论文标题
在近乎最佳的控制器设计中找到最近的负面虚构系统
Finding the Nearest Negative Imaginary System with Application to Near-Optimal Controller Design
论文作者
论文摘要
由于反馈互连的NI系统的鲁棒性特性，负面的（NI）系统理论引起了人们的兴趣。但是，对于此类系统类别的完整输出最佳控制器合成方法尚未存在。为了开发解决此问题的解决方案，我们首先开发一种方法，以找到与非NI系统的最接近的NI系统。后来的问题如下：对于由状态空间矩阵$（a，b，c，d）$定义的任何线性时间不变（LTI）系统，找到最近的NI系统，带有状态空间矩阵$（a+Δ_A，b+Δ_b，c+Δ_b，c+Δ_c，d+Δ_____________________最小化。然后，该方法将用于为给定的NI植物找到最近的最佳控制器。换句话说，对于给定的NI系统，最佳控制方法（例如LQG）用于设计满足特定性能度量的最佳控制器。然后，使用找到最近的NI系统的开发方法，用作近乎最佳的控制合成方法，以找到与设计的最佳控制器的最接近的NI系统。因此，合成的控制器满足了Ni属性，因此保证了通过控制的负虚构系统的强大反馈回路。
The negative imaginary (NI) systems theory has attracted interests due to the robustness properties of feedback interconnected NI systems. However, a full output optimal controller-synthesis methodology, for such class of systems, is yet to exist. In order to develop a solution towards this problem, we first develop a methodology to find the nearest NI system to a non NI system. This later problem stated as follows: for any linear time invariant (LTI) system defined by the state space matrices $(A, B, C, D)$, find the nearest NI system, with the state space matrices $(A+Δ_A,B+Δ_B,C+Δ_C,D+Δ_D)$, such that the norm of $(Δ_A,Δ_B,Δ_C,Δ_D)$ is minimized. Then, this methodology will be used to find the nearest optimal controller for a given NI plant. In other words, for a given NI system, an optimal control methodology, such as LQG, is used to design an optimal controller that satisfy a particular performance measure. Then, the developed methodology of finding the nearest NI system is used, as a near-optimal control synthesis methodology, to find the nearest NI system to the designed optimal controller. Hence, the synthesized controller satisfy the NI property and therefore guarantee a robust feedback loop with the negative imaginary system under control.
