A note on modeling some classes of nonlinear systems from data

We study the modeling of bilinear and quadratic systems from measured data. The measurements are given by samples of higher order frequency response functions. These values can be identified from the corresponding Volterra series of the underlying nonlinear system. We test the method for examples from structural dynamics and chemistry

Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

Realization Theory for LPV State-Space Representations with Affine Dependence

In this paper we present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA representations). We deal both with the discrete-time and the continuous-time cases. We show that such a LPV-SSA representation is a minimal (in the sense of having the least number of state-variables) representation of its input-output function, if and only if it is observable and span-reachable. We show that any two minimal LPV-SSA representations of the same input-output function are related by a linear isomorphism, and the isomorphism does not depend on the scheduling variable.We show that an input-output function can be represented by a LPV-SSA representation if and only if the Hankel-matrix of the input-output function has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart of partial realization theory for LPV-SSA representation and prove correctness of the Kalman-Ho algorithm. These results thus represent the basis of systems theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as follows: typos have been fixe

Looking Beyond Appearances: Synthetic Training Data for Deep CNNs in Re-identification

Re-identification is generally carried out by encoding the appearance of a subject in terms of outfit, suggesting scenarios where people do not change their attire. In this paper we overcome this restriction, by proposing a framework based on a deep convolutional neural network, SOMAnet, that additionally models other discriminative aspects, namely, structural attributes of the human figure (e.g. height, obesity, gender). Our method is unique in many respects. First, SOMAnet is based on the Inception architecture, departing from the usual siamese framework. This spares expensive data preparation (pairing images across cameras) and allows the understanding of what the network learned. Second, and most notably, the training data consists of a synthetic 100K instance dataset, SOMAset, created by photorealistic human body generation software. Synthetic data represents a good compromise between realistic imagery, usually not required in re-identification since surveillance cameras capture low-resolution silhouettes, and complete control of the samples, which is useful in order to customize the data w.r.t. the surveillance scenario at-hand, e.g. ethnicity. SOMAnet, trained on SOMAset and fine-tuned on recent re-identification benchmarks, outperforms all competitors, matching subjects even with different apparel. The combination of synthetic data with Inception architectures opens up new research avenues in re-identification.Comment: 14 page