Iterative data-driven generalized minimum variance regulatory control via ℓ<inf>2</inf>-regularization

Abstract

The paper proposes iterative data-driven generalized minimum variance (GMV) regulatory control via L 2 — regularization. The proposed approach reformulates the derivation of the GMV regulatory control as a L 2 -regularized optimization problem, and employs an iterative design approach that repeats the same routine as the one-shot GMV regulatory control via L 2 -regularization. The L 2 -regularization assures the uniqueness of control parameters as well as moderate high variance estimates. However, the penalty term for L 2 — regularization causes bias of estimation values. The proposed method solves the problem by employing iterative design approach. The penalty term that evaluates the deviation from initial parameters is updated at each iteration, which leads to the convergence to the true GMV control parameters without any bias. The paper provides some analytical results for the convergence property. The effectiveness of the proposed method is assured through a numerical example.