论文标题
二元性和$ h _ {\ infty} $ - 耦合ode-pde系统的最佳控制
Duality and $H_{\infty}$-Optimal Control Of Coupled ODE-PDE Systems
论文作者
论文摘要
在本文中，我们提出了$ h _ {\ infty} $的凸公式 - 耦合线性ode-pde系统具有一个空间维度的最佳控制问题。首先，我们将耦合的ODE-PDE系统重新将部分积分方程式（PIE）系统重新调整，并表明PIE系统的稳定性和$ h _ {\ infty} $性能暗示了ODE-PDE系统的稳定性。然后，我们构建一个双派系统，并表明双重系统的渐近稳定性和$ h _ {\ infty} $性能等效于原始派系。接下来，我们使用线性PI不平等（LPI）框架构成了稳定性的凸双配方和$ h _ {\ infty} $ - 性能问题。 LPI是LMI对部分积分（PI）运算符的概括，可以使用MATLAB工具箱Pietools解决。接下来，我们使用双重性结果来制定稳定功能，$ h _ {\ infty} $ - 最佳状态反馈控制问题作为LPI。最后，我们通过为几个数值示例构造控制器来说明算法的准确性和可扩展性。
In this paper, we present a convex formulation of $H_{\infty}$-optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE) system and show that stability and $H_{\infty}$ performance of the PIE system implies that of the ODE-PDE system. We then construct a dual PIE system and show that asymptotic stability and $H_{\infty}$ performance of the dual system is equivalent to that of the primal PIE system. Next, we pose a convex dual formulation of the stability and $H_{\infty}$-performance problems using the Linear PI Inequality (LPI) framework. LPIs are a generalization of LMIs to Partial Integral (PI) operators and can be solved using PIETOOLS, a MATLAB toolbox. Next, we use our duality results to formulate the stabilization and $H_{\infty}$-optimal state-feedback control problems as LPIs. Finally, we illustrate the accuracy and scalability of the algorithms by constructing controllers for several numerical examples.
