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Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems. (English) Zbl 1481.93148

Summary: The development of procedures based on fractional calculus is an emerging research area. This paper presents a new perspective regarding the fractional least mean square (FLMS) adaptive algorithm, called multi innovation FLMS (MIFLMS). We verify that the iterative parameter adaptation mechanism of the FLMS uses merely the current error value (scalar innovation). The MIFLMS expands the scalar innovation into a vector innovation (error vector) by considering data over a fixed window at each iteration. Therefore, the MIFLMS yields better convergence speed than the standard FLMS by increasing the length of innovation vector. The superior performance of the MIFLMS is verified through parameter identification problem of input nonlinear systems. The statistical performance indices based on multiple independent trials confirm the consistent accuracy and reliability of the proposed scheme.

MSC:

93E35 Stochastic learning and adaptive control
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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[1] Cheng, S.; Wei, Y.; Sheng, D.; Wang, Y., Identification for hammerstein nonlinear systems based on universal spline fractional order LMS algorithm, Commun. Nonlinear Sci. Numer. Simul., 79, 104901 (2019) · Zbl 1508.93065
[2] Khan, Z. A.; Zubair, S.; Chaudhary, N. I.; Raja, M. A.Z.; Khan, F. A.; Dedovic, N., Design of normalized fractional SGD computing paradigm for recommender systems, Neural Computing and Applications, 1-18 (2019)
[3] Cheng, S.; Wei, Y.; Sheng, D.; Chen, Y.; Wang, Y., Identification for hammerstein nonlinear ARMAX systems based on multi-innovation fractional order stochastic gradient, Signal Processing, 142, 1-10 (2018)
[4] Yin, W.; Wei, Y.; Liu, T.; Wang, Y., A novel orthogonalized fractional order filtered-x normalized least mean squares algorithm for feedforward vibration rejection, Mech. Syst. Signal Process., 119, 138-154 (2019)
[5] Chaudhary, N. I.; Manzar, M. A.; Raja, M. A.Z., Fractional volterra LMS algorithm with application to hammerstein control autoregressive model identification, Neural Computing and Applications, 31, 9, 5227-5240 (2019)
[6] Chaudhary, N. I.; Raja, M. A.Z., Identification of hammerstein nonlinear ARMAX systems using nonlinear adaptive algorithms, Nonlinear Dyn., 79, 2, 1385-1397 (2015) · Zbl 1345.93045
[7] Chaudhary, N. I.; Ahmed, M.; Khan, Z. A.; Zubair, S.; Raja, M. A.Z.; Dedovic, N., Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems, Appl. Math. Model., 55, 698-715 (2018) · Zbl 1480.93456
[8] Zubair, S.; Chaudhary, N. I.; Khan, Z. A.; Wang, W., Momentum fractional LMS for power signal parameter estimation, Signal Processing, 142, 441-449 (2018)
[9] Shoaib, B.; Qureshi, I. M., A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction, Chin. Phys. B, 23, 3, 030502 (2014)
[10] Wan, L.; Ding, F., Decomposition-and gradient-based iterative identification algorithms for multivariable systems using the multi-innovation theory, Circuits, Systems, and Signal Processing, 38, 7, 2971-2991 (2019)
[11] Ma, P.; Ding, F.; Zhu, Q., Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation, Int. J. Syst. Sci., 49, 5, 920-928 (2018) · Zbl 1482.93656
[12] Yavari, M.; Nazemi, A., On fractional infinite-horizon optimal control problems with a combination of conformable and caputo fabrizio fractional derivatives, ISA Transactions. (2020)
[13] Zhang, Q.; Shang, Y.; Li, Y.; Cui, N.; Duan, B.; Zhang, C., A novel fractional variable-order equivalent circuit model and parameter identification of electric vehicle li-ion batteries, ISA Trans., 97, 448-457 (2020)
[14] Machado, J. T.; Lopes, A. M., Multidimensional scaling locus of memristor and fractional order elements, Journal of Advanced Research. (2020)
[15] He, S.; Banerjee, S., Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection, Physica A, 501, 408-417 (2018) · Zbl 1514.92127
[16] Sun, H.; Zhang, Y.; Baleanu, D.; Chen, W.; Chen, Y., A new collection of real world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci. Numer. Simul., 64, 213-231 (2018) · Zbl 1509.26005
[17] Feliu-Talegon, D.; Feliu-Batlle, V.; Tejado, I.; Vinagre, B. M.; HosseinNia, S. H., Stable force control and contact transition of a single link flexible robot using a fractional-order controller, ISA Trans., 89, 139-157 (2019)
[18] Chaudhary, N. I.; Raja, M. A.Z.; Khan, J. A.; Aslam, M. S., Identification of input nonlinear control autoregressive systems using fractional signal processing approach, The Scientific World Journal, 2013 (2013)
[19] Shoaib, B.; Qureshi, I. M.; Khan, S. U.; Butt, S. A., Kernel fractional affine projection algorithm, Applied Informatics, 2, 1, 1-12 (2015)
[20] Tan, Y.; He, Z.; Tian, B., A novel generalization of modified LMS algorithm to fractional order, IEEE Signal Process. Lett., 22, 9, 1244-1248 (2015)
[21] Cheng, S.; Wei, Y.; Chen, Y.; Li, Y.; Wang, Y., An innovative fractional order LMS based on variable initial value and gradient order, Signal Processing, 133, 260-269 (2017)
[22] Cheng, S.; Wei, Y.; Chen, Y.; Liang, S.; Wang, Y., A universal modified LMS algorithm with iteration order hybrid switching, ISA Trans., 67, 67-75 (2017)
[23] Chen, Y.; Gao, Q.; Wei, Y.; Wang, Y., Study on fractional order gradient methods, Appl. Math. Comput., 314, 310-321 (2017) · Zbl 1426.65077
[24] Shah, S. M.; Samar, R.; Naqvi, S. M.R.; Chambers, J. A., Fractional order constant modulus blind algorithms with application to channel equalisation, Electron. Lett., 50, 23, 1702-1704 (2014)
[25] Shah, S. M.; Samar, R.; Khan, N. M.; Raja, M. A.Z., Fractional-order adaptive signal processing strategies for active noise control systems, Nonlinear Dyn., 85, 3, 1363-1376 (2016)
[26] Chaudhary, N. I.; Zubair, S.; Raja, M. A.Z., A new computing approach for power signal modeling using fractional adaptive algorithms, ISA Trans., 68, 189-202 (2017)
[27] Shoaib, B.; Qureshi, I. M., Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction, Chin. Phys. B, 23, 5, 00503 (2014)
[28] Raja, M. A.Z.; Akhtar, R.; Chaudhary, N. I.; Zhiyu, Z.; Khan, Q.; Rehman, A. U.; Zaman, F., A new computing paradigm for the optimization of parameters in adaptive beamforming using fractional processing, The European Physical Journal Plus, 134, 6, 275 (2019)
[29] Khan, Z. A.; Chaudhary, N. I.; Zubair, S., Fractional stochastic gradient descent for recommender systems, Electronic Markets, 29, 2, 275-285 (2019)
[30] Geravanchizadeh, M.; Ghalami Osgouei, S., Speech enhancement by modified convex combination of fractional adaptive filtering, Iranian Journal of Electrical and Electronic Engineering, 10, 4, 256-266 (2014)
[31] Raja, M. A.Z.; Chaudhary, N. I., Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems, Signal Processing, 107, 327-339 (2015)
[32] Chaudhary, N. I.; Raja, M. A.Z., Design of fractional adaptive strategy for input nonlinear box,jenkins systems, Signal Processing, 116, 141-151 (2015)
[33] Aslam, M. S.; Chaudhary, N. I.; Raja, M. A.Z., A sliding-window approximation-based fractional adaptive strategy for hammerstein nonlinear ARMAX systems, Nonlinear Dyn., 87, 1, 519-533 (2017) · Zbl 1371.93205
[34] Chaudhary, N. I.; Raja, M. A.Z.; Khan, A. U.R., Design of modified fractional adaptive strategies for hammerstein nonlinear control autoregressive systems, Nonlinear Dyn., 82, 4, 1811-1830 (2015) · Zbl 1437.93138
[35] Chaudhary, N. I.; Zubair, S.; Raja, M. A.Z.; Dedovic, N., Normalized fractional adaptive methods for nonlinear control autoregressive systems, Appl. Math. Model., 66, 457-471 (2019) · Zbl 1481.93147
[36] Chaudhary, N. I.; Zubair, S.; Aslam, M. S.; Raja, M. A.Z.; Machado, J. T., Design of momentum fractional LMS for hammerstein nonlinear system identification with application to electrically stimulated muscle model, The European Physical Journal Plus, 134, 8, 407 (2019)
[37] Chaudhary, N. I.; Aslam, M. S.; Baleanu, D.; Raja, M. A.Z., Design of sign fractional optimization paradigms for parameter estimation of nonlinear hammerstein systems, Neural Computing and Applications. (2019)
[38] Wang, C.; Zhu, L., Parameter identification of a class of nonlinear systems based on the multi-innovation identification theory, J. Franklin Inst., 352, 10, 4624-4637 (2015) · Zbl 1395.93261
[39] Mao, Y.; Ding, F., A novel data filtering based multi-innovation stochastic gradient algorithm for hammerstein nonlinear systems, Digit Signal Process., 46, 215-225 (2015)
[40] Mao, Y.; Ding, F., Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory, Int. J. Comput. Math., 93, 11, 1869-1885 (2016) · Zbl 1353.93109
[41] Xu, L.; Ding, F., Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling, Circuits, Systems, and Signal Processing, 36, 4, 1735-1753 (2017) · Zbl 1370.94286
[42] Chaudhary, N. I.; Zubair, S.; Raja, M. A.Z., Design of momentum LMS adaptive strategy for parameter estimation of hammerstein controlled autoregressive systems, Neural Computing and Applications, 30, 4, 1133-1143 (2018)
[43] Raja, M. A.Z.; Shah, A. A.; Mehmood, A.; Chaudhary, N. I.; Aslam, M. S., Bio-inspired computational heuristics for parameter estimation of nonlinear hammerstein controlled autoregressive system, Neural Computing and Applications, 29, 12, 1455-1474 (2018)
[44] Le, F.; Markovsky, I.; Freeman, C. T.; Rogers, E., Identification of electrically stimulated muscle models of stroke patients, Control Eng. Pract., 18, 4, 396-407 (2010)
[45] Le, F.; Markovsky, I.; Freeman, C. T.; Rogers, E., Recursive identification of hammerstein systems with application to electrically stimulated muscle, Control Eng. Pract., 20, 4, 386-396 (2012)
[46] Zhang, G.; Wu, Z., Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives, Appl. Math. Model., 77, 1294-1309 (2020) · Zbl 1481.34014
[47] Shahri, E. S.A.; Alfi, A.; Machado, J. T., Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation, Appl. Math. Model., 81, 663-672 (2020) · Zbl 1481.93103
[48] Chaudhary, N. I.; Latif, R.; Raja, M. A.Z.; Machado, J. T., An innovative fractional order LMS algorithm for power signal parameter estimation, Appl. Math. Model., 83, 703-718 (2020) · Zbl 1481.94050
[49] Lin, N.; Chi, R.; Huang, B., Data-driven recursive least squares methods for non-affined nonlinear discrete-time systems, Appl. Math. Model., 81, 787-798 (2020) · Zbl 1481.93141
[50] Todorčević, V., Harmonic quasiconformal mappings and hyperbolic type metrics (2019), Springer International Publishing. · Zbl 1435.30003
[51] Dukic, D.; Paunovic, L.; Radenovic, S., Convergence of iterates with errors of uniformly quasi-lipschitzian mappings in cone metric spaces, Kragujevac Journal of Mathematics, 35, 3, 399-410 (2011) · Zbl 1289.47160
[52] Hussain, A.; Kanwal, T.; Adeel, M.; Radenovic, S., Best proximity point results in b-metric space and application to nonlinear fractional differential equation, Mathematics, 6, 11, 221 (2018) · Zbl 06994824
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