Closed-Loop Identification of Stabilized Models Using Dual Input-Output Parameterization

Abstract: This paper introduces a dual input-output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input-output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is \emph{stabilized} by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP neither requires a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.