Identification of the inputs of quasilinear systems (Q927583)

The paper deals with the problem of recovering input signal (meant as initial state and external excitation) of the non-stationary quasi-linear (with weighted additive nonlinearity) observable dynamical system from inaccurate output measurements. To this end Tikhonov's regularization method is used. Error estimates of the obtained solution are derived and sufficient conditions for its convergence to the true input are given. Further, the conditions of representability of the unknown system input by the power series of a small non-linearity weighting parameter along with the explicit form of the series coefficients are established. Rigorously proved theoretical results are illustrated by an example and numerical experiment.