Solving systems of polynomial equations - a tensor approach

Speaker: Mariya Ishteva (K.U.Leuven)

Abstract: Polynomial relations are at the heart of mathematics. The fundamental problem of solving polynomial equations shows up in a wide variety of (applied) mathematics, science and engineering problems. Although different approaches have been considered in the literature, the problem remains difficult and requires further study.

We propose a solution based on tensor techniques. In particular, we build a partially symmetric tensor from the coefficients of the polynomials and compute its canonical polyadic decomposition. Due to the partial symmetry, a structured canonical polyadic decomposition is needed. The factors of the decomposition can then be used for building systems of linear equations, from which we find the solutions of the original system.

In this seminar, we present our new approach and illustrate it with a detailed example. Although this approach is not applicable for solving an arbitrary system of polynomial equations, it is applicable to a large class of sub-problems. Future work includes comparing the proposed method to existing methods and extending the class of sub-problems, for which the method can be applied.

Data-driven simulation for NARX systems

Speaker: Vikas Kumar Mishra

Abstract: Data-driven approaches to systems theory are witnessing considerable interests in recent times and they are well flourished for linear time-invariant systems. However, for nonlinear systems, they are still limited, and attempts have been made to generalize the results for linear systems to nonlinear systems. This talk will discuss the problem and challenges in data-driven simulation in the context of nonlinear autoregressive exogenous (NARX) systems: compute the output trajectory from a given input trajectory and initial conditions without explicitly identifying the analytical model; the model is implicitly identified by observed trajectory. 

Nonlinear model estimation via linearization around large signals

Speaker: Mehrad Ghasem Sharabiany

Abstract: In this seminar, a method for identifying a class of nonlinear systems from input-output data based on the linearization of the system around a varying working point will be presented. For this purpose, the system will be excited twice with an arbitrary input signal, called large signal, and with the same signal plus a small perturbation. It will be shown that in this manner, the system can be approximated as an LPV model around the large signals. Then, it will be shown that a nonlinear approximation can be derived from this LPV model with a technique presented in this work. This nonlinear model somehow reveals the structure of the nonlinear system with an initial estimate of its parameters. Finally, this nonlinear model will be used as a starting point for nonlinear system identification from noisy input-noisy output data along the same trajectory.

Frequency Response Function Measurements via Local rational Modeling, Revisited

online via TEAMS

Speaker: Rik Pintelon

Abstract: A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leakage) errors cause important bias and variance errors in the FRF estimate. To decrease these errors, several local modeling techniques have been proposed in the literature. In this presentation, a new local modeling approach is described that combines the small bias error of the local rational approximation with the low noise sensitivity of the local polynomial approximation. It is based on an automatic local model order selection procedure applied to a specific subclass of rational functions.

Human joint impedance identification, under a more clinical point of view

online via TEAMS

Speaker: Gaia Cavallo

Improved transfer function estimation by Gaussian process regression with prior knowledge

online via TEAMS

Speaker: Noël Hallemans

Abstract: Kernel-based modelling of dynamical systems offers important advantages such as imposing stability, causality and smoothness on the estimate of the model. Here, we improve the existing frequency domain kernel-based approach for estimating the transfer function of a linear time-invariant system from noisy data. This is done by introducing prior knowledge in the kernel. We use a local rational modelling technique to determine the most significant poles, and include these poles as prior knowledge in the kernel. This results in accurate models for the identification of lightly-damped systems.

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