论文标题
部分可观测时空混沌系统的无模型预测
Solving Infinite-Dimensional Harmonic Lyapunov and Riccati equations
论文作者
论文摘要
在本文中，我们解决了解决无限次谐波代数Lyapunov和Riccati方程的问题，直到任意小误差。对于周期性系统的分析和稳定，包括周期性轨迹的跟踪，这个问题至关重要。我们首先在L 2矩阵函数的一般环境中给出了floquet分解的封闭形式，并研究了无限维谐波矩阵及其截断版本的光谱特性。这项光谱研究使我们能够提出一种通用和数值有效的算法，以求解无限的谐波代数Lyapunov方程，最多是一个任意的小误差。我们将该算法与Kleinman算法相结合，以求解无限二维的谐波riccati方程，并将提出的结果应用于使用周期性轨迹跟踪的谐波LQ控制的设计。
In this paper, we address the problem of solving infinite-dimensional harmonic algebraic Lyapunov and Riccati equations up to an arbitrary small error. This question is of major practical importance for analysis and stabilization of periodic systems including tracking of periodic trajectories. We first give a closed form of a Floquet factorization in the general setting of L 2 matrix functions and study the spectral properties of infinite-dimensional harmonic matrices and their truncated version. This spectral study allows us to propose a generic and numerically efficient algorithm to solve infinite-dimensional harmonic algebraic Lyapunov equations up to an arbitrary small error. We combine this algorithm with the Kleinman algorithm to solve infinite-dimensional harmonic Riccati equations and we apply the proposed results to the design of a harmonic LQ control with periodic trajectory tracking.
