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Optimal finite-dimensional spectral densities for the identification of continuous-time MIMO systems
I.M.MITHUN,ShravanMOHAN,BharathBHIKKAJI
0
(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 continuous-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 product φu(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.
关键词:  System identification, optimal input design, fisher information matrix, quadratically constrained quadratic program
DOI:
基金项目:
Optimal finite-dimensional spectral densities for the identification of continuous-time 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 continuous-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 product φu(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.
Key words:  System identification, optimal input design, fisher information matrix, quadratically constrained quadratic program