A Novel Online Pseudospectral Method for Approximation of Nonlinear Systems Dynamics

This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of sampling instants (Chebyshev nodes) within each sliding window is selected dynamically based on a proposed node-selection criterion that guarantees desired approximation accuracy. The system states are measured at these aperiodic instants and used to estimate the coefficients of the basis polynomials using least squares. An adaptive state estimator is also proposed to reconstruct the continuous states using the approximated dynamics. The boundedness of the parameter and state estimation errors is proven analytically and validated numerically.