A duality-based approach to identification of linear time-varying systems

Abstract

In this report a novel approach for the identification of linear time-varying systems is presented. We exploit the fact that external structures at the level of the inputs and outputs are reflected in the internal ones at the level of the state. Our approach first computes state trajectories from matrices of input-output data. A novel factorisation of the state trajectories from the input-output data matrices is developed. Then a state space representation compatible with the data is computed. We do not impose conditions in the time variation properties of the to-be-identified system.

A procedure for the identification of self-adjoint systems is developed. We exploit the fact that linear time-varying systems as well as nonlinear systems are self-adjoint if they have an internal representation as a linear Hamiltonian.

Finally, we utilise reproducing kernel Hilbert spaces to formalise the building of time functions for data and embed it into the duality-based approach.

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