Linear Systems Research Articles

Linearization Decoupling Method and Control Stability Analysis of Maglev Train in Two-Dimensional Wide Domain Spaces

The electromagnetic forces exerted by a maglev train are highly nonlinear with respect to the varying currents and gaps in a two-dimensional wide domain space. As the speed of the vehicle increases, the difficulty of achieving stability in controlling the levitation gap will progressively increase to the point of impossibility. The Taylor series method is employed to decouple the electromagnetic force into the product of two separated variables, with current and gap serving as independent variables. Second, the optimal first-order approximation polynomials and Chebyshev orthogonal polynomials are employed to linearize the electromagnetic force based on the error distribution, respectively. Third, a dual-loop proportional integral derivative (PID) control model with voltage feedback for high-speed magnetic levitation vehicles is constructed based on this linearized decoupled model. The derivation of each control parameter is provided without loss of generality. In conclusion, a hybrid simulation model of a linear control system and a nonlinear magnetic field is constructed, and the control stability of the vehicle is analyzed using the German low interference track, which was used in the Shanghai Maglev commercial demonstration line. It is demonstrated that the two-dimensional spatial linearization method offers significant performance advantages over alternative control system methodologies. Furthermore, the absolute vibration value of the solenoid exhibits an order of magnitude advantage over conventional methods at specific speed conditions. Additionally, the reduction in current variation and current variability can significantly diminish the hardware resource requirements necessary for the control system. It is noteworthy that the control system based on this linear approach exhibits reduced sensitivity to vehicle speed. Over the speed range of the Maglev train, which varies from 300[Formula: see text]km/h to 600[Formula: see text]km/h, the control system demonstrates remarkable robustness.

Recursive Filtering for Two‐Dimensional Markov Jump Linear System With Time Correlated Multiplicative Noises and Energy Harvesting Constrains

ABSTRACTThis article investigates the linear minimum mean square error estimation for the two‐dimensional Markovian jump linear system with time‐correlated multiplicative noises and energy harvesting sensor. The time‐correlated multiplicative noise is described by a linear dynamic model driven by white noise. The sensor harvests energy from the natural environment, and the energy levels at the energy harvester are characterized by some random variables that follow a certain probability distribution. The transmission of measurements is closely related to the energy level of the sensor, and only when the current energy storage exceeds the transmission energy consumption, the measurements are transmitted to the remote estimator. The main goal of this study is to formulate an iterative coupled new‐type estimator with jumping parameters and design the estimated gain reasonably to guarantee the minimum error covariance at each step. Firstly, two new‐type coupling estimators are derived by introducing several new recursive terms. By employing the induction method, the unbiasedness of the proposed two estimators is first ensured and the parameters of the estimator are supplied. Subsequently, an upper bound on the estimation error covariance with the jumping property is given based on the spectral norm. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed estimation scheme.

Robust controllability and robust near-controllability of driftless discrete-time bilinear systems

Near-controllability is a recently established notion which can be used to not only better characterise nonlinear systems but also prove controllability. In this paper, it is further shown that near-controllability is more robust than controllability. Specifically, driftless discrete-time bilinear systems are considered and the robust controllability and robust near-controllability problems are dealt with through two different approaches. By improving a result on robust controllability of linear time-invariant systems, sufficient conditions for robust controllability and robust near-controllability of the bilinear systems are first derived, respectively, if the interval matrices are sign-invariant. Then the general case, i.e. the interval matrices are not sign-invariant, is considered and an interval scalar operation approach is proposed to prove robust controllability and robust near-controllability. Examples are provided to demonstrate the obtained results and it is found that the bounds of the uncertainties for the systems to be robustly nearly-controllable are greater than those for the systems to be robustly controllable.

The evolution of human-type consciousness – a by-product of mammalian innovation mechanism – a preliminary hypothesis

Human consciousness is often viewed as one of the pinnacles of evolution, with most theories positioning it as an upgrade of pre-existing cognitive skills. However, conscious perception, memory, action, and in some situations even decision-making, are often inferior—less complex, slower, and less accurate—than their nonconscious (subliminal) counterparts. The interface hypothesis challenges this perspective, proposing that human-type consciousness is not an advanced version of earlier cognitive capacities but a novel function that entered the arena of cognitive and operational processes and fundamentally changed its rules. According to this hypothesis, the neocortex emerged as part of an advanced innovation mechanism, where its unpredictable, chaotic activity is used to generate alternative patterns. The process of cropping these alternatives from the chaotic neocortex and mediating them to the constrained, goal-oriented, linear control system requires a serially functioning interface. Consciousness, it is suggested, arose as a byproduct or a side effect of this interface, eventually expanding its influence to a wide range of cognitive and operational functions. This perspective has significant implications for our understanding of human cognition, creativity, and the distinctive capacities of human consciousness, potentially bridging the gap between neuroscientific findings and phenomenological experiences of consciousness.

Thermoelectric performance of quantum dots embedded in an Aharonov-Bohm ring: a Pauli master equation approach

Within linear response theory using the Pauli master equation approach, we have investigated the thermoelectric properties of quantum dots (QDs) embedded in an Aharonov-Bohm (AB) ring weakly coupled to two metallic electrodes. This study explores the impact of magnetic flux on thermoelectric transport, emphasizing the role of quantum interference induced by the flux. When the magnetic flux is varied from 0 to one quantum of flux , both the electrical conductance and the thermoelectric figure of merit () significantly increase by two orders of magnitude. Moreover, our investigation into the effects of onsite and inter-site Coulomb interactions in this nanojunction indicates that an optimal ZT is attained with moderate onsite Coulomb interaction and minimal inter-site Coulomb interaction. We briefly discussed the effects of asymmetric arrangements of triple QDs within an AB ring. However, within our parameter regime, a symmetric arrangement offers superior thermoelectric performance compared to asymmetric configurations. Furthermore, we explored how increasing the number of QDs in the ring enhances the thermoelectric properties, resulting in a potential ZT value of around 0.43. This study shows that arranging multiple QDs symmetrically in an AB ring can result in significant thermoelectric performance in a nanostructured system at low temperatures.

Diffusing Winding Gradients (DWG): A Parallel and Scalable Method for 3D Reconstruction from Unoriented Point Clouds

This article presents Diffusing Winding Gradients (DWG) for reconstructing watertight surfaces from unoriented point clouds. Our method exploits the alignment between the gradients of the screened generalized winding number (GWN) field—a robust variant of the standard GWN field—and globally consistent normals to orient points. Starting with an unoriented point cloud, DWG initially assigns a random normal to each point. It computes the corresponding screened GWN field and extracts a level set whose iso-value is the average of GWN values across all input points. The gradients of this level set are then utilized to update the point normals. This cycle of recomputing the screened GWN field and updating point normals is repeated until the screened GWN level sets stabilize and their gradients cease to change. Unlike conventional methods, DWG does not rely on solving linear systems or optimizing objective functions, which simplifies its implementation and enhances its suitability for efficient parallel execution. Experimental results demonstrate that DWG significantly outperforms existing methods in terms of runtime performance. For large-scale models with 10 to 20 million points, our CUDA implementation on an NVIDIA GTX 4090 GPU achieves speeds 30 to 120 times faster than iPSR, the leading sequential method, tested on a high-end PC with an Intel i9 CPU. Furthermore, by employing a screened variant of GWN, DWG demonstrates enhanced robustness against noise and outliers and proves effective for models with thin structures and real-world inputs with overlapping and misaligned scans. For source code and additional results, visit our project webpage: https://dwgtech.github.io/ .

Uncoupling of General Linear Multi-Degree-of-Freedom Structural and Mechanical Systems Through Quasi-Diagonalization

Abstract This article develops a fundamental result in linear algebra by providing the necessary and sufficient conditions for the simultaneous quasi-diagonalization of two symmetric matrices and two skew-symmetric matrices by a real orthogonal congruence. This result is used to study the uncoupling of general linear multi-degree-of-freedom (MDOF) structural and mechanical systems described by arbitrary damping and stiffness matrices through quasi-diagonalization, and real orthogonal coordinate transformations. The uncoupling leads to independent subsystems, each having at most two degrees-of-freedom with a specific structure. The results encompass the different physical categories of linear MDOF systems identified by engineers, mathematicians, and physicists and provide the necessary and sufficient conditions for their maximal uncoupling. A total of 16 conditions are shown to exist. However, the number of such conditions for physical systems that are commonly met in nature as well as in aerospace, civil, and mechanical engineering are shown to be considerably less, dwindling at times to two or three, thereby making the results applicable to numerous high-order real-life linear MDOF dynamical systems. Several new analytical results are obtained and corroborated through numerical examples.

A magnon band analysis of GdRu2Si2 in the field-polarized state

Understanding the formation of skyrmions in centrosymmetric materials is a problem of fundamental and technological interest. GdRu2Si2 is a candidate material that hosts a variety of multi-Q magnetic phases, including in zero-field. Here, inelastic neutron scattering is used to measure the spin excitations in the field-polarized phase of GdRu2Si2. Linear spin wave theory and a method of interaction invariant path analysis are used to derive a Hamiltonian accounting for the spectra. The Hamiltonian, dominated by bilinear (Ruderman-Kittel-Kasuya-Yosida) Heisenberg exchange, compares favorably to ab initio calculations. Dipolar interactions are a secondary energy scale to consider, with JD.D~ 0.05JRKKY. However, it is shown that in the field-polarized phase the dipolar interactions ‘self screen’ so that their effect is largely suppressed. No specific evidence for higher-order exchange is found. These aspects are discussed in the context of the lower field multi-Q states and the anisotropy of the system.

Conjectures on the Stability of Linear Control Systems on Matrix Lie Groups

Thestability of a control system is essential for its effective operation. Stability implies that small changes in input, initial conditions, or parameters do not lead to significant fluctuations in output. Various stability properties, such as inner stability, asymptotic stability, and BIBO (Bounded Input, Bounded Output) stability, are well understood for classical linear control systems in Euclidean spaces. This paper aims to thoroughly address the stability problem for a class of linear control systems defined on matrix Lie groups. This approach generalizes classical models corresponding to the latter when the group is Abelian and non-compact. It is important to note that this generalization leads to a very difficult control system, due to the complexity of the state space and the special dynamics resulting from the drift and control vectors. Several mathematical concepts help us understand and characterize stability in the classical case. We first show how to extend these algebraic, topological, and dynamical concepts from Euclidean space to a connected Lie group of matrices. Building on classical results, we identify a pathway that enables us to formulate conjectures about stability in this broader context. This problem is closely linked to the controllability and observability properties of the system. Fortunately, these properties are well established for both classes of linear systems, whether in Euclidean spaces or on Lie groups. We are confident that these conjectures can be proved in future work, initially for the class of nilpotent and solvable groups, and later for semi-simple groups. This will provide valuable insights that will facilitate, through Jouan’s Equivalence Theorem, the analysis of an important class of nonlinear control systems on manifolds beyond Lie groups. We provide an example involving a three-dimensional solvable Lie group of rigid motions in a plane to illustrate these conjectures.

Roughness-induced boundary-layer instability beneath internal solitary waves

We investigate the effects of bottom roughness on bottom boundary-layer (BBL) instability beneath internal solitary waves (ISWs) of depression. Applying both two-dimensional (2-D) numerical simulations and linear stability theory, an extensive parametric study explores the effect of the Reynolds number, pressure gradient, roughness (periodic bump) height $h_b$ and roughness wavelength $\lambda _b$ on BBL instability. The simulations show that small $h_b$ , comparable to that of laboratory-flume materials ( $\sim$ 100 times less than the thickness of the viscous sublayer $\delta _v$ ), can destabilize the BBL and trigger vortex shedding at critical Reynolds numbers much lower than what occurs for numerically smooth surfaces. We identify two mechanisms of vortex shedding, depending on $h_b/\delta _v$ . For $h_b/\delta _v \gtrapprox 1$ , vortices are forced directly by local flow separation in the lee of each bump. Conversely, for $h_b/\delta _v \lessapprox 10^{-1}$ the roughness seeds perturbations in the BBL, which are amplified by the BBL flow. Roughness wavelengths close to those associated with the most unstable BBL mode, as predicted by linear instability theory, are preferentially amplified. This resonant amplification nature of the BBL flow, beneath ISWs, is consistent with what occurs in a BBL driven by surface solitary waves and by periodic monochromatic waves. Using the $N$ -factor method for Tollmien–Schlichting waves, we propose an analogy between the roughness height and seed noise required to trigger instability. Including surface roughness, or more generally an appropriate level of seed noise, reconciles the discrepancies between the vortex-shedding threshold observed in the laboratory versus that predicted by otherwise smooth-bottomed 2-D spectral simulations.

Preconditioned Single‐step Transforms for Non‐rigid ICP

AbstractNon‐rigid iterative closest point (ICP) is a popular framework for shape alignment, typically formulated as alternating iteration of correspondence search and shape transformation. A common approach in the shape transformation stage is to solve a linear least squares problem to find a smoothness‐regularized transform that fits the target shape. However, completely solving the linear least squares problem to obtain a transform is wasteful because the correspondences used for constructing the problem are imperfect, especially at early iterations. In this work, we design a novel framework to compute a transform in single step without the exact linear solve. Our key idea is to use only a single step of an iterative linear system solver, conjugate gradient, at each shape transformation stage. For this single‐step scheme to be effective, appropriate preconditioning of the linear system is required. We design a novel adaptive Sobolev‐Jacobi preconditioning method for our single‐step transform to produce a large and regularized shape update suitable for correspondence search in the next iteration. We demonstrate that our preconditioned single‐step transform stably accelerates challenging 3D surface registration tasks.

Spin dynamics in linear magnetoelectric material Mn3Ta2O8

We performed inelastic neutron scattering experiments on single crystal samples of a linear magnetoelectric material Mn3Ta2O8, which exhibits a collinear antiferromagnetic order, to reveal the spin dynamics. Numerous modes observed in the neutron spectra were reasonably reproduced by linear spin-wave theory on the basis of the spin Hamiltonian including eight Heisenberg interactions and an easy-plane type single-ion anisotropy. The presence of strong frustration was found in the identified spin Hamiltonian.

Donor and Geometry Optimization: Fresh Perspectives for the Design of Polyoxometalate Charge Transfer Chromophores.

Three linear, dipolar arylimido-polyoxometalate (POM) and one 2-dimensional bis-functionalized arylimido-polyoxometalate charge transfer chromophore, with diphenylacetylene bridges, have been synthesized and studied by spectroelectrochemistry, hyper-Rayleigh scattering (HRS), and DFT/TD-DFT calculations. The linear systems show that with julolidinyl (Jd) and -NTol2 donor groups, the alkyne bridge yields high second-order nonlinear optical (NLO) coefficients β (Jd, β0,zzz = 318 × 10-30 esu; -NTol2, β0,zzz = 222 × 10-30 esu), indeed the Jd compound gives the highest NLO activity of any organoimido-POM to date with minimal decrease in transparency. The bis-functionalized 2D (C2v) POM derivative showed increased activity over its monofunctionalized analogue with no decrease in transparency, although the NLO response was only minimally two dimensional. Spectroelectrochemistry and TD-DFT calculations showed switchable linear optical responses for the monofunctionalized derivatives due to the weakened charge transfer character of the electronic transitions in the reduced state, while TD-DFT also indicated potential for switched NLO responses. These have been demonstrated by electrochemistry-HRS for the Jd compound, but cyclability is limited by relatively poor stability in the reduced state. IR and CV studies for these sterically protected arylimido polyoxometalates indicate that decomposition proceeds via a breakdown of the {Mo6} cluster in the reduced state, rather than simple solvolysis of the Mo≡N bond.

Mean Square Stability and Stabilization for Linear Parabolic Stochastic Partial Difference Systems

This paper studies the mean square stability and stabilization of linear parabolic stochastic partial difference systems, which contain space–time characteristics and stochastic noise. A definition of the mean square stability for this system is proposed. Using stochastic analysis and some mathematical analysis methods, a strict decreasing sequence is constructed to represent the expectation of the sum of squares of the state variable along the spatial dimension. The sufficient conditions of the mean square stability are established based on system parameters, and then the convergence along the time axis is rigorously proven by the Squeeze criterion. Moreover, some stabilization criteria are derived by designing a linear feedback controller. Finally, two examples are given to illustrate the effectiveness of the results.

Stochastic probabilistic robust control for discrete-time system with parametric uncertainties

This paper presents a novel robust controller design method for discrete linear systems with stochastic uncertainties. Traditional probabilistic robust control methods rely on extensive sampling, leading to high computational complexity. To address this issue, Lyapunov stability theory is applied to establish an approximate functional relationship between the system's robust performance indices and control parameters. This innovative approach enables efficient evaluation of system robustness and transforms the control problem into a standard convex optimisation problem. Monte Carlo simulations were used to validate the proposed method's performance under varying system parameters. The results show that the method meets control performance index requirements with high probability and outperforms traditional LMI and LQR control approaches in terms of probabilistic robustness. By achieving a favourable balance between control efficacy and computational efficiency, this approach shows considerable potential for applications requiring stringent control requirements.

Practical tracking control of permanent magnet linear servo system with adaptive fractional-order predefined performance control

Practical tracking control of permanent magnet linear servo system with adaptive fractional-order predefined performance control

Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity

In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The linear inverse model (LIM) is a class of data-driven methods that extract dynamic and stochastic information from finite time-series data of complex systems. In this study, we introduce a new variant of LIM, called colored LIM, which models stochasticity using Ornstein-Uhlenbeck colored noise. Despite the nontrivial correlation between observable and colored noise, we show that colored LIM unveils the desired information merely from the correlation function of the observable. Therefore, this approach not only accounts for the memory effects of environmental noise, traditionally represented by time-uncorrelated white noise in the classical-LIM framework, but does so using the same observational dataset without requiring additional data. Furthermore, we show that colored LIM does not reduce to classical LIM in the white noise limit, underscoring the importance of temporal dependencies in stochastic systems. In this paper, we rigorously develop the colored LIM, explore its connections with the classical LIM, dynamic mode decomposition, and vector autoregressive moving average models, and validate its effectiveness on both ideal linear and nonlinear systems. In addition, we illustrate the potential applications and implications of colored LIM for real-world problems, including the El Niño–southern oscillation and the electricity network of Tohoku University. Published by the American Physical Society 2025

Impulsive Observer of Linear Systems: An Adaptive Impulsive Gain Approach.

This article provides a new impulsive observation approach called impulsive adaptive observer, impulsive adaptive observation (IAO) for a class of linear systems. A discrete-time-based adaptive rule for the impulsive observer gain is designed using only output information at discrete-time intervals (or impulsive instants), overcoming the real-time data requirement of continuous-time adaptive observation frameworks. The IAO effectively estimates the states of a continuous-time system and demonstrates outstanding state tracking performance in practical implementations. Furthermore, the IAO-based feedback controller is designed to stabilize the controlled plant. Stability criteria for the IAO protocols are established, showing improved performance over existing schemes by reducing computational load and enhancing control flexibility. The simulations for the electrical system are presented finally to confirm the effectiveness of the IAO and its control approach.

Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Black-box security of stream ciphers under the quantum algorithm for linear systems of equations

In this paper, we analyse the impact of the HHL quantum algorithm on stream ciphers in a black-box setting. We assume a black-box access to an oracle MS defining the output of the stream cipher. For a state k encapsulating the key material, the value MS·k is the keystream (k1′,k2′,...,kN′) generated by some stream cipher S. We translate this scenario into the quantum setting and describe how the HHL algorithm could be used to attack this construction. Further, we give simple and verifiable criteria under which a black-box attack on stream ciphers with the HHL algorithm is not efficiently feasible. Usually, these criteria follow from already known design principles for symmetric ciphers and should apply to the ciphers used today. We complement the criteria with a simple test, which confirms the resistance of said cipher. Moreover, we use our technique to test the currently used stream ciphers: Trivium, HC-128, and Salsa20.