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An approach for estimating abruptly changing parameters of integrable nonlinear continuous-time systems.An approach for estimating abruptly changing parameters of integrable nonlinear continuous-time systems.

Daniel-Berhe S., Unbehauen H.

Systems Science

1999

Vol. 25, nr 1

15-26

A new estimation algorithm capable of estimating the parameters of an integrable nonlinear continuous-time system varying in a discontinous way is presented. Specifically, a class of nonlinear systems that are subject to parameter jumps of unknown magnitudes or abrupt parameter changes occurring at unknown time instants is investigated via the Hartley modulating functions method. The proposed approach is based on available sampled input-output batch data records where the observation contains additive Gaussian noise. The method first estimates the system parameters based on initial batch data and considers a new input-output data sample to update the initial record data by appending a new column and deleting the first column of the data vector. Then it estimates the abruptly changing unknown parameters by shifting a batch data one step forward at each sampling time applying the frequency weighted last squares Hartley modulating functions algorithm. This technique is potentially useful in the design of failure detection and diagnosis applications.

Batch scheme Hartley modulating functions method for abruptly changing parameters identification of nonlinear continuous-time systems.

Daniel-Berhe S., Unbehauen H.

Systems Science

1998

Vol. 24, nr 3

67-87

In this work, a class of Hammerstein and integrable nonlinear continuous-time systems that are subject to parameters jump of unknown magnitudes or abrupt parameter changes occurring at unknown time instants are investigated via the batch scheme Hartley modulating functions (HMF) method. This new batch scheme HMF-algorithm is capable of parameter identification of nonlinear continuous-time systems varying in a discontinuous way. Considering the batch data records of input and noise corrupted output, the proposed approach first estimates the abruptly changing system parameters based on initial batch data and considers a new input-output data sample to update the initial record data by appending a new column and deleting the first column of the data vector. Then, it estimates the abruptly changing unknown parameters by shifting a batch data step forward at each sampling time applying the frequency weighted least squares HMF-algorithm. This technique is potentially useful in the design of failure detection and diagnosis applications. Illustrative simulation studies of Hammerstein and integrable nonlinear continuous-time systems are investigated to show the performance and potential of the proposed approach in the presence of measurement noises.