Optimal finite-dimensional spectral densities for the identification of continuous-time MIMO systems

作     者：I.M.MITHUN Shravan MOHAN Bharath BHIKKAJI 

作者机构：Department of Electrical Engineering Indian Institute of Technology Madras Chennai 600036 India 

出 版 物：《Control Theory and Technology》 (控制理论与技术（英文版）)

年 卷 期：2019年第17卷第3期

页      面：276-296页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 

主　　题：System identification optimal input design fisher information matrix quadratically constrained quadratic program 

摘      要：This paper presents a method for designing in puts to identify linear con tinuous-time multiple-input multiple-output (MIMO) systems. The goal here is to design a T-optimal band-limited spectrum satisfying certain input/output power constraints. The input power spectral density matrix is parametrized as the productφu(jω)= 1/2H(jω)H^H(jω),where H(jω) is a matrix polynomial. This parametrization transforms the T-optimal cost function and the constraints into a quadratically constrained quadratic program (QCQP). The QCQP turns out to be a non-convex semidefinite program with a rank one constraint. A convex relaxation of the problem is first solved. A rank one solution is constructed from the solution to the relaxed problem. This relaxation admits no gap between its solution and the original non-convex QCQP problem. The constructed rank one solution leads to a spectrum that is optimal. The proposed input design methodology is experimentally validated on a cantilever beam bonded with piezoelectric plates for sensing and actuation. Subspace identification algorithm is used to estimate the system from the input-output data.