Nuclear norm system identification with missing inputs and outputs

Table 5: Validation fit for models obtained by a regularized nuclear norm optimization method, applied toten DaISy problems with different percentages of missing inputs and outputs.Data set 0% 10% 20% 30% 40% 50%1 72.0 72.4 72.2 71.8 72.5 71.02 84.7 86.2 85.3 85.4 85.2 83.73 84.4 88.6 84.7 84.2 80.6 81.04 29.7 45.1 35.6 − − −5 84.3 83.9 84.0 83.9 82.9 83.46 95.9 95.5 95.5 95.9 89.9 79.47 86.5 86.5 86.7 86.3 86.3 85.38 67.5 67.4 67.0 66.5 67.5 64.59 49.5 34.1 31.5 40.3 44.7 43.210 44.1 44.5 41.5 30.7 41.8 29.2References[1] M.Fazel, H.Hindi, S.Boyd, Arankminimizationheuristicwithapplicationtominimumordersystemapproximation, in: ProceedingsoftheAmericanControlConference, 2001,pp. 4734–4739.[2] M.Fazel, Matrixrankminimizationwithapplications, Ph.D.thesis, StanfordUniversity(2002).[3] E. J. Candès, B. Recht, Exact matrix completion via convex optimization, Foundationsof Computational Mathematics 9 (6) (2009) 717–772.[4] B. Recht, M. Fazel, P. A. Parrilo, Guaranteed minimum-rank solutions of linear matrixequations via nuclear norm minimization, SIAM Review 52 (3) (2010) 471–501.[5] E. J. Candès, Y. Plan, Matrix completion with noise, Proceedings of the IEEE 98 (6)(2010) 925–936.[6] E. J. Candès, T. Tao, The power of convex relaxation: near-optimal matrix completion,IEEE Transactions on Information Theory 56 (5) (2010) 2053–2080.[7] L. Ljung, System Identification, 2nd Edition, Prentice Hall, Upper Saddle River, NewJersey, USA, 1999.[8] M. Verhaegen, V. Verdult, Filtering and System Identification, Cambridge UniversityPress, New York, 2007.[9] Z. Liu, L. Vandenberghe, Interior-point method for nuclear norm approximation withapplicationtosystemidentification, SIAMJournalonMatrixAnalysisandApplications31 (3) (2009) 1235–1256.18