Multi-innovation gradient identification for input nonlinear state space systems

Abstract This paper presents a multi-innovation stochastic gradient algorithm for an input nonlinear state space system by deriving the identification model of the system and by decomposing the model into two sub-models. The basic idea is to design a state observer to estimate the unmeasurable states and to estimate interactively the unknown parameters of two subsystems by using the hierarchical identification principle. The simulation results show that the proposed algorithm is efficient.

[1]  Hosam K. Fathy,et al.  Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory , 2011, Autom..

[2]  Feng Ding,et al.  Performance analysis of the recursive parameter estimation algorithms for multivariable Box-Jenkins systems , 2014, J. Frankl. Inst..

[3]  Mikko Valkama,et al.  Subband Energy Based Reduced Complexity Spectrum Sensing Under Noise Uncertainty and Frequency-Selective Spectral Characteristics , 2016, IEEE Transactions on Signal Processing.

[4]  Changyun Wen,et al.  Convergence of fixed-point iteration for the identification of Hammerstein and Wiener systems , 2013 .

[5]  Biao Huang,et al.  On simultaneous on-line state and parameter estimation in non-linear state-space models , 2013 .

[6]  Lennart Ljung,et al.  Maximum likelihood identification of Wiener models , 2008, Autom..

[7]  Huiping Li,et al.  Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays , 2012, Autom..

[8]  Feng Ding,et al.  Combined state and least squares parameter estimation algorithms for dynamic systems , 2014 .

[9]  Xiao Chen,et al.  Modeling of pH neutralization process using fuzzy recurrent neural network and DNA based NSGA-II , 2014, J. Frankl. Inst..

[10]  Johan Schoukens,et al.  Identification of systems with localised nonlinearity: From state-space to block-structured models , 2013, Autom..

[11]  Feng Ding,et al.  Identification of Hammerstein nonlinear ARMAX systems , 2005, Autom..

[12]  Jens Timmer,et al.  A numerically efficient implementation of the expectation maximization algorithm for state space models , 2014, Appl. Math. Comput..

[13]  Feng Yu,et al.  Recursive parameter identification of Hammerstein-Wiener systems with measurement noise , 2014, Signal Process..

[14]  Er-Wei Bai,et al.  Iterative identification of Hammerstein systems , 2007, Autom..

[15]  Jozef Vörös,et al.  Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities , 2007, Syst. Control. Lett..

[16]  Bernard C. Levy,et al.  Robust State Space Filtering Under Incremental Model Perturbations Subject to a Relative Entropy Tolerance , 2010, IEEE Transactions on Automatic Control.

[17]  Jozef Vörös,et al.  Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities , 1999, IEEE Trans. Autom. Control..

[18]  J. Voros.  Identification of Hammerstein systems with time-varying piecewise-linear characteristics , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[19]  Haranath Kar,et al.  An improved LMI-based criterion for the design of optimal guaranteed cost controller for 2-D discrete uncertain systems , 2011, Signal Process..

[20]  Chongyang Liu,et al.  From the SelectedWorks of Chongyang Liu 2013 Modelling and parameter identification for a nonlinear time-delay system in microbial batch fermentation , 2017 .

[21]  Kok Lay Teo,et al.  Time-delay estimation for nonlinear systems with piecewise-constant input , 2013, Appl. Math. Comput..

[22]  Laurent Bako,et al.  Parameterization and identification of multivariable state-space systems: A canonical approach , 2011, Autom..

[23]  Han-Xiong Li,et al.  Design of distributed H∞ fuzzy controllers with constraint for nonlinear hyperbolic PDE systems , 2012, Autom..

[24]  Raja Muhammad Asif Zahoor,et al.  Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems , 2015, Signal Process..

[25]  Feng Ding,et al.  Two-stage parameter estimation algorithms for Box-Jenkins systems , 2013, IET Signal Process..

[26]  Miroslav Krstic.  On using least-squares updates without regressor filtering in identification and adaptive control of nonlinear systems , 2009, Autom..

[27]  Cishen Zhang,et al.  A New Deterministic Identification Approach to Hammerstein Systems , 2014, IEEE Transactions on Signal Processing.

[28]  Tao Tang,et al.  Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique , 2014 .

[29]  Junhong Li,et al.  Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration , 2013, Appl. Math. Lett..

[30]  F. Ding.  Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling , 2013 .

[31]  Bin Jiang,et al.  Parameter fault detection and estimation of a class of nonlinear systems using observers , 2005, J. Frankl. Inst..

[32]  Hamid Reza Karimi,et al.  Robust finite-time fuzzy H∞ control for uncertain time-delay systems with stochastic jumps , 2014, J. Frankl. Inst..

[33]  Er-Wei Bai,et al.  Convergence of the iterative Hammerstein system identification algorithm , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[34]  F. Ding,et al.  Least squares algorithm for an input nonlinear system with a dynamic subspace state space model , 2014 .

[35]  José Ragot,et al.  Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs , 2012, J. Frankl. Inst..

[36]  Feng Ding,et al.  Parameter estimation for an input nonlinear state space system with time delay , 2014, J. Frankl. Inst..

[37]  Lennart Ljung,et al.  Linear approximations of nonlinear FIR systems for separable input processes , 2005, Autom..

[38]  Er-Wei Bai.  An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998, Autom..

[39]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..