Parameter Estimation of Switched Hammerstein Systems

This paper deals with the parameter estimation problem of the Single-Input-Single-Output (SISO) switched Hammerstein system. Suppose that the switching law is arbitrary but can be observed online. All subsystems are parameterized and the Recursive Least Squares (RLS) algorithm is applied to estimate their parameters. To overcome the difficulty caused by coupling of data from different subsystems, the concept "intrinsic switch" is introduced. Two cases are considered: i) The input is taken to be a sequence of independent identically distributed (i.i.d.) random variables when identification is the only purpose; ii) A diminishingly excited signal is superimposed on the control when the adaptive control law is given. The strong consistency of the estimates in both cases is established and a simulation example is given to verify the theoretical analysis.Comment: 16 pages, 3 figures; Accepted for publication by Acta Mathematicae Applicatae Sinica (http://link.springer.com/journal/10255

Stochastic mean-square performance analysis of an adaptive Hammerstein filter

Journal ArticleAbstract-This paper presents an almost sure mean-square performance analysis of an adaptive Hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence. The system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter. A bound for the long-term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment. This bound consists of two terms, one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system. One consequence of this result is that the long-term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time-invariant