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Optimal finitedimensional spectral densities for the identification of continuoustime MIMO systems 
I.M.MITHUN,ShravanMOHAN,BharathBHIKKAJI 

(Department of Electrical Engineering, Indian Institute of Technology, Madras, Chennai 600036, India) 

摘要: 
This paper presents a method for designing inputs to identify linear continuoustime multipleinput multipleoutput (MIMO)
systems. The goal here is to design a Toptimal bandlimited spectrum satisfying certain input/output power constraints. The input
power spectral density matrix is parametrized as the product φu(jω) =1/2H(jω){H^H}(jω), where H(jω) is a matrix polynomial. This
parametrization transforms the Toptimal cost function and the constraints into a quadratically constrained quadratic program
(QCQP). The QCQP turns out to be a nonconvex 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 nonconvex 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 inputoutput data. 
关键词: System identification, optimal input design, fisher information matrix, quadratically constrained quadratic program 
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基金项目: 

Optimal finitedimensional spectral densities for the identification of continuoustime MIMO systems 
I. M. MITHUN,Shravan MOHAN,Bharath BHIKKAJI 
(Department of Electrical Engineering, Indian Institute of Technology, Madras, Chennai 600036, India) 
Abstract: 
This paper presents a method for designing inputs to identify linear continuoustime multipleinput multipleoutput (MIMO)
systems. The goal here is to design a Toptimal bandlimited spectrum satisfying certain input/output power constraints. The input
power spectral density matrix is parametrized as the product φu(jω) =1/2H(jω){H^H}(jω), where H(jω) is a matrix polynomial. This
parametrization transforms the Toptimal cost function and the constraints into a quadratically constrained quadratic program
(QCQP). The QCQP turns out to be a nonconvex 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 nonconvex 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 inputoutput data. 
Key words: System identification, optimal input design, fisher information matrix, quadratically constrained quadratic program 

