2017/06/13 by Shravan Mohan, Mohan, Shravan, Mithun Im +3
Engineering · #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Structural Health Monitoring Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1706.03982
openalex publication_date 2017/06/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The aim of this paper is to design a band-limited optimal input with power\nconstraints for identifying a linear multi-input multi-output system. It is\nassumed that the nominal system parameters are specified. The key idea is to\nuse the spectral decomposition theorem and write the power spectrum as\n\φu(j\ω)=\(1)/(2)H(j\ω)H^*(j\ω). The matrix H(j\ω)\nis expressed in terms of a truncated basis for\n\L2\(\[-\ω\cut-off,\ω\cut-off\]\).\nWith this parameterization, the elements of the Fisher Information Matrix and\nthe power constraints turn out to be homogeneous quadratics in the basis\ncoefficients. The optimality criterion used are the well-known\n\D-optimality, \A-optimality, \T-optimality\nand \E-optimality. The resulting optimization problem is non-convex\nin general. A lower bound on the optimum is obtained through a bi-linear\nformulation of the problem, while an upper bound is obtained through a convex\nrelaxation. These bounds can be computed efficiently as the associated problems\nare convex. The lower bound is used as a sub-optimal solution, the\nsub-optimality of which is determined by the difference in the bounds.\nInterestingly, the bounds match in many instances and thus, the global optimum\nis achieved. A discussion on the non-convexity of the optimization problem is\nalso presented. Simulations are provided for corroboration.\n