An Algebraic Approach to the Identification of Linear Continuous Systems Using Laguerre Networks

This paper presents an algebraic approach to linear continuous system identification using Laguerre networks. The proposed approach provides an indirect calculation of the coefficients for the Laguerre expansion of the system's transfer function, based on the Laguerre representations of the system's input and output. The algorithm's computational complexity can be significantly reduced for two specific choices of the input excitation function. The algorithm convergence properties and computational complexity is compared with the classical gradient algorithms. Furthermore, an optimal LQR controller with a state observer is designed using the Laguerre representation of the unknown linear system. Simulation results on a coupled-mass system with unknown parameters and unknown system order demonstrate the effectiveness of the proposed system identification and control methods.