Computationally Efficient Identification of Global ARX Parameters With Guaranteed Stability

Identification of stable parametric models from input-output data of a process (stable) is an essential task in system identification. For a stable process, the identified parametric model may be unstable due to one or more of the following reasons: 1) presence of noise in the measurements, 2) plant disturbances, 3) finite sample effects 4) over/under modeling of the process and 5) nonlinear distortions. Therefore, it is essential to impose stability conditions on the parameters during model estimation. In this technical note, we develop a computationally efficient approach for the identification of global ARX parameters with guaranteed stability. The computational advantage of the proposed approach is derived from the fact that a series of computationally tractable quadratic programming (QP) problems are solved to identify the globally optimal parameters. The importance of identifying globally optimal stable model parameters is high lighted through illustrative examples; this does not seem to have been discussed much in the literature.