Direct identification of continuous-time linear systems

Abstract

In this thesis we present a non-parametric, “power”-based approach to system identification based on exploiting the Dirac structure of port-Hamiltonian systems, which relates a bilinear form on the external variables of a port-Hamiltonian system (inputs, outputs, resistive efforts- and flows) and an associated bilinear form on the state variables. Generalized orthonormal basis representations of the system trajectories are used to derive a structured matrix equation, i.e. a Lyapunov equation, from the Dirac structure, relating a set of basis coefficients for the external trajectories to that of the associated state trajectories. Moreover, by factorizing the solution to this Lyapunov equation one can obtain generalized orthonormal basis representations of the state trajectories. Consequently solving a set of linear equations in the input-state-output data, a variety of unfalsified input-state-output models can be derived.

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Identifiers

ORCID for Bing Chu: orcid.org/0000-0002-2711-8717

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