We present an algorithm for data-driven identification and reduction of nonlinear cascaded systems with Hammerstein structure. The proposed algorithm relies on the Loewner framework (LF) which constitutes a non-intrusive algorithm for identification and reduction of dynamical systems based on interpolation. We address the following problem: the actuator (control input) enters a static nonlinear block. Then, this processed signal is used as an input for a linear time-invariant system (LTI). Additionally, it is considered that the orders of the linear transfer function and of the static nonlinearity are not a priori known.
Introduction: Irreversible Electroporation (IRE) is a non-thermal ablation technique with promising results for treating locally advanced pancreatic cancer (LAPC). This study was conducted to evaluate safety and efficacy of IRE in the management of LAPC. Methods: This was e retrospective single center study of ten patients with radiographic and biopsy proven stage III pancreatic head or body cancer that received open IRE with intraoperative ultrasound imaging. Perioperative complications at 90 days, tumor volume measurements, local recurrence and survival were recorded. Results: 20 patients, with a median age of 62, underwent IRE for locally advanced pancreatic head cancer (n=11) and body cancer (n=9). All patients were treated successfully with an open IRE approach. Nine patients experiences grade II (Clavien-Dindo) procedure related complications. There were no grade 3 to 5 complications. Median follow up was 30 monts. Tumor volume decrease at 6 months imaging follow up was found in 70% of patients (n=14). Local disease progression was observed in two patients, and there was evidence of metastatic disease in 7 patients. 8 patients died with a mean of 15, 2 months and 12 patients are still alive with a mean of 17,3 months. Median overall survival was 16,5 months. Conclusion: Our initial experience with IRE showed encouraging results regarding safety, feasibility and efficacy in patients with locally advanced pancreatic head or body cancer. Further investigation is needed.
In this study, four data-driven interpolation-based methods are compared. The aim is to construct reduced-order models for which the corresponding rational transfer function matches the original non-rational one at selected interpolation points. The primary method of this study is the Loewner framework [2] which addresses this problem in a natural and direct way. The other methods that were studied, vector fitting (VF) [5], and adaptive Antoulas-Anderson (AAA) [4], are instead based on an iterative and adaptive selection procedure. In order to present the adaptive selection as a feature in the Loewner framework and to reduce the time complexity at the same time, we introduced a Loewner CUR method based on the cross approximation algorithm [6,7]. The performance of the above methods is tested by a classical example in approximation theory: the inverse of the Bessel function of the first kind. 1 SISO: Single Input Single Output. Where E, A ∈ C n×n and B, C T ∈ C n×1 , and a scalar D ∈ C. 2 real symmetryH(s) = H(s): we can obtain a real model [2]. Where(·) denotes the complex conjugate and (·) * the complex conjugate transpose.
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