L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems

Rotorcraft stability is an inherently multidisciplinary area, including aerodynamics of rotor and fuselage, structural dynamics of flexible structures, actuator dynamics, control, and stability augmentation systems. The related engineering models can be formulated with increasing complexity due to the asymmetric nature of rotorcraft and the airflow on the rotors in forward flight conditions. As a result, linear time-invariant (LTI) models are drastic simplifications of the real problem, which can significantly affect the evaluation of the stability. This usually reveals itself in form of periodic governing equations and is solved using Floquet’s method. However, in more general cases, the resulting models could be non-periodic, as well, which requires a more versatile approach. Lyapunov Characteristic Exponents (LCEs), as a quantitative method, can represent a solution to this problem. LCEs generalize the stability solutions of the linear models, i.e., eigenvalues of LTI systems and Floquet multipliers of linear time-periodic (LTP) systems, to the case of non-linear, time-dependent systems. Motivated by the need for a generic tool for rotorcraft stability analysis, this work investigates the use of LCEs and their sensitivity in the stability analysis of time-dependent, comprehensive rotorcraft models. The stability of a rotorcraft modeled using mid-fidelity tools is considered to illustrate the equivalence of LCEs and Floquet’s characteristic coefficients for linear time-periodic problems.

L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

A Survey on Model-Based Fault Detection Techniques for Linear Time-Invariant Systems with Numerical Analysis

With the ongoing increase in complexity, less tolerance to performance degradation and safety requirements of practical systems has increased the necessity of fault detection (FD) as early as possible. During the last few decades, many research findings have been developed in fault diagnosis that addresses the issue of fault detection and isolation in linear and nonlinear systems. The paper’s objective is to present a survey on various state-of-art model-based FD techniques developed for linear time-invariant (LTI) systems for the interested readers to learn about recent development in this field. Model-based FD techniques for LTI systems are classified as parameter-estimation methods, parity-space-based methods, and observer-based methods. The background and recent progress, in context to fault detection, of each of these methods and their practical applications are discussed in this paper. Furthermore, two different FD techniques are compared via analytical equations and simulation results obtained from the DC motor model. In the end, possible future research directions in model-based FD, particularly for the LTI system, are highlighted for prosperous researchers. A comparison and emerging research topic make this contribution different from the existing survey papers on FD.

On Parametrizations of State Feedbacks and Static Output Feedbacks and Their Applications

In this chapter, we provide an explicit free parametrization of all the stabilizing static state feedbacks for continuous-time Linear-Time-Invariant (LTI) systems, which are given in their state-space representation. The parametrization of the set of all the stabilizing static output feedbacks is next derived by imposing a linear constraint on the stabilizing static state feedbacks of a related system. The parametrizations are utilized for optimal control problems and for pole-placement and exact pole-assignment problems.

Impedance matching to axion dark matter: considerations of the photon-electron interaction

We introduce the concept of impedance matching to axion dark matter by posing the question of why axion detection is difficult, even though there is enough power in each square meter of incident dark-matter flux to energize a LED light bulb. By quantifying backreaction on the axion field, we show that a small axion-photon coupling does not by itself prevent an order-unity fraction of the dark matter from being absorbed through optimal impedance match. We further show, in contrast, that the electromagnetic charges and the self-impedance of their coupling to photons provide the principal constraint on power absorption integrated across a search band. Using the equations of axion electrodynamics, we demonstrate stringent limitations on absorbed power in linear, time-invariant, passive receivers. Our results yield fundamental constraints, arising from the photon-electron interaction, on improving integrated power absorption beyond the cavity haloscope technique. The analysis also has significant practical implications, showing apparent tension with the sensitivity projections for a number of planned axion searches. We additionally provide a basis for more accurate signal power calculations and calibration models, especially for receivers using multi-wavelength open configurations such as dish antennas and dielectric haloscopes.

Interpolation-Based Modeling Methodology for Efficient Aeroelastic Control of a Folding Wing

The aeroelastic model of a folding wing varies with different configurations, so it actually represents a parameter-varying system. Firstly, a new approach based on interpolation of local models is proposed to generate the linear parameter-varying model of a folding wing. This model is capable of predicting the aeroelastic responses during the slow morphing process and is suitable for subsequent control synthesis. The underlying inconsistencies among local linear time-invariant (LTI) models are solved through the modal matching of structural modes and the special treatment of the rational functions in aerodynamic models. Once the local LTI models are represented in a coherent state-space form, the aeroservoelastic (ASE) model at any operating point can be immediately generated by the matrix interpolation technique. Next, based on the present ASE model, the design of a parameterized controller for suppressing the gust-induced vibration is studied. The receptance method is applied to derive fixed point controllers, and the effective independence method is adopted and modified for optimal sensor placement in variable configurations, which can avoid solving ill-conditioned feedback gains. Numerical simulation demonstrates the effectiveness of the proposed interpolation-based modeling approach, and the parameterized controller exhibits a good gust mitigation effect within a wide parameter-varying range. This paper provides an effective and practical solution for modeling and control of the parameterized aeroelastic system.