Specialized Interior Point Algorithm for Stable Nonlinear System Identification
This work addresses a computational bottleneck for researchers and practitioners in system identification, offering an incremental improvement over prior Lagrangian relaxation methods.
The paper tackles the computational inefficiency of existing semidefinite programming methods for stable nonlinear system identification by developing a specialized interior point algorithm that reduces complexity from cubic to linear growth with data length, enabling superior generalization in empirical comparisons.
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper we develop a path-following interior point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the data set. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.