续时间l∞诱导范数最小化的综合问题。主要思想是发展一种称为分段线性核近似（PLKA）方法的近似方法，通过该方法，输入算子的核函数和输出算子的保持函数在采样数据系统的提升表示中由分段线性函数近似。通过定义足够的预伴随算子，PLKA方法对于在近似参数n下近似进行最优控制器综合时可达到的l∞诱导范数性能恶化具有1/ n2的相关收敛率。与另一种通过不同近似处理的控制器合成方法（分段线性输入近似法）相比，我们进一步证明了所提出的PLKA方法在性能退化方面有一个定量改进的界。最后，通过数值算例验证了该方法的有效性。
This article provides a new framework for the so‐calledL1optimal control problem of sampled‐data systems, that is, the synthesis problem of a discrete‐time optimal controller minimizing the continuous‐timeL∞‐induced norm of the closed‐loop system for a given continuous‐time plant. The main idea is to develop the approximation method called the piecewise linear kernel approximation (PLKA) method, by which the kernel function of the input operator together with the hold function of the output operator in the lifted representation of sampled‐data systems are approximated by piecewise linear functions. By defining adequate preadjoint operators, the PLKA method is shown to have the associated convergence rate of 1/N2for the deterioration of the attainableL∞‐induced norm performance when the optimal controller synthesis is conducted approximately under the approximation parameterN. Compared with another existing procedure for controller synthesis through different approximation treatment called the piecewise linear input approximation method, we further show that the proposed PLKA method has a quantitatively improved bound on the performance deterioration. Finally, numerical examples are studied to verify the effectiveness of the proposed PLKA method.