Constrained subspace method for the identification of structured state-space models (cosmos)

In this article, a unified identification framework called constrained subspace method for structured state-space models (COSMOS) is presented, where the structure is defined by a user-specified linear or polynomial parametrization. The new approach operates directly from the input and output data, which differs from the traditional two-step method that first obtains a state-space realization followed by the system-parameter estimation. The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. To alleviate this problem, the linear regression formulation is imposed by structured and low-rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters. The nonconvex nature of the constrained optimization problem is dealt with by transforming the problem into a difference-of-convex optimization problem, which is then handled by the sequential convex programming strategy. Numerical simulation examples show that the proposed identification method is more robust than the classical prediction-error method initialized by random initial values in converging to local minima, but at the cost of heavier computational burden.