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Aalborg Universitet Model Reduction of Linear Switched Systems and LPV State-Space Models
| Content Provider | Semantic Scholar |
|---|---|
| Author | Baştuğ |
| Copyright Year | 2015 |
| Abstract | A linear switched system (LSS) is a concatenation of more than one linear subsystems, for which the operating subsystem at each time instant is chosen by a function called the “switching signal”, whose range is the set of discrete modes. The allowed set of switching sequences for an LSS can be arbitrary (user defined) or constrained due to the modeled physical process itself or due to the physical constraints on choosing the input. In this work, some methods are presented to approximate the input output behavior of an LSS with arbitrary or restricted switching, with another LSS of smaller complexity. Smaller system complexity in this context refers to “smaller continuous state-space dimension”. The methods are based on a non-trivial generalization of Krylov subspace-based moment matching methods, to the linear switched systems. The newly developed methods are numerically much more efficient than some naive approaches appeared in the literature previously for the same problem. The numerical advantage of the given methods stems from the fact that they do not rely on computing the finite Hankel matrices of an LSS, whose size increases exponentially with the number of discrete modes (linear subsystems) of an LSS. The work consists of five major parts. The first four parts state model order reduction methods for LSSs. The first method can be interpreted as the complete analogue of the solution to the moment matching problem in the linear case, for linear switched systems. The second method is more general and it is based on the so-called “nice selections” of some basis vectors, for some subspaces of reachability/unobservability spaces of an LSS; and it allows for choosing the order of the reduced LSS a priori. In the third part, the problem of model reduction of LSSs with constrained switching is considered. The proposed method (whenever possible) computes a reduced order LSS from a given LSS whose input-output behavior is exactly the same with the one of the original LSS. The fourth part further discusses this method, constructing its ties with system theoretical properties like reachability and observability. Namely, the definitions of reachability and observability of LSSs with respect to a constrained set of switching sequences are proposed, and a method to reduce an unreachable and/or unobservable LSS to a reduced order reachable and/or observable LSS (with respect to the same set of constrained switching) is given. The method again preserves the complete input-output behavior. In the last part of the work, a similar approach based on moment matching is taken for the purpose of model reduction of linear parameter varying (LPV) state-space (SS) representations with affine dependence on the scheduling variable. This jump from linear switched systems to LPV-SS representations is possible by observing the Markov parameters (moments) uniquely defining |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://vbn.aau.dk/ws/portalfiles/portal/233586041/PHD_Mert_Bastug_E_pdf2.pdf |
| Alternate Webpage(s) | http://vbn.aau.dk/files/233586041/PHD_Mert_Bastug_E_pdf2.pdf |
| Alternate Webpage(s) | https://vbn.aau.dk/ws/portalfiles/portal/316414377/PHD_Mert_Bastug_E_pdf2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
