Combined state and multi‐innovation parameter estimation for an input non‐linear state‐space system using the key term separation

Identification of nonlinear block-oriented systems with backlash and saturation

“…In the case of saturation, the slopes m R2 and m L2 are equal to zero. The three-block cascade model description can be created by consecutive substitutions of (4) into (8) and then the result of this substitution into (11). However, this will result in a very complex equation with crossmultiplications of parameters.…”

“…To get a unique parameterization, one parameter has to be fixed in at least two blocks. For application of the key term separation principle, it is appropriate to choose a 1 = 1 in (8), and m R1 = 1 in (11).…”

“…Finally, the output equation of this cascade model can be constructed by half-substituting (15) into (11), ie only for the first term in the description of output block…”

“…The identification techniques mainly distinguish themselves in the way the static nonlinearity is represented and in the form of optimization problem that is finally obtained. Known approaches for different types of nonlinearities and estimation methods can be found eg in [1][2][3][4][5][6][7][8][9][10][11][12][13]. The Wiener model has a linear dynamic block followed by a nonlinear static block and many techniques have been proposed to solve the identification problems typically encountered in using this model, see, eg [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

The parameter estimation algorithms based on the dynamical response measurement data

“…36,37 Wang and colleagues 38,39 suggested the hierarchical estimation algorithms to reduce the complexity. Wang and colleagues 40,41 considered a multi-innovation parameter estimation method for Hammerstein nonlinear system to enhance the accuracy. The objective of this article is to propose the identification algorithms to obtain high accuracy and low complexity.…”