Arbitrary Signal Research Articles

Nonlinear switched singular systems in discrete time: The one-step map and stability under arbitrary switching signals

The solvability of nonlinear nonswitched and switched singular systems in discrete time is studied. We provide necessary and sufficient conditions for solvability. The one-step map that generates equivalent nonlinear (ordinary) systems for solvable nonlinear singular systems under arbitrary switching signals is introduced. Moreover, the stability is studied by utilizing this one-step map. A sufficient condition for stability is provided in terms of (switched) Lyapunov functions.

Neural‐network‐based event‐triggered adaptive security path following control of autonomous ground vehicles subject to abnormal actuator signal

AbstractThe malicious physical attacks from both sensor and actuator sides make real threats to the security and safety of autonomous ground vehicles (AGVs). This paper focuses on the problem of neural‐network‐based event‐triggered adaptive security control (ET‐ASC) scheme for path following of AGVs subject to arbitrary abnormal actuator signal. First, we assume that an arbitrary abnormal signal is caused by arbitrary malicious attacks or disturbances from actuators. Then, radial basis function neural network (RBF‐NN) is used to reconstruct such abnormal actuator signal. Second, modelling issues on security path following control of AGVs with Sigmoid‐like ETC scheme are shown when the AGV is suffering from abnormal actuator signal. In what follows, an ET‐ASC scheme is developed to mitigate the adverse effects of abnormal actuator signal with the reconstructed abnormal signal based on a novel Sigmoid‐like event‐triggered communication scheme. By using the proposed RBF‐NN‐based ET‐ASC scheme, control performance can be guaranteed under arbitrary malicious actuator signal rather than such attacks following a specific probability distribution. Final, some simulation experiments are provided to verify the effectiveness of proposed ET‐ASC scheme.

Low-cost adaptive prescribed time tracking control for switched nonlinear systems

ABSTRACT This paper addresses a low-cost adaptive prescribed time tracking control strategy for switched nonlinear systems with input quantisation and unknown backlash-like hysteresis. Initially, a transformation function is introduced into the control design, which allows the tracking error of the controlled systems to a specified accuracy within a preassigned settling time. Unlike the existing prescribed time control scheme that only uses transformation function technique in the first step of the backstepping design, the transformation function is introduced to each step of the controlled systems, which makes only one adaptive parameter that needs to be updated online. Then, to synthesise a low-cost control scheme, a first-order sliding mode differentiator and a single-parameter estimation method are implemented based on the newly constructed coordinate transformations. Meanwhile, the Nussbaum technique successfully solves the effects caused by the unknown control direction, unknown backlash-like hysteresis and quantised input. All signals of the closed-loop systems are bounded under the proposed control scheme with arbitrary switching signal. Finally, the validity of the presented method is confirmed via two simulation examples.

Subsonic cavity flow control with Micro-Magneto-Mechanical Systems (MMMS) microvalves

Flow control consists in modifying a flow natural state in order to converge towards another state which is considered as favorable, as drag or noise radiation might be reduced. In this paper, open-loop flow control experiments are carried out on a subsonic open-cavity flow. In the case of unstable flow control, the control focus is brought onto the flow fluctuations modifications rather than modification of the mean flow properties. Therefore, the forcing flexibility using arbitrary signals and the forcing linearity are essential for such flow control cases. In that sense, a linear array of Micro Magneto-Electro-Mechanical Systems actuators has been implemented to perform open-loop flow control experiments on an open-cavity. The actuators are able to generate both quasi-steady and pulsed jets with linear behavior. We proved the microvalves efficiency to damp the cavity oscillations. The quasi-steady jets reached a reduction of 20 dB in the cavity fundamental amplitude sound pressure level. Pulsed jets enabled an additional cavity tone amplitude reduction, which depends on the pulsating frequency and on the forcing amplitude. These results are a first step towards the implementation of the closed-loop control of the open-cavity flow.

On the performance of non‐contiguous carrier aggregation in presence of subspectral errors

AbstractCarrier aggregation can not only increase communication bandwidth, but also improve spectrum efficiency and communication security. Considering the non‐contiguous multi‐subspectrum aggregation for the spectrum division transmission of arbitrary signal, the paper analyzes the performance impact on the demodulation of aggregated signal in the presence of subspectral amplitude and phase errors in receiver. The theoretical bit‐error rates (BER) of quaternary phase‐shift keying and M‐ary phase‐shift keying are derived to clarify the subspectrum synchronization accuracy requirements in non‐contiguous carrier aggregation. In addition, two adaptive equalizers requiring no pilot overhead are introduced to correct the distortion of aggregated signal caused by the subspectral errors. Both algorithms need no estimation of synchronization error but also have the tracking capability of phase error even with subspectral carrier error. Simulation results show the reliability of the theoretical BER performance and the excellent performance of the equalization algorithms.

Price Discrimination in Selection Markets

Abstract Should insurance prices vary with age? I consider competitive markets for lemons where a signal (e.g., age) partitions consumers (e.g., young and old). I study the continuum of policies from zero price-discrimination (zero- PD, equal prices) to full-PD (no restrictions). Restricting PD can increases welfare if high-cost markets exhibit greater adverse selection, or when the high-cost market “unravels.” I characterize optimal PD, and show how it is affected by changes in cost. In a calibration, optimal PD increases welfare by about $30/person-year. I extend the model to arbitrary signal structures, behavioral consumers, a monopolized industry, and multi-product firms.

Adaptive Output Feedback Fuzzy Fault-Tolerant Control for Nonlinear Full-State-Constrained Switched Systems.

In this article, an output feedback adaptive fuzzy tracking control method for a class of switched uncertain nonlinear systems with actuator failures and full-state constraints is proposed under an arbitrary switching signal combining the dynamic surface technique. Since the state variables of the system under study are not measurable, a fuzzy observer is constructed to identify the unmeasured states. The actuator failures are considered in the system. To compensate this failure, a fault-tolerant controller is proposed. Moreover, each state needs to be kept within the constraints, so the tangent Barrier Lyapunov function is selected to solve the full-state constraint problem, and the unknown nonlinear function is approximated by fuzzy-logic systems (FLSs). We also proved that all signals in the closed-loop system are bounded. Furthermore, the states can be kept within the predetermined range even if the actuator fails. Finally, a simulation example is given to verify the effectiveness of the proposed control strategy.

Автоматизированный синтез многополосовых согласующих устройств

When solving a number of technical problems, it often becomes necessary to create devices that operate in multiple operating frequency bands. This leads to the problem of designing multiband filters, which is solved quite simply with a purely active internal resistance of the signal source and load. In the case when the internal resistance of the signal source and load are complex, Along with this, there is also the problem of coordination. This leads to the need to solve the problem synthesis of broadband multiband circuits connecting complex internal resistance signal source and load. In this paper, the use of methods for constructing a good initial approximations that make it possible to obtain the structure of the eigenfunctions of the device of an adequately problem with subsequent optimization on a computer, allows the synthesis of broadband multiband matching circuits in a lumped element basis for arbitrary admittances signal source and load.

Energy saving control and operation strategy analysis of thermal coupling system of fuel cell and metal hydride tank

The thermal coupling system (TCS), where the heat generated by proton exchange membrane fuel cell (PEMFC) is transferred to the metal hydride (MH) tank, has been investigated extensively and proved beneficial to system compactness as well as capital cost. However, there is a lack of attention to the regulation of hydrogen desorption to increase the efficiency of hydrogen-to-power/heat (ηh−p), especially when the TCS is used in a distributed energy system (DES) combining power and heat. In this study, an energy saving control strategy for a TCS applied in DES is proposed to increase the ηh−p on the premise of the satisfaction of cosine-form hydrogen demand. The threshold temperature is introduced to characterize the maximum of ηh−p, and a prediction framework of threshold temperature for arbitrary signal is proposed based on its functional relationship with five operation parameters and Fourier decomposition method (FDM). The operation strategy of two-tank TCS is also discussed. The results indicate that up to 7.26 × 103 kJ more heat could be utilized by energy saving control strategy compared with the reference case. The relative error of predicted threshold temperature within 0.14% is obtained for a square wave and aperiodic signal, verifying the generalization capability of the proposed framework. Besides, the operation strategy that the rated hydrogen demand is supplied by both MH tanks, is suggested in a two-tank TCS to increase the hydrogen utilization and extend the supply duration.

Analysis of time‐domain response of series‐parallel fractional‐order RCα and RLβ circuits based on Cole distribution function

SummaryFractional‐order circuits, which contain fractance devices ( and ) described by fractional‐order differential equations, are widely used in interdisciplinary engineering research. The application of time‐domain response (TDR) measurement increases rapidly in analyzing the characteristics of fractance devices and fractional‐order circuits. However, the previous methods are mainly focused on deducing TDR expressions of a single fractance device or series fractional‐order circuits in some specific input signals, while overlook the TDR analysis of series‐parallel fractional‐order circuits (SPFOC) that are commonly applied in modeling electrochemical impedance or electrical bioimpedance. This paper proposes a novel method to derive TDR expressions of SPFOC in an arbitrary periodic signal. First, a discretization method to represent the SPFOC as the sum of first‐order circuits is proposed in Cole distribution function, which could approximate the transfer function of fractional‐order impedance/admittance. Second, the TDR expression of SPFOC in sinusoidal input signals is deduced in inverse Laplace transform, which can be applied as the components of a general TDR expression of SPFOC in an arbitrary periodic signal based on the Fourier series theory. Finally, both TDR simulations and experiments on Cole impedance model (a basic SPFOC) are conducted to verify the proposed method, which shows excellent agreement compared to theorical analysis. This paper presents a TDR solution to SPFOC that consist of a or element. In future, the theoretical and application extension of the proposed TDR analysis method is still necessary on analysis of more general fractional‐order circuits.

Ultrasound shear wave phase velocity imaging using black-box system identification (BSI): a data-driven approach

Objective. Shear wave elasticity imaging (SWEI) is an established approach for diagnosing lesions in human tissue. However, the shear wavelengths used by traditional SWEI are usually not short enough, leading to inferior accuracy in small-target (<10 mm) reconstruction. To exploit short shear wavelengths (high-frequency content), this study introduces a new phase velocity (PV) estimation technique as an alternative to the conventional group velocity (GV) modality. Approach. We propose using a black-box model instead of a fully physics-based model to describe the transition process of two arbitrary shear wave signals. With this representation, local PV can be obtained via black-box system identification (BSI). For validation, two PV estimation scenarios were established: (numerical) dispersion measurements in viscoelastic media, and (real) imaging targets in a CIRS elasticity phantom. BSI was compared with a state-of-the-art PV imaging method that uses local wavenumber estimation (LWE). Main results. BSI showed excellent accuracy in the dispersion estimation for all three viscoelastic media in the simulations. In the phantom study, the two PV methods exhibited good agreement in the frequency dependence of target quantification, and could both generate a higher target reconstruction accuracy than GV. LWE images were strongly affected by noise-induced faulty estimates, whereas BSI showed no notable artifacts. Significance. This study demonstrates the advantage of the PV modality over the GV modality as the former can achieve better target visualization by increasing imaging frequency. It also implies the feasibility of data-driven modeling for soft tissue characterization.

Реакция на произвольный сигнал динамической системы виброизолирующего устройства станка в условиях плавучей мастерской

В статье приведены результаты анализа и теоретических исследований реакции динамической системы на внешние воздействия в условиях плавучей мастерской. Для обеспечения качества поверхностей при шлифовании разработана процедура вычисления реакции линейной системы с сосредоточенными параметрами на сигнал произвольной формы (без преобразования входного сигнала). На основании предложенной методики представлена процедура преобразования дифференциального уравнения системы виброизолирующего устройства станка, сведения его к операторной форме и разделения переменных, получения операторной передаточной функции, по которой для сравнения можно вычислить реакцию на стандартный сигнал. Одно из полученных решений, либо их комбинация могут быть применены для вычисления реакции системы на произвольный дискретно заданный входной сигнал. Рассмотрен пример моделирования технологической системы круглошлифовального станка, оснащенной виброизолирующим устройством. Приведены графики реакции системы при изменениях параметров, графики переходных характеристик и погрешностей. Погрешность полученного численного решения зависит от величины шага квантования. Введенный коэффициент демпфирования позволяет оценить качество работы виброизолирующей опоры и эффект от ввода коррекции её параметров. Для реализации метода целесообразно предложить ряд конструктивных решений по обеспечению эффективного управления демпфированием виброизолирующей опоры металлорежущего станка при внешних воздействиях, что позволит существенно повысить качество изготовления деталей в условиях плавучей мастерской. The article presents the results of analysis and theoretical studies of the reaction of a dynamic system to external influences in a floating workshop. To ensure the quality of surfaces during grinding, a procedure has been developed for calculating the response of a linear system with lumped parameters to an arbitrary waveform (without converting the input signal). On the basis of the proposed technique, a procedure is presented for transforming the differential equation of the vibration isolation system of a machine tool, reducing it to an operator form and separating variables, obtaining an operator transfer function, which can be used to calculate the response to a standard signal for comparison. One of the solutions obtained, or a combination of them, can be used to calculate the system's response to an arbitrary discretely given input signal. An example of modeling the technological system of a circular grinding machine equipped with a vibration isolation device is considered. The graphs of the system's response to changes in parameters, graphs of transient characteristics and errors are presented. The error of the obtained numerical solution depends on the size of the quantization step. The introduced damping coefficient makes it possible to evaluate the quality of the vibration-isolating support and the effect of entering the correction of its parameters. To implement the method, it is advisable to propose a number of design solutions to ensure effective damping control of the vibration-insulating support of a metal-cutting machine under external influences, which will significantly improve the quality of parts manufacturing in a floating workshop.

Biorthogonal harmonics for the decomposition of gravitational radiation. I. Angular modes, completeness, and the introduction of adjoint-spheroidal harmonics

The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications in signal modeling and data analysis. This problem is complicated by most astrophysically relevant systems not having modes that are analytically tractable. A ubiquitous workaround is to use not modes, but multipole moments defined by spin-weighted spherical harmonics. However, spherical multipole moments are only related to the modes of systems without angular momentum. As a result, they can obscure the underlying physics of astrophysically relevant systems, such as binary black hole merger and ringdown. In such cases, spacetime angular momentum means that radiative modes are not spherical, but spheroidal in nature. Here, we work through various problems related to spheroidal harmonics. We show for the first time that spheroidal harmonics are not only capable of representing arbitrary gravitational wave signals, but that they also possess a kind of orthogonality not used before in general relativity theory. Along the way we present a new class of spin-weighted harmonic functions dubbed ``adjoint-spheroidal'' harmonics. These new functions may be used for the general estimation of spheroidal multipole moments via complete biorthogonal decomposition (in the angular domain). By construction, adjoint-spheroidal harmonics suppress mode-mixing effects known to plague spherical harmonic decomposition; as a result, they better approximate a system's true radiative modes. We discuss potential applications of these results. Lastly, we briefly comment on the challenges posed by the analogous problem with Teukolsky's radial functions.

Design of a robust model predictive control for nonlinear switched systems: A low‐conservative and recursive feasibility strategy

AbstractThis article proposes a robust H∞ based model predictive control scheme for Lipschitz nonlinear switched systems with persistent dwell time. In the developed method, the constraints corresponding to the recursive feasibility are included and the recursive feasibility is guaranteed. In this scheme, the existence of unstabilizable sub‐systems and exogenous disturbances are included which makes it possible to avoid considering an ideal and simplistic assumption about switched systems. By simultaneously designing the controller and the switching signal and using multiple Lyapunov functions, the unacceptable conservatism in methods involving common Lyapunov functions and arbitrary switching signals is avoided. In the proposed solution, a time‐varying prediction horizon is used for finite horizon cost functions, which in turn will be effective in reducing conservatism. In the suggested design strategy, the non‐convex control scheme is formulated as an optimization problem in the framework of linear matrix inequality. Finally, a numerical example is developed and the performance of the proposed scheme is evaluated.

Adaptive Coexistence of Synchronization and Anti-Synchronization for a Class of Switched Chaotic Systems

This paper addresses the problem of coexistence of synchronization and anti-synchronization (CSAS) for a class of switched chaotic systems by adaptive control method, where the switched system is realized by unified chaotic systems under arbitrary switching signal. Firstly, necessary and sufficient conditions for the CSAS of the chaotic systems are proposed from two perspectives, one is by analyzing the parity of the system expression, and the other is by decomposing the system. Secondly, according to the obtained necessary and sufficient conditions, two algorithms are given to search the synchronization variables and anti-synchronization variables in the chaotic systems. Thirdly, the CSAS of the switched chaotic system can be achieved by a designed adaptive global controller with only one input channel under the arbitrary switching signal. Finally, the numerical simulation results verify the validity and effectiveness of the method we obtained.

Passive Amplification and Noise Mitigation of Optical Signals Through Talbot Processing

Noise is one of the rare aspects of experimental work that crosses all boundaries. It is present from scientific fields like ultrafast optical signal detection to applied fields such as image processing, or even in our day-to-day lives when we are simply trying to have a conversation in a loud room. In all these cases, incoherent, stochastic noise tends to drown a signal we aim to detect, and various techniques may need to be employed to improve the clarity of the waveform, which is characterized by the signal-to-noise ratio (SNR). Yet, considering the ubiquity of noise in scientific and technology fields, it may be surprising how few methods there exists for denoising a signal. Active amplification techniques alone cannot be employed for weak, noisy signals, since the SNR is inevitably degraded due to fundamental laws of physics, while bandpass filtering schemes necessarily lead to an attenuation of the signal. In this article, we review recent advances on the concept of passive amplification techniques based on the Talbot effect to enhance the noise properties of signals through coherent energy redistribution. We demonstrate the basic framework starting from pulse repetition rate multiplication with the Talbot effect. We then extend this theory to show the principle behind passive amplification of periodic waveforms, and then how this idea can be extended to arbitrary (generally, aperiodic) signals. Methods for passive amplification of both the time-domain and the frequency-domain representations of the signal of interest are reviewed. While here we focus on the application of the technique for optical signals in the standard telecommunication band (near wavelengths of 1550 nm), the proposed denoising scheme relies on widely available wave manipulations, such that it may offer exciting opportunities for any kind of physical wave support, such as acoustics, plasmonics and other regimes of the electromagnetic spectrum, like microwaves or X-rays.

О ВЛИЯНИИ ДИСПЕРСИИ ПОГЛОЩЕНИЯ НА ВРЕМЕННУЮ ЗАВИСИМОСТЬ ГОЛОНОМНОГО УЗКОПОЛОСНОГО СИГНАЛА ВДАЛИ ОТ ТОЧКИ ИЗЛУЧЕНИЯ

It is well known that when a narrow-band signal propagates in any medium with a sufficient length of the path, the amplitude-frequency spectrum of the signal inevitably begins to deform due to the dispersion of the absorption coefficient of the medium, that is, due to the dependence of the absorption coefficient on frequency. Therefore, the time dependence of the signal «at infinity» significantly depends not only on the dispersion of the real part of refractive index, but also on the dispersion of the absorption. In this work, we consider the propagation and distortion of a narrow-band holonomic signal in a homogeneous dispersive medium (by the example of a weakly collisional plasma) taking into account the absorption dispersion. It turns out that the absorption dispersion manifests itself differently for different types of holonomic signals – for holonomic signals with a limited spectrum, the spectrum of which is identically equal to zero outside a certain spectral interval, and for holonomic signals with an unlimited spectrum, the spectrum of which does not vanish with increasing frequency. It is shown that for holonomic signals with an unlimited starting spectrum, the absorption dispersion with increasing path length leads to a shift in the carrier frequency towards lower absorption and to normalization of the spectrum intensity, and hence to normalization of the time dependence of the signal, which becomes Gaussian at infinity. At the same time the signal continues to remain narrow-band. For holonomic signals with a limited spectrum, the absorption dispersion leads to a narrowing of the spectrum, which «presses» it against the boundary of the original signal spectrum. This time, as in the case of signals with an unlimited spectrum, the “standardization” of the time dependence of the signal also occurs, but now the time dependence of an arbitrary signal turns out to be not Gaussian, but “Lorentzian”.

Millihertz magnetic resonance spectroscopy combining the heterodyne readout based on solid-spin sensors.

The sensitivities of quantum sensing in metrology and spectroscopy are drastically influenced by the resolution of the frequency spectrum. However, the resolution is hindered by the decoherence effect between the sensor and the environment. Along these lines, the continue-wave optically detected magnetic resonance (CWODMR) method combined with the heterodyne readout was proposed to break the limitation of the sensor's coherence time. The frequency of the magnetic field was swept to match the unknown signal, and the signal can be transformed to a real-time frequency-domain curve via the heterodyne readout, with a frequency resolution of 4.7 millihertz. Using the nitrogen-vacancy (NV) center ensemble in a diamond as the solid-spin sensors, it was demonstrated that the frequency resolution and precision could be improved proportionally to the low-pass filter parameters of Tc -1 and Tc -1.5, respectively. Furthermore, the introduced method performed the sensing of arbitrary audio signals with a sensitivity of 7.32 nT·Hz-1/2@10 kHz. Our generic approach can be extended to several fields, such as molecular structure determination and biomagnetic field detection, where high-fidelity detection properties across multiple frequency bands are required within small sensing volumes (∼ mm3).

Stability analysis of time-varying switched systems via indefinite difference Lyapunov functions

Asymptotic stability of time-varying switched systems is investigated in this paper. The less conservative sufficient criteria for asymptotic stability of time-varying discrete-time switched systems are proposed via common indefinite difference Lyapunov functions and multiple indefinite difference Lyapunov functions introduced in this note, respectively. Common indefinite difference Lyapunov functions can be used to analyze stability of a switched system with asymptotic stable subsystems and arbitrary switching signal. Multiple indefinite difference Lyapunov functions can be used to investigate stability of a switched system with unstable subsystems and a given switching signal. The difference of the proposed Lyapunov function may be positive at some instants for an asymptotically stable subsystem. We compare these main results and illustrate the effectiveness of the obtained theorems by three numerical examples.

Robust controllability and stabilization of switched Boolean control networks subject to multi-bit function perturbations

This paper develops a new multi-bit perturbed controllability matrix method for solving the robust controllability and stabilization of switched Boolean control networks (SBCNs) with multi-bit function perturbations. By constructing both perturbed position index matrix and multi-bit perturbed controllability matrix for SBCNs, the space of state pairs is divided into two disjointed parts, which determine whether or not the paths between two arbitrary states are affected by function perturbations. Then, a sequence of perturbed reachable sets is constructed, and several criteria are presented for the robust controllability of SBCNs under the multi-bit function perturbations. As a generalization, a perturbed position index matrix and a sequence of perturbed reachable sets are designed for the closed-loop system, based on which, a necessary and sufficient condition is presented for the robust state-feedback stabilization of SBCNs under arbitrary switching signal. Numerical examples demonstrate that our new criteria work well for the multi-bit function perturbations and thus have more practical significance.