Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities

Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems

“…The Hammerstein model represents a class of input nonlinear systems, where the nonlinear block is prior to the linear one. It can flexibly approximate various input nonlinearities, such as saturation, dead zone, backlash and hysteresis, thus having been extensively employed in realistic applications [7][8][9][10][11].…”

A Redundant Parameter Based Recursive Least Squares Algorithm for Nonlinear Additive Systems with Unknown Time-Delay

“…The basic idea of the key term separation principle is first to apply some mathematical functions to turn the model of the hard nonlinear systems into an identification model and then use the linear system identification methods to estimate the unknown parameters [14,15]. For example, Chen et al defined switching function to simplify a saturation and dead-zone nonlinearity and proposed an identification method for the nonlinear system [16]. Jacob et al applied a direct weight optimization method for nonlinear systems with hard nonlinearities [17].…”

A Multi-innovation Recursive Least Squares Algorithm with a Forgetting Factor for Hammerstein CAR Systems with Backlash

“…Generally, Hammerstein models are composed of a static nonlinear block, which is followed by a linear dynamic block [4]. In this study, we examine the identification problem of Hammerstein model with backlash or backlash-like hysteresis nonlinearities.…”

“…However, some difficulties of identification arise from the unmeasurable inner variablesū(t − i) (in φ s (t) of φ(t) ), the unknown corrected output y c (t) (in Y c ( p, t) ), and the unknown parameters c L and c R (in(4) and(5)), so the FF-MRLS algorithm cannot be applied to estimate θ =θ f θ s . The solution is based on the auxiliary model identification approach [9,10] and the interactive estimation theory: letθ (t) = θ f (t) θ s (t) represent the estimates of θ = θ f θ s at time t. The unmeasurable inner variablesū(t) are replaced by the output of the auxiliary modelû(t) at time t and the unknown corrected output y c (t) and parameters c L and c R are replaced by their estimatesŷ c (t),ĉ L andĉ R at time t.…”