Tensor networks for MIMO LPV system identification

References

• Balas, G. J. (2002). Linear, parameter-varying control and its application to aerospace systems. ICAS Congress proceedings, Toronto, Canada (pp. 541.1–541.9).
   Google Scholar
• Batselier, K., Chen, Z., & Wong, N. (2017). Tensor network alternating linear scheme for MIMO Volterra system identification. Automatica, 84, 26–35. doi: 10.1016/j.automatica.2017.06.033
   Web of Science ®Google Scholar
• Bianchi, F. D., Mantz, R. J., & Christiansen, C. F. (2005). Gain scheduling control of variable-speed wind energy conversion systems using quasi-LPV models. Control Engineering Practice, 13(2), 247–255. doi: 10.1016/j.conengprac.2004.03.006
   Web of Science ®Google Scholar
• Brewer, J. (1978). Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems, 25(9), 772–781. doi: 10.1109/TCS.1978.1084534
   Google Scholar
• Chen Z., Batselier K., Suykens J. A., & Wong N. (2016). Parallelized tensor train learning for polynomial pattern classification. arXiv preprint arXiv:1612.06505.
   Google Scholar
• Chiuso, A. (2007). The role of vector autoregressive modeling in predictor-based subspace identification. Automatica, 43(6), 1034–1048. doi: 10.1016/j.automatica.2006.12.009
   Web of Science ®Google Scholar
• Cox, P., & Tóth, R. (2016). Alternative form of predictor based identification of LPV-SS models with innovation noise. 2016 IEEE 55th conference on decision and control (CDC), Las Vegas, United States of America (pp. 1223–1228).
   Google Scholar
• De Caigny, J., Camino, J. F., & Swevers, J. (2009). Interpolating model identification for SISO linear parameter-varying systems. Mechanical Systems and Signal Processing, 23(8), 2395–2417. doi: 10.1016/j.ymssp.2009.04.007
   Web of Science ®Google Scholar
• De Silva, V., & Lim, L.-H. (2008). Tensor rank and the ill-posedness of the best low-rank approximation problem. SIAM Journal on Matrix Analysis and Applications, 30(3), 1084–1127. doi: 10.1137/06066518X
   Web of Science ®Google Scholar
• Felici, F., Van Wingerden, J.-W., & Verhaegen, M. (2007). Subspace identification of MIMO LPV systems using a periodic scheduling sequence. Automatica, 43(10), 1684–1697. doi: 10.1016/j.automatica.2007.02.027
   Web of Science ®Google Scholar
• Gebraad, P. M., van Wingerden, J.-W., Fleming, P. A., & Wright, A. D. (2011). LPV subspace identification of the edgewise vibrational dynamics of a wind turbine rotor. 2011 IEEE International Conference on Control Applications (CCA), Denver, United States of America (pp. 37–42).
   Google Scholar
• Gebraad, P. M., van Wingerden, J.-W., Fleming, P. A., & Wright, A. D. (2013). LPV identification of wind turbine rotor vibrational dynamics using periodic disturbance basis functions. IEEE Transactions on Control Systems Technology, 21(4), 1183–1190. doi: 10.1109/TCST.2013.2257775
   Web of Science ®Google Scholar
• Giarré, L., Bauso, D., Falugi, P., & Bamieh, B. (2006). LPV model identification for gain scheduling control: An application to rotating stall and surge control problem. Control Engineering Practice, 14(4), 351–361. doi: 10.1016/j.conengprac.2005.01.013
   Web of Science ®Google Scholar
• Golub, G. H., Heath, M., & Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21(2), 215–223. doi: 10.1080/00401706.1979.10489751
   Web of Science ®Google Scholar
• Gunes B., van Wingerden J.-W., & Verhaegen M. (2016). Tensor nuclear norm LPV subspace identification. Transactions on Automatic Control, conditionally accepted.
   PubMed Web of Science ®Google Scholar
• Gunes, B., van Wingerden, J.-W., & Verhaegen, M. (2017). Predictor-based tensor regression (PBTR) for LPV subspace identification. Automatica, 79, 235–243. doi: 10.1016/j.automatica.2017.01.039
   Web of Science ®Google Scholar
• Håstad, J. (1990). Tensor rank is NP-complete. Journal of Algorithms, 11(4), 644–654. doi: 10.1016/0196-6774(90)90014-6
   Web of Science ®Google Scholar
• Holtz, S., Rohwedder, T., & Schneider, R. (2012). The alternating linear scheme for tensor optimization in the tensor train format. SIAM Journal on Scientific Computing, 34(2), A683–A713. doi: 10.1137/100818893
   Web of Science ®Google Scholar
• Knudsen, T. (2001). Consistency analysis of subspace identification methods based on a linear regression approach. Automatica, 37(1), 81–89. doi: 10.1016/S0005-1098(00)00125-4
   Web of Science ®Google Scholar
• Larimore, W. E., & Buchholz, M. (2012). ADAPT-LPV software for identification of nonlinear parameter-varying systems. IFAC Proceedings Volumes, 45(16), 1820–1825. doi: 10.3182/20120711-3-BE-2027.00418
   Google Scholar
• Laurain, V., Gilson, M., Tóth, R., & Garnier, H. (2010). Refined instrumental variable methods for identification of LPV Box–Jenkins models. Automatica, 46(6), 959–967. doi: 10.1016/j.automatica.2010.02.026
   Web of Science ®Google Scholar
• Oseledets, I. V. (2011). Tensor-train decomposition. SIAM Journal on Scientific Computing, 33(5), 2295–2317. doi: 10.1137/090752286
   Web of Science ®Google Scholar
• Remmlinger, J., Buchholz, M., & Dietmayer, K. (2013). Identification of a bilinear and parameter-varying model for lithium-ion batteries by subspace methods. 2013 American control conference (ACC), Washington, DC, United States of America (pp. 2268–2273).
   Google Scholar
• Rohwedder, T., & Uschmajew, A. (2013). On local convergence of alternating schemes for optimization of convex problems in the tensor train format. SIAM Journal on Numerical Analysis, 51(2), 1134–1162. doi: 10.1137/110857520
   Web of Science ®Google Scholar
• Scherer, C. W. (2001). LPV control and full block multipliers. Automatica, 37(3), 361–375. doi: 10.1016/S0005-1098(00)00176-X
   Web of Science ®Google Scholar
• Shamma, J. S. (2012). An overview of LPV systems. In J. Mohammadpour, & C. W. Scherer (Eds.), Control of linear parameter varying systems with applications (pp. 3–26). Boston, MA: Springer.
   Google Scholar
• Tóth, R. (2010). Modeling and identification of linear parameter-varying systems (Vol. 403). Springer.
   Google Scholar
• Tóth, R., Abbas, H. S., & Werner, H. (2012). On the state-space realization of LPV input–output models: Practical approaches. IEEE Transactions on Control Systems Technology, 20(1), 139–153.
   Web of Science ®Google Scholar
• Turkington, D. A. (2013). Generalized vectorization, cross-products, and matrix calculus. Cambridge: Cambridge University Press.
   Google Scholar
• van der Maas, R., van der Maas, A., & Oomen, T. (2015). Accurate frequency response function identification of LPV systems: A 2D local parametric modeling approach. 2015 IEEE 54th annual conference on decision and control (CDC), Osaka, Japan (pp. 1465–1470).
   Google Scholar
• van der Veen, G., van Wingerden, J.-W., Bergamasco, M., Lovera, M., & Verhaegen, M. (2013). Closed-loop subspace identification methods: An overview. IET Control Theory & Applications, 7(10), 1339–1358. doi: 10.1049/iet-cta.2012.0653
   Web of Science ®Google Scholar
• van Wingerden, J.-W., & Verhaegen, M. (2009). Subspace identification of bilinear and LPV systems for open- and closed-loop data. Automatica, 45(2), 372–381. doi: 10.1016/j.automatica.2008.08.015
   Web of Science ®Google Scholar
• Verdult V., Bergboer N., & Verhaegen M. (2003). Identification of fully parameterized linear and nonlinear state-space systems by projected gradient search. Proceedings of the 13th IFAC symposium on system identification, Rotterdam.
   Google Scholar
• Wassink, M. G., van de Wal, M., Scherer, C., & Bosgra, O. (2005). LPV control for a wafer stage: Beyond the theoretical solution. Control Engineering Practice, 13(2), 231–245. doi: 10.1016/j.conengprac.2004.03.008
   Web of Science ®Google Scholar
• White, S. R. (1992). Density matrix formulation for quantum renormalization groups. Physical Review Letters, 69(19), 2863. doi: 10.1103/PhysRevLett.69.2863
   PubMed Web of Science ®Google Scholar