System identification of multi-input multi-output (MIMO) linear system through the use of active set methods
This project performed multi-input multi-output (MIMO) system identification using randomized active-set methods. The system fidelity term may incorporate time-domain and frequency-domain data. A MIMO-aware regularizer was developed by an L1/Linfinity group-lasso strategy (over pole coefficients), and optimization occured using Fully Corrective Frank-Wolfe (FCFW). The full-correction steps allowed poles to be added and dropped as necessary while maintaining a monotonically decreasing objective error, whereas the (Forward) Frank-Wolfe scheme never drops poles and results in a high-order system.
Comparison of system order and objective convergence for Forward vs. Fully Corrective Frank-Wolfe for MIMO sysid.
The algorithm has two phases: Randomize and Reweight. The Randomize phase picks out poles at random and performs FCFW steps over this active set. After sufficiently many iterations (user-specified), the Reweight phase sparsifies the set of poles while retaining monotonicity in objective by adjusting the weights of the regularizer.
Both the cost and the number of active poles decrease after reweighting.
MIMO System Identification by Randomized Active-Set Methods
MIMO (multi-input multi-output) system identification is a particular instance of a parsimonious model selection problem. If the observed data is assumed to arise from a stable and low order plant, then the representing model should also be stable and have few poles in its realization. These constraints are challenging to impose in an L 1 or nuclear norm framework, especially when observations are non-uniformly sampled. This paper implements MIMO identification by randomized active-set methods, as realized by Fully Corrective Frank-Wolfe (FCFW). Reweighting pole-group penalties allow for further system sparsification while monotonically decreasing the regularized fitting error. Efficacy of the approach is shown on two examples.