A structure preserving minimal representation of a nonlinear port-Hamiltonian system

Abstract

CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Abstract-In this paper an approach to reduce nonlinear non-observable and non-strongly accessible port-Hamiltonian systems to an observable and strongly accessible portHamiltonian system, respectively, is treated. A local state decomposition (the nonlinear version of the Kalman decomposition) is instrumental for the approach that preserves the port-Hamiltonian structure. The strongly accessible reduction scheme goes along similar lines as the linear scheme. However, the observable reduction scheme is somewhat more involved. Under some additional assumptions, the reduction can be performed along the lines of the linear scheme. If these assumptions are not fulfilled, a reduction scheme for a zero-observable representation using duality in the co-energy coordinates is developed. Finally, the possibilities to apply the approaches of this paper to approximate order reduction by e.g., use of balancing procedures, is discussed.

Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems

“…Rewriting these equations into the form (17), and applying the general effort-constraint reduction method (20) from the previous section, yields (assuming that Q 22 is invertible) the reduced order port-Hamiltonian model (30). …”

“…A recent overview of portHamiltonian model reduction methods can be found in [18]. Model reduction of nonlinear port-Hamiltonian systems is discussed in [19,20]. Model reduction of general nonlinear systems is gaining more attention in recent years, see for example [21][22][23][24] and references therein.…”

Structure Preserving Truncation of Nonlinear Port Hamiltonian Systems

“…This could be further "decoupled" per coordinates as in [15]. The paper [21] gives a similar but computationally different method for obtaining the form (6), which can be used in stead of the method in [13].…”

“…is a PHS, and (6). ◁ In the z H -coordinates, the controllability function and the internal energy (Hamiltonian) are brought in an almost semibalanced form (for a fully semi-balanced form, a transformation of the form…”

“…To benefit from the structure of a PHS, it is natural to develop a model reduction method preserving the PH structure. Structure preserving model reduction methods for PHSs have been studied in several ways such as through Kalman decomposition [5], [6], interpolation [7], moment matching [8]- [10], and modified balanced truncation for limited subclasses [11], [12]. In particular, [6], [9], [11], [12] study nonlinear PHSs.…”