Aperiodic Sensing and Data-Driven System Identification of Nonlinear Systems Using Chebyshev Pseudospectral Approach
Arian Yousefian, Avimanyu Sahoo, Vignesh Narayanan · 2024
This paper presents a novel aperiodic sensing scheme for reconstructing the dynamics of a nonlinear continuous-time system online using the Chebyshev pseudospectral (PS) method. Unlike traditional system identification via adaptive control techniques, where the sensor measures the system states periodically, this research employs an aperiodic sensing scheme for online data collection using the idea of Chebyshev nodes that guarantee an arbitrary approximation accuracy. A moving time window approach is introduced to determine the sensing time instances within each time window online. The number of nodes (sensing times) within a window is incremented or decremented adaptively until the desired approximation accuracy is reached. The least-square approach is employed to estimate the coefficients of the Chebyshev basis function for the time window. An adaptive identifier is also proposed to estimate the system states using the piecewise approximated system dynamics. The convergence of the state estimation and parameter estimation errors is ensured analytically using the Lyapunov stability theory. Numerical results are also included to show the efficacy of the sensing and identification scheme with a 2D example.