Parameter Estimation of Switched Hammerstein Systems
This work addresses parameter estimation for switched nonlinear systems, a problem relevant to control theory, but the approach is incremental as it extends existing RLS methods with a data-coupling solution.
The paper proposes a recursive least squares algorithm with an 'intrinsic switch' concept to estimate parameters of switched Hammerstein systems under arbitrary but observable switching, achieving strong consistency of estimates in both open-loop and adaptive control scenarios, validated by simulation.
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.