ae3e2b99-05ac-41ac-b0c1-f5ac2fcbf16e20210806035522965wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SIGNAL PROCESSING2224-34881790-505210.37394/232014http://wseas.org/wseas/cms.action?id=4062331202133120211710.37394/232014.2021.17https://wseas.org/wseas/cms.action?id=23315OSCARIBARRA-MANZANODepartment of Electronics Engineering, University of Guanajuato Salamanca, 36885, MEXICOJOSEANDRADE-LUCIODepartment of Electronics Engineering, University of Guanajuato Salamanca, 36885, MEXICOYURIY S.SHMALIYDepartment of Electronics Engineering, University of Guanajuato Salamanca, 36885, MEXICOYUANXUSchool of Electrical Engineering, University of Jinan, Jinan 250022, CHINAInformation loss often occurs in industrial processes under unspecified impacts and data errors. Therefore robust predictors are required to assure the performance. We design a one-step H2 optimal finite impulse response (H2-OFIR) predictor under persistent disturbances, measurement errors, and initial errors by minimizing the squared weighted Frobenius norms for each error. The H2-OFIR predictive tracker is tested by simulations assuming Gauss-Markov disturbances and data errors. It is shown that the H2-OFIR predictor has a better robustness than the Kalman and unbiased FIR predictor. An experimental verification is provided based on the moving robot tracking problem862021862021879212https://wseas.com/journals/sp/2021/a245114-010(2021).pdf10.37394/232014.2021.17.12https://wseas.com/journals/sp/2021/a245114-010(2021).pdfP. P. Kanjilal, Adaptive Prediction and Predictive Control, London, UK: Peter Peregrinus, 1995. A. Liu, W. Zhang, and L. Yu, “Robust predictive tracking control for mobile robots with intermittent measurement and quantization,” IEEE Trans. Ind. Electron., vol. 68, no. 1, pp. 509-518, Jan. 2021. 10.1109/tie.2016.2588463J. Hua, C. Li, and H.0L. Shen, “Distributed learning of predictive struc- tures from multiple tasks over networks,” IEEE Trans. Ind. Electron., vol. 64, no. 5, pp. 4246-4256, May 2017. Z. Li, C. Zhang, P. Zeng, H. Yu, S. Li, and J. Bian, “Control of a grid- forming inverter based on sliding-mode and mixed H2/H∞ control,” IEEE Trans. Ind. Electron., vol. 64, no. 5, pp. 3862-3872, May 2017. 10.1109/jsen.2017.2654306M. Vazquez-Olguin, Y. S. Shmaliy, Choon Ki Ahn, and O. Ibarra- Manzano, “Blind robust estimation with missing data for smart sensors using UFIR filtering,” IEEE Sensors J., vol. 17, no. 6, pp. 1819–1827, Mar. 2017. 10.1109/tac.2019.2937850K. Uribe-Murcia, Y. S. Shmaliy, C. K. Ahn, and S. Zhao, “Unbiased FIR filtering for time-stamped discretely delayed and missing data,” IEEE Trans. Autom. Control, vol. 65, no. 5, pp. 2155–2162, May 2020. 10.1109/tie.2017.2760839T. Liu, P. Garcia, Y. Chen, X. Ren, P. Albertos, and R. Sanz, “New predictor and 2DOF control scheme for industrial processes with long time delay,” IEEE Trans. Ind. Electron., vol. 65, no. 5, pp. 4247-4256, May 2018.10.1109/tie.2017.2774758C. Zhang, G. Wu, F. Rong, J. Feng, L. Jia, J. He, and S. Huang, “Robust fault-tolerant predictive current control for permanent magnet synchronous motors considering demagnetization fault,” IEEE Trans. Ind. Electron., vol. 65, no. 7, pp. 5324–5334, Jul. 2018. 10.1109/proc.1975.9792J. Makhoul, “Linear prediction: A tutorial review,” Proc. IEEE, vol. 63, no. 4, pp. 561-580, Apr. 1975. 10.1007/s11760-008-0064-5Y. S. Shmaliy, “An unbiased p-step predictive FIR filter for a class of noise free discrete-time models with independently observed states,” Signal, Image Video Process., vol. 3, no. 2, pp. 127–135, Jun. 2009. 10.1109/tie.2012.2236994F. Auger, M. Hilairet, J. M. Guerrero, E. Monmasson, T. Orlowska- Kowalska, and S. Katsura, “Industrial applications of the Kalman filter: A review,” IEEE Trans. Ind. Electron., vol. 60, no. 12, pp. 5458–5471, Dec. 2013.10.1109/access.2017.2697072G. F. Basso, T. G. Silva De Amorim, A. V. Brito, and T. P. Nasci- mento, “Kalman filter with dynamical setting of optimal process noise covariance,” IEEE Access., vol. 5, pp. 8385–8393, 2017. 10.1109/tsp.2010.2045422Y. S. Shmaliy, “Linear optimal FIR estimation of discrete time-invariant state-space models,” IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3086–3096, 2010. 10.1002/acs.1274Y. S. Shmaliy and O. Ibarra-Manzano, “Time-variant linear optimal finite impulse response estimator for discrete state-space models,” Int. J. Adapt. Contr. Signal Process., vol. 26, no. 2, pp. 95–104, 2012. 10.1109/tuffc.2006.1632677Y. S. Shmaliy, “An unbiased FIR filter for TIE model of a local clock in applications to GPS-based timekeeping,” IEEE Trans. on Ultrason., Ferroel., Freq. Contr., vol. 53, no. 5, pp. 862–870, May 2006. W. H. Kwon and S. Han, Receding Horizon Control: Model Predictive Control for State Models. London, UK: Springer, 2005. 10.1016/0005-1098(89)90027-7O. K. Kwon, W. H. Kwon, and K. S. Lee, “FIR filters and recursive forms for discrete-time state-space models,” Automatica, vol. 25, no. 5, pp. 715–728, 1989.Y. S. Lee, S. H. Han, and W. H. Kwon, “H2/H∞ FIR filters for discrete-time state space models,” Int. J. of Contr. Autom. and Systems., vol. 4, no. 5, pp. 645–652, Oct. 2006. 10.1109/tcsii.2017.2749006C. K. Ahn, Y. S. Shmaliy, and S. Zhao, “A new unbiased FIR filter with improved robustness based on Frobenius norm with exponential weight,” IEEE Trans. Circuits Syst. II Express Briefs., vol. 65, no. 4, pp. 521–525, Apr. 2018. 10.1109/tcsii.2016.2613959C. K. Ahn, S. Zhao, Y. S. Shmaliy, and H. Li, “On the ℓ2 − ℓ∞ and H∞ performance of the continuous-time deadbeat H2 FIR filter,” IEEE Trans. Circuits Syst. II Express Briefs., vol. 65, no. 11, pp. 1798–1802, Nov. 2018.10.1109/tcsii.2020.3021674S. Zhao, Y. S. Shmaliy, and F. Liu, “Optimal FIR filter for discrete- time LTV systems and fast iterative algorithm,” IEEE Trans. Circuits Syst. II, Express Briefs (to be published). 10.1016/0167-6911(91)90011-3W. M. Haddad, D. S. Bernstein, and D. Mustafa, “Mixed-norn H2/H∞ regulation and estimation: The discrete-time case,” Syst. & Contr. Lett., vol. 16, pp. 235–247, 1991. 10.1002/rnc.1643M. D. S. Aliyu and E. K. Boukas, “Discrete-time mixed H2/H∞ nonlinear filtering,” Int. J. Robust Nonlinear Cont., vol. 21, pp. 1257– 1282, 2011. 10.1007/bf01269915Z. Tan, Y. C. Soh, and L. Xie, “Envelope-constrained H2 FIR filter design,” Circ. Syst. Signal Process., vol. 18, no. 6, pp. 539–551, 1999. 10.1016/s0165-1684(99)00130-9B.-S. Chen and J.-C. Hung, “Fixed-order H2 and H∞ optimal decon- volution filter designs,” Signal Process., vol. 80, no. 2, pp. 311–331, 2000. 10.1109/78.863088S. Wang, L. Xie, and C. Zhang, “H2 optimal inverse of periodic FIR digital filters,” IEEE Trans. Signal Process., vol. 48, no. 9, no. 9, pp. 2696–2700, 2000. 10.1016/s0165-1684(01)00105-0S. Wang, L. Xie, and C. Zhang “Mixed H2/H∞ deconvolution of uncertain periodic FIR channels,” Signal Process., vol. 81, no. 10, pp. 2089–2103, Oct. 2001. K. Zhou, J. C. Doyle, and K. Glover Robust and Optimal Control, Upper Saddle River, NJ: Prentice-Hall, 1996. 10.1137/1.9781611970760B. Hassibi, A. H. Sayed, and T. Kailath, Indefinite-Quadratic Esti- mation and Control: A Unified Approach to H2 and H∞ Theories, Philadelphia, PA: SIAM, 1999. F. L. Lewis, L. Xie, and D. Popa, Optimal and Robust Estimation with an Introduction to Stochastic Control Theory, 2nd Ed., Boca Raton, FL: CRC Press, 2008. C. Scherer and S. Weiland, Linear Matrix Inequalities in Control, Stuttgart, DE: University of Stuttgart, 2015. 10.1109/tsp.2011.2129516Y. S. Shmaliy, “An iterative Kalman-like algorithm ignoring noise and initial conditions,” IEEE Trans. Signal Process., vol. 59, no. 6, pp. 2465–2473, Jun. 2011. 10.1109/mcs.2017.2718830Y. S. Shmaliy, S. Zhao, and C. K. Ahn, “Unbiased FIR filtering: an iterative alternative to Kalman filtering ignoring noise and initial conditions,” IEEE Contr. Syst. Mag., vol. 37, no. 5, pp.