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 highlighted through illustrative examples; this does not seem to have been discussed much in the literature.