Error Bounds for Port-Hamiltonian Model and Controller Reduction Based on System Balancing
Computers & mathematics with applications(2022)
摘要
We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is port-Hamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reduced-order controller via balancing and subsequent truncation. This approach is closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are able to determine an optimal pH representation of the full-order system in the sense that the error bound is minimized. In addition, we discuss consequences for pH-preserving balanced truncation model reduction which results in two different classical H ∞-error bounds. Finally, we illustrate the theoretical findings by means of two numerical examples.
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关键词
Port-Hamiltonian systems,Model order reduction,LQG control design,Error bounds
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