A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems - Pan,W; Yuan,Y; Goncalves,J; Stan,G-B (IEEE Transactions on Automatic Control, 2015)
This technical note considers the identification ofnonlinear discrete-time systems with additive process noise butwithout measurement noise. In particular, we propose a methodand its associated algorithm to identify the system nonlinear functionalforms and their associated parameters from a limited numberof time-series data points. For this, we cast this identificationproblem as a sparse linear regression problem and take a Bayesianviewpoint to solve it. As such, this approach typically leads tononconvex optimizations. We propose a convexification procedurerelying on an efficient iterative re-weighted 1-minimization algorithmthat uses general sparsity inducing priors on the parametersof the system and marginal likelihood maximisation. Using thisapproach, we also show how convex constraints on the parameterscan be easily added to the proposed iterative re-weighted1-minimization algorithm. In the supplementary material availableonline (arXiv:1408.3549), we illustrate the effectiveness of theproposed identification method on two classical systems in biologyand physics, namely, a genetic repressilator network and a largescale network of interconnected Kuramoto oscillators.