Filtering-based recursive least-squares identification algorithm for controlled autoregressive moving average systems using the maximum likelihood principle
Restricted accessResearch articleFirst published online November, 2015
Filtering-based recursive least-squares identification algorithm for controlled autoregressive moving average systems using the maximum likelihood principle
This paper considers the parameter estimation problem of controlled autoregressive moving average systems. The basic idea is to use the noise polynomial to filter the input-output data, then a controlled moving average identification model and a noise model are obtained. A maximum likelihood recursive least squares algorithm and a recursive least squares algorithm are used to interactively estimate the parameters of the two identification models by using the hierarchical identification principle. A numerical example is provided to show the effectiveness of the proposed algorithms.
AgüeroJCGoodwinGCVan den HofPMJ (2011) A virtual closed loop method for closed loop identification. Automatica47(8): 16261637.
2.
DingF (2013a) Coupled-least-squares identification for multivariable systems. IET Control Theory and Applications7(1): 6879.
3.
DingF (2013b) Decomposition based fast least squares algorithm for output error systems. Signal Processing93(5): 12351242.
4.
DingF (2013c) System Identification – New Theory and Methods, Beijing: Science Press.
5.
DingF (2014) Combined state and least squares parameter estimation algorithms for dynamic systems. Applied Mathematical Modelling38(1): 403412.
6.
DingFDuanHH (2013) Two-stage parameter estimation algorithms for Box–Jenkins systems. IET Signal Processing7(8): 646654.
7.
DingFLiuXGChuJ (2013a) Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory and Applications7(2): 176184.
8.
DingJFanCXLinJX (2013b) Auxiliary model based parameter estimation for dual-rate output error systems with colored noise. Applied Mathematical Modelling37(6): 40514058.
9.
DingJHanLLChenXM (2010) Time series AR modeling with missing observations based on the polynomial transformation. Mathematical and Computer Modelling51(5–6): 527536.
10.
DingFLiuXMChenHBYaoGY (2014) Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems. Signal Processing97: 3139.
11.
FangHWuJShiY (2014) Genetic adaptive state estimation with missing input/output data. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering224(5): 611617.
12.
HaciogluYYagizN (2012) Adaptive back stepping control with estimation for the vibration isolation of buildings. Journal of Vibration and Control18(13): 19962005.
13.
HagenbladALjungLWillsA (2008) Maximum likelihood identification of Wiener models. Automatica44(11): 26972705.
14.
HanQLiCDHuangJJ (2010) Estimation on error bound of lag synchronization of chaotic systems with time delay and parameter mismatch. Journal of Vibration and Control16(11): 17011711.
15.
HaryantoAHongKS (2013) Maximum likelihood identification of Wiener–Hammerstein models. Mechanical Systems and Signal Processing41(1–2): 5470.
16.
JiangHQYanZBLiuXG (2013) Melt index prediction using optimized least squares support vector machines based on hybrid particle swarm optimization algorithm. Neurocomputing119: 469477.
17.
KhotSMYelveNP (2012) Estimation of geometrical parameters of machine elements based on statistical methods to avoid resonance. Journal of Vibration and Control18(2): 209213.
18.
LeFMMarkovskyIFreemanCTRogersE (2012) Recursive identification of Hammerstein systems with application to electrically stimulated muscle. Control Engineering Practice20(4): 386396.
19.
LiJH (2013) Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Applied Mathematics Letters26(1): 9196.
20.
LiJHDingF (2011) Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique. Computers & Mathematics with Applications62(11): 41704177.
21.
LiJHDingFHuaL (2014) Maximum likelihood Newton recursive and the Newton iterative estimation algorithms for Hammerstein CARAR systems. Nonlinear Dynamics75(1–2): 235245.
22.
LiJHDingFYangGW (2012) Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Mathematical and Computer Modelling55(3–4): 442450.
23.
LiuXGLuJ (2010) Least squares based iterative identification for a class of multirate systems. Automatica46(3): 549554.
24.
LiuYJDingR (2013) Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises. International Journal of Computer Mathematics90(9): 18401852.
25.
Liu YJ, Ding F and Shi Y (2014) An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica. Epub ahead of print 28 January 2014. DOI: 10.1016/j.automatica.2013.12.025.
26.
SalimifardMJafariMDehghaniM (2012) Identification of nonlinear MIMO block-oriented systems with moving average noises using gradient based and least squares based iterative algorithms. Neurocomputing94(1): 2231.
27.
Shen QY and Ding F (2014) Iterative estimation methods for Hammerstein controlled autoregressive moving average systems based on the key-term separation principle. Nonlinear Dynamics. Epub ahead of print 26 October 2013. DOI: 10.1007/s11071-013-1097-z.
28.
ShiJLiuXG (2006) Melt index prediction by weighted least squares support vector machines. Journal of Applied Polymer Science101(1): 285289.
29.
ShiPLuanXLiuF (2012) H-Infinity filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Transactions on Industrial Electronics59(6): 27322739.
30.
ShiYChenT (2006) Multirate crosstalk identification in xDSL systems. IEEE Transactions on Communications54(10): 18781886.
31.
ShiYChenTDingF (2006) 2-Norm based recursive design of transmultiplexers with designable filter length. Circuits, Systems and Signal Processing25(4): 447462.
32.
ShiYFangH (2010) Kalman filter based identification for systems with randomly missing measurements in a network environment. International Journal of Control83(3): 538551.
33.
SunJLLiuXG (2013) A novel APSO-aided maximum likelihood identification method for Hammerstein systems. Nonlinear Dynamics73(1–2): 449462.
34.
SöderströmTHongMSchoukensJPintelonR (2010) Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification. Automatica46(4): 721727.
35.
VörösJ (1999) Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Transactions on Automatic Control44(11): 21452149.
36.
VörösJ (2003) Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Transactions on Automatic Control48(12): 22032206.
37.
WangDQ (2011) Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory and Applications5(14): 16481657.
38.
WangDQDingF (2012) Hierarchical least squares estimation algorithm for Hammerstein–Wiener systems. IEEE Signal Processing Letters19(12): 825828.
39.
WangDQDingFLiuXM (2014) Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dynamics75(1–2): 4961.
40.
WillsASchönTBLjungLNinnesB (2013) Identification of Hammerstein–Wiener models. Automatica49(1): 7081.
41.
ZhangMLiuXG (2013) Melt index prediction by fuzzy functions and weighted least squares support vector machines optimized by particle swarm optimization. Chemical Engineering Technology36(9): 15771584.
42.
ZhangYCuiGM (2011) Bias compensation methods for stochastic systems with colored noise. Applied Mathematical Modelling35(4): 17091716.
43.
ZhuDQBaiJLiuQ (2010) Multi-fault diagnosis method for sensor system based on PCA. Sensors10(1): 241253.
44.
ZhuDQGuW (2008) Sensor fusion for integrated circuit fault diagnosis using a belief function model. International Journal of Distributed Sensor Networks4(3): 247261.
45.
ZhuDQHuangHYangSX (2013) Dynamic task assignment and path planning of multi-AUV system based on an improved self-organizing map and velocity synthesis method in 3D underwater workspace. IEEE Transactions on Cybernetics43(2): 504514.
46.
ZhuDQKongM (2007) Adaptive fault-tolerant control of nonlinear system: An improved CMAC based fault learning approach. International Journal of Control80(10): 15761594.
47.
ZhuDQLiuQHuZ (2012a) Fault-tolerant control algorithm of the manned submarine with multi-thruster based on quantum behaved particle swarm optimization. International Journal of Control84(11): 18171829.
48.
ZhuDQLiuJYangSX (2011) Particle swarm optimization approach to thruster fault-tolerant control of unmanned underwater vehicles. International Journal of Robotics and Automation26(3): 426432.
49.
ZhuDQLiuQYangYS (2008) An active fault-tolerant control method of unmanned underwater vehicles with continuous and uncertain faults. International Journal of Advanced Robotic Systems5(4): 411418.
50.
ZhuDQZhaoYYanMZ (2012b) A bio-inspired neurodynamics based backstepping path-following control of an AUV with ocean current. International Journal of Robotics and Automation27(3): 280287.
51.
ZuFLMakCM (2011) Estimation of best mounting positions for vibratory equipment in buildings. Journal of Vibration and Control17(2): 301310.
