An Improved Subspace Identification Method with Variance Minimization and Input Design

Subspace identification has received considerable attention due to its noniterative way of estimating the system model by linear algebraic steps, which identifies the parameter matrices of the system by projecting them into a subspace related to input and output. However, since the cost function is not explicitly defined in the subspace method, the statistical analysis is complicated. Without the variance analysis in the subspace method, it is difficult to obtain the optimal input to achieve stable identification results with the minimum variance. In this paper, we propose an improved subspace method, which has an explicit identification function related to the input and output to facilitate the variance analysis, and then design the input to minimize the identification variance. The proposed method identifies the Markov parameter matrix of an LTI system and obtains the identification function by constructing a block Hankel matrix related to the input and output. The non-convex optimization problem of variance minimization input design is solved by splitting it into two sub-problems, which are solved with guaranteed optimal solutions. We prove the convergence of our method. Simulation demonstrates the effectiveness of our method.