A guided residual search for nonlinear state-space identification

Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and efficiency of the estimation process by decomposing the overall optimization problem into a sequence of tractable subproblems. Based on an initial linear model, nonlinear residual dynamics are first estimated via a guided residual search and subsequently refined using multiple-shooting optimization. Experimental results on two benchmarks demonstrate competitive performance relative to state-of-the-art black-box methods and improved convergence compared to naive initialization.

A sliding-window approach for latent restoring force modeling

Restoring force surface (RFS) methods offer an attractive nonparametric framework for identifying nonlinear restoring forces directly from data, but their reliance on complete kinematic measurements at each degree of freedom limits scalability to multidimensional systems. The aim of this paper is to overcome these measurement limitations by proposing an identification framework with relaxed sensing requirements that exploits periodic multisine excitation. Starting from an initial linear model, a sliding-window feedback approach reconstructs latent states and nonlinear restoring forces nonparametrically, enabling identification of the nonlinear component through linear-in-parameters regression instead of highly non-convex optimization. Validation on synthetic and experimental datasets demonstrates high simulation accuracy and reliable recovery of physical parameters under partial sensing and noisy conditions.