Solving Infinite-Dimensional Harmonic Lyapunov and Riccati equations
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Subspace Decomposition for Graphon LQR: Applications to VLSNs of Harmonic Oscillators
Graphon control has been proposed and developed in [1]-[3] to approximately solve control problems for very large-scale networks (VLSNs) of linear dynamical systems based on graphon limits. This paper provides a solution…
Harmonic-Copuled Riccati Equations and its Applications in Distributed Filtering
The coupled Riccati equations are cosisted of multiple Riccati-like equations with solutions coupled with each other, which can be applied to depict the properties of more complex systems such as markovian systems or mul…
Automatic differentiation of Sylvester, Lyapunov, and algebraic Riccati equations
Sylvester, Lyapunov, and algebraic Riccati equations are the bread and butter of control theorists. They are used to compute infinite-horizon Gramians, solve optimal control problems in continuous or discrete time, and d…
On solving infinite-dimensional Toeplitz Block LMIs
This paper focuses on the resolution of infinite-dimensional Toeplitz Block LMIs, which are frequently encountered in the context of stability analysis and control design problems formulated in the harmonic framework. We…
Construction of Lyapunov Functions Using Vector Field Decomposition
In the present paper, a novel vector field decomposition based approach for constructing Lyapunov functions is proposed. For a given dynamical system, if the defining vector field admits a decomposition into two mutually…