pysib: Open-Source Python Toolbox Solves Nonconvex System ID with 100% Success

Diego Eckhard has released pysib, an open-source Python toolbox for linear system identification of single-input single-output (SISO) discrete-time polynomial models, including ARX, ARMAX, OE, and Box-Jenkins structures. Traditional prediction-error methods for OE, ARMAX, and BJ models suffer from nonconvex finite-sample criteria, meaning the estimate a user obtains depends heavily on initialization and optimization procedure, not just asymptotic theory. pysib addresses this with a dedicated multistage optimization strategy: an ARX-based initialization, a smoothed-gradient phase, an incremental Gauss-Newton refinement, and a filtered continuation technique that shapes the cost function to avoid local minima.

The results are striking. On a moderate-noise OE benchmark, pysib's estimates are far more concentrated around the true parameters compared to a general-purpose nonlinear-programming solver. On a harder, more nonconvex benchmark, filtered continuation raises the success rate from 60% to 100%. The toolbox also provides a common five-polynomial representation, shared prediction and simulation routines, and complete scripts to reproduce the experiments. The paper (8 pages, 2 figures, 6 tables) documents the strategy in full, and the code is available under an open-source license. This fills a gap for control engineers who need reliable system identification without manual tuning of optimization parameters.