Particle filtering-based recursive identification for controlled auto-regressive systems with quantised output. (English) Zbl 07907014
Summary: Recursive prediction error method is one of the main tools for analysis of controlled auto-regressive systems with quantised output. In this study, a recursive identification algorithm is proposed based on the auxiliary model principle by modifying the standard stochastic gradient algorithm. To improve the convergence performance of the algorithm, a particle filtering technique, which approximates the posterior probability density function with a weighted set of discrete random sampling points is utilised to correct the linear output estimates. It can exclude those invalid particles according to their corresponding weights. The performance of the particle filtering technique-based algorithm is much better than that of the auxiliary model-based one. Finally, results are verified by examples from simulation and engineering.
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93E12 | Identification in stochastic control theory |
| 93E24 | Least squares and related methods for stochastic control systems |
Keywords:
stochastic processes; parameter estimation; least squares approximations; filtering theory; gradient methods; autoregressive processes; recursive estimation; probability; particle filtering (numerical methods); auxiliary model principle; standard stochastic gradient algorithm; novel particle filtering technique; posterior probability density function; discrete random sampling points; linear output estimates; invalid particles; particle filtering technique-based algorithm; auxiliary model-based; particle filtering-based recursive identification; controlled auto-regressive systems; quantised output; recursive prediction error method; main tools; novel recursive identification algorithmReferences:
| [1] | GuoJ.WangL.Y., and YinG.et al.: ‘Identification of Wiener systems with quantized inputs and binary‐valued output observations’, Automatica, 2017, 78, pp. 280-286 · Zbl 1357.93101 |
| [2] | MattssonP., and WigrenT.: ‘Convergence analysis for recursive Hammerstein identification’, Automatica, 2016, 71, pp. 179-186 · Zbl 1343.93091 |
| [3] | DingF.XuL., and AlsaadiF.E.et al.: ‘Iterative parameter identification for pseudo‐linear systems with ARMA noise using the filtering technique’, IET Control Theory Applic., 2018, 12, (7), pp. 892-899 |
| [4] | NairG.N.FagnaniF., and ZampieriS.et al.: ‘Evans, feedback control under data rate constraints: an overview’, Proc. IEEE, 2007, 95, (1), pp. 108-137 |
| [5] | LiQ.ZhangB.H., and CuiL.G.et al.: ‘Epidemics on small worlds of tree‐based wireless sensor networks’, J. Syst. Sci. Complex., 2014, 27, (6), pp. 1095-1120 · Zbl 1325.68027 |
| [6] | WangL.Y.ZhangJ.F., and YinG.G.: ‘System identification using binary sensors’, IEEE Trans. Autom. Control, 2003, 48, (11), pp. 1892-1907 · Zbl 1364.93836 |
| [7] | GuoJ.WangL.Y., and YinG.et al.: ‘Asymptotically efficient identification of FIR systems with quantized observations and general quantized inputs’, Automatica, 2015, 57, pp. 113-122 · Zbl 1330.93065 |
| [8] | GodoyB.I.GoodwinG.C., and AgüeroJ.C.et al.: ‘On identification of FIR systems having quantized output data’, Automatica, 2011, 47, (9), pp. 1905-1915 · Zbl 1227.93121 |
| [9] | GómezJ.C.: ‘Recursive identification of IIR systems with multilevel output quantization and lossy memoryless channels with transmission errors’, IFAC‐PapersOnLine, 2018, 51, (15), pp. 909-914 |
| [10] | WangY.J.DingF., and WuM.: ‘Recursive parameter estimation algorithm for multivariate output‐error systems’, J. Franklin Inst., 2018, 355, (12), pp. 5163-5181 · Zbl 1395.93288 |
| [11] | ZhaiQ., and WangY.: ‘Noise effect on signal quantization in an array of binary quantizers’, Signal Process., 2018, 152, pp. 265-272 |
| [12] | YaoD.LuR., and XuY.et al.: ‘Robust \(H_\infty\) filtering for Markov jump systems with mode‐dependent quantized output and partly unknown transition probabilities’, Signal Process., 2017, 137, pp. 328-338 |
| [13] | LiZ.M.ChangX.H., and MathiyalaganK.et al.: ‘Robust energy‐to‐peak filtering for discrete‐time nonlinear systems with measurement quantization’, Signal Process., 2017, 139, pp. 102-109 |
| [14] | WangF.ChenB., and LinC.et al.: ‘Adaptive neural network finite‐time output feedback control of quantized nonlinear systems’, IEEE Trans. Cybern., 2018, 48, (6), pp. 1839-1848 |
| [15] | MairetF., and GouzéJ.L.: ‘Hybrid control of a bioreactor with quantized measurements’, IEEE Trans. Autom. Control, 2016, 61, (5), pp. 1385-1390 · Zbl 1359.93370 |
| [16] | LiM.H., and LiuX.M.: ‘The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique’, Signal Process., 2018, 147, pp. 23-34 |
| [17] | WigrenT.: ‘Recursive prediction error identification using the nonlinear Wiener model’, Automatica, 1993, 29, (4), pp. 1011-1025 · Zbl 0776.93006 |
| [18] | MattssonP., and WigrenT.: ‘Recursive identification of Hammerstein models’. American Control Conf., Portland, USA, June 2014, pp. 2498-2503 |
| [19] | ColinetE., and JuillardJ.: ‘A weighted least‐squares approach to parameter estimation problems based on binary measurements’, IEEE Trans. Autom. Control, 2010, 55, (1), pp. 148-152 · Zbl 1368.93675 |
| [20] | LiL.RenX., and GuoF.: ‘Modified multi‐innovation stochastic gradient algorithm for Wiener-Hammerstein systems with backlash’, J. Franklin Inst., 2018, 355, (9), pp. 4050-4075 · Zbl 1390.93821 |
| [21] | ZhangY., and LuoG.: ‘Recursive prediction algorithm for non‐stationary Gaussian process’, J. Syst. Softw., 2017, 127, pp. 295-301 |
| [22] | MaL., and LiuX.: ‘Recursive maximum likelihood method for the identification of Hammerstein ARMAX system’, Appl. Math. Model., 2016, 40, (13-14), pp. 6523-6535 · Zbl 1465.93222 |
| [23] | WigrenT.: ‘Approximate gradients, convergence and positive realness in recursive identification of a class of nonlinear systems’, Int. J. Adapt. Control Signal Process., 1995, 9, (4), pp. 325-354 · Zbl 0834.93058 |
| [24] | ZhaoY.WangL.Y., and YinG.G.et al.: ‘Identification of Wiener systems with binary‐valued output observations’, Automatica, 2007, 43, (10), pp. 1752-1765 · Zbl 1119.93067 |
| [25] | DingF.ChenH.B., and XuL.et al.: ‘A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation’, J. Franklin Inst., 2018, 355, (8), pp. 3737-3752 · Zbl 1390.93818 |
| [26] | ZhangY.ZhaoZ., and CuiG.M.: ‘Auxiliary model method for transfer function estimation from noisy input and output data’, Appl. Math. Model., 2015, 39, (15), pp. 4257-4265 · Zbl 1443.93132 |
| [27] | YuanY.TianC., and LuX.: ‘Auxiliary loss multimodal GRU model in audio‐visual speech recognition’, IEEE Access, 2018, 6, pp. 5573-5583 |
| [28] | DingF.WangF.F., and XuL.et al.: ‘Parameter estimation for pseudo‐linear systems using the auxiliary model and the decomposition technique’, IET Control Theory Applic., 2017, 11, (3), pp. 390-400 |
| [29] | LiM.H., and LiuX.M.: ‘Auxiliary model based least squares iterative algorithms for parameter estimation of bilinear systems using interval‐varying measurements’, IEEE Access, 2018, 6, pp. 21518-21529 |
| [30] | JinQ.WangZ., and LiuX.: ‘Auxiliary model‐based interval‐varying multi‐innovation least squares identification for multivariable OE‐like systems with scarce measurements’, J. Process Control, 2015, 35, pp. 154-168 |
| [31] | WangD.Q.LiL.W., and JiY.et al.: ‘Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method’, Appl. Math. Model., 2018, 54, pp. 537-550 · Zbl 1480.93431 |
| [32] | DingF.LiuG.J., and LiuX.P.: ‘Parameter estimation with scarce measurements’, Automatica, 2011, 47, (8), pp. 1645-1655 · Zbl 1232.62043 |
| [33] | ChenJ.LiuY., and DingF.et al.: ‘Gradient‐based particle filter algorithm for an ARX model with nonlinear communication output’, IEEE Trans. Syst. Man Cybern., Syst., 2018, doi:10.1109/TSMC.2018.2810277 |
| [34] | DengJ., and HuangB.: ‘Identification of nonlinear parameter varying systems with missing output data’, AIChE J., 2012, 58, (11), pp. 3454-3467 |
| [35] | ChenJ.LiJ., and LiuY.: ‘Gradient iterative algorithm for dual‐rate nonlinear systems based on a novel particle filter’, J. Franklin Inst., 2017, 354, pp. 4425-4437 · Zbl 1380.93251 |
| [36] | WigrenT.: ‘MATLAB Software for recursive identification of systems with output quantization‐revision 1’ (Department of Information Technology, Uppsala University, Sweden, 2007) |
| [37] | SimonD.: ‘Optimal state estimation: Kalman, H_∞, and nonlinear approaches’ (Wiley, Hoboken, NJ, USA, 2006) |
| [38] | DoucetA.GodsillS., and AndrieuC.: ‘On sequential Monte Carlo sampling methods for Bayesian filtering’, Stat. Comput., 2000, 10, (3), pp. 197-208 |
| [39] | LiangZ.: ‘Energy‐based balance control approach to the ball and beam system’, Int. J. Control, 2009, 82, (6), pp. 981-992 · Zbl 1168.93398 |
| [40] | DaISy: ‘STADIUS’s Identification Database’. Available at http://homes.esat.kuleuven.be/smc/daisy/daisydata.html |
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