Approach for estimating abruptly changing parameters of integrable nonlinear continuous-time systems

A new estimation algorithm capable of estimating the parameters of an integrable nonlinear continuous-time system varying in a discontinuous 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 least squares Hartley modulating functions algorithm. This technique is potentially useful in the design of failure detection and diagnosis applications.