论文标题
线性输入延迟系统通过动态状态反馈控制器的耗散稳定：一种基于优化的方法
Dissipative stabilization of linear input delay systems via dynamical state feedback controllers: an optimization based approach
论文作者
论文摘要
在本说明中，我们提供了一种有效的解决方案，用于稳定受耗散约束的线性输入延迟系统，而输入延迟的所有效果都由具有新结构的控制器补偿。该方法的灵感来自分布式延迟和预测控制器的数学处理中的最新发展，这对于溶液的推导至关重要。一个重要的概念创新是使用参数化的动态状态反馈控制器（DSFC），其中控制器的尺寸等于控制输入的尺寸。通过Krasovskii功能方法获得了耗散DSFC的足够条件，其中该条件包括双线性基质不等式（BMI）。为了解决BMI，我们应用了内部凸近似算法，该算法可以根据预测器控制器增益的明确构造来初始化。所提出的DSFC可以被视为经典预测器控制器的扩展，从而能够补偿点式输入延迟的所有效果，同时满足耗散性约束。给出了一个数字示例来说明我们提出的方法的有效性。
In this note, we present an effective solution to the stabilization of linear input delay systems subject to dissipative constraints while all the effect of input delay is compensated by a controller with novel structure. The method is inspired by the recent development in the mathematical treatment of distributed delays and predictor controllers, which are critical for the derivation of the solution. An important conceptual innovation is the use of a parameterized dynamical state feedback controller (DSFC), where the dimension of the controller equals the dimension of the control input. A sufficient condition for the existence of a dissipative DSFC is obtained via the Krasovskii functional approach, where the condition includes a bilinear matrix inequality (BMI). To solve the BMI, we apply an inner convex approximation algorithm which can be initialized based on an explicit construction of a predictor controller gain. The proposed DSFC can be considered as an extension of the classical predictor controller, thereby capable of compensating all the effects of the pointwise input delay while satisfying dissipative constraints. A numerical example is given to illustrate the effectiveness of our proposed methodology.
