Specialized algorithm for identification of stable linear systems using Lagrangian relaxation

Recently Lagrangian relaxation has been used to generate convex approximations of the challenging simulation error minimization problem arising in system identification. In this paper, we present a specialized algorithm to optimize the convex bounds generated by Lagrangian relaxation, applicable to linear state-space models. The algorithm demonstrates superior scalability over general-purpose semidefinite programming solvers. In addition, we show empirically that Lagrangian relaxation is more resilient to a biasing effect commonly observed in other identification methods that guarantee model stability.