Port-Hamiltonian dynamic mode decomposition. (English) Zbl 1523.37086
Summary: We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively, operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.
MSC:
| 37M99 | Approximation methods and numerical treatment of dynamical systems |
| 37N35 | Dynamical systems in control |
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 93B30 | System identification |
| 93C05 | Linear systems in control theory |
Keywords:
dynamic mode decomposition; port-Hamiltonian systems; system identification; dissipation inequality; passivity; knowledge-driven realizationReferences:
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