Linear Systems Research Articles

Memory State‐Feedback Control for a Linear System With Time‐Varying Delay Based on the Tuning Matrix Search Algorithm

ABSTRACTA multiple augmented Lyapunov function (MALF) is a function that includes more than one augmented matrix, allowing for a more precise evaluation of the relationships between different states within a system and facilitating the analysis of system stability. However, employing multiple augmented matrices can complicate the process of designing controllers. For this issue, this article proposes a controller synthesis algorithm to address the complexity of controller design resulting from multiple augmentation matrices. First, a memory state‐feedback control criterion with tuning matrices is derived by constructing an MALF. Second, a tuning matrix search algorithm is proposed to provide appropriate tuning matrices for the memory state‐feedback control criterion, leading to the determination of optimal controller gains. Finally, the effectiveness and advantage are verified by simulation of load frequency control for in the power system and control for a linear singular time‐delay system.

Efficient second-order accurate exponential time differencing for time-fractional advection–diffusion–reaction equations with variable coefficients

Time-fractional advection–diffusion–reaction type equations are useful for characterizing anomalous transport processes. In this paper, linearly implicit as well as explicit generalized exponential time differencing (GETD) schemes are proposed for solving a class of such equations having time–space dependent coefficients. The implicit scheme, being unconditionally stable, is robust in handling the numerical instabilities in problems where the advection term is dominant. Regarding the error analysis, uniformly optimal second-order convergence rates are derived using time-graded meshes to counter the effect of the inherent singularity of the continuous solution. Implementation of generalized exponential integrators requires computing the action of Mittag-Leffler function of matrices on a vector, or on a matrix in the case of the implicit scheme. For cost-effective implementation, using global Padé approximants these computation tasks get reduced to solving linear systems. A new approach based on Sylvester equation formulation of the resulting linear systems is developed in this paper. This technique leads to significantly faster algorithms for implementing the GETD schemes. Numerical experiments are provided to illustrate the theoretical findings and to assert the efficiency of the Sylvester equation based approach. Application of this approach to an existing GETD scheme for solving a nonlinear subdiffusion problem is also discussed.

GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations

In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently.

Microbiome science of human excrement composting.

Linear waste management systems are unsustainable and contribute to environmental degradation, economic inequity, and health disparities. Among the array of environmental challenges stemming from anthropogenic impacts, the management of human excrement (human feces and urine) stands as a significant concern. Over two billion people do not have access to adequate sanitation, signifying a global public health crisis. Composting is the microbial biotechnology aimed at cycling organic waste, including human excrement, for improved public health, agricultural productivity and safety, and environmental sustainability. Applications of modern microbiome -omics and related technologies have the capacity to support continued advances in composting science and praxis. In this article, we review literature focused on applications of microbiome technologies to study composting systems and reactions. The studies we survey generally fall into the categories of animal manure composting, biosolids composting, and human excrement composting. We review experiments utilizing microbiome technologies to investigate strategies for enhancing pathogen suppression and accelerating the biodegradation of organic matter. Additionally, we explore studies focused on the bioengineering potential of microbes as inoculants to facilitate degradation of toxins such as pharmaceuticals or per- and polyfluoroalkyl substances. The findings from these studies underscore the importance of advancing our understanding of composting processes through the integration of emerging microbiome -omics technologies. We conclude that work to-date has demonstrated exciting basic and applied science potential from studying compost microbiomes, with promising implications for enhancing global environmental sustainability and public health.

Circular agro-economies (CAE): reducing waste and increasing profitability in agriculture

This paper explores the concept of Circular Agro-Economies (CAE), a sustainable agricultural model focused on recycling agricultural by-products to minimize waste and maximize profitability for farmers. In contrast to traditional linear agricultural systems, CAE promotes resource efficiency and the development of new value chains through the reuse of organic materials. The paper examines the environmental, economic, and social benefits of adopting CAE, including waste reduction, cost savings, rural development, and job creation. It also discusses the significant barriers to adoption, such as technological limitations, financial constraints, and policy-related challenges. Finally, practical recommendations for farmers, policymakers, and businesses are provided to support the successful implementation of CAE, highlighting the collaborative efforts needed to overcome existing challenges and realize the full potential of this model. Keywords: Circular Agro-Economies, Agricultural Waste Recycling, Sustainable Agriculture, Resource Efficiency, Rural Development, Profitability in Farming.

Unified linear response theory of quantum electronic circuits

Modeling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic losses, and (ii) semiclassical theory, which captures dynamic dissipation effects well but is only accurate at low frequencies. Here, we develop a unifying theory, valid for arbitrary frequencies, that captures both the small-signal quantum behavior and the non-unitary effects introduced by relaxation and dephasing. The theory allows a multi-level system to be described by a universal small-signal equivalent-circuit model, a resonant RLC circuit, whose topology only depends on the number of energy levels. We apply our model to a double-quantum-dot charge qubit and a Majorana qubit, showing the capability to continuously describe the systems from adiabatic to resonant and from coherent to incoherent, suggesting new and realistic experiments for improved quantum state readout. Our model will facilitate the design of hybrid quantum–classical circuits and the simulation of qubit control and quantum state readout.

Reverse-Bent Modular Coil Structure with Enhanced Output Stability in DWPT for Arbitrary Linear Transport Systems.

Dynamic wireless power transfer (DWPT) systems with segmented transmitters suffer from output pulsations during the moving process. Although numerous coil structures have been developed to mitigate this fluctuation, the parameter design process is complicated and restricted by specific working conditions (e.g., air gaps). To solve these problems, a novel reverse-bent modular transmitter structure is proposed for DWPT in industrial automatic application scenarios such as linear transport systems. Considering the heterogeneous current density distribution in the adjacent region between two coils which causes a drop in magnetic field, the proposed coil structure attempts to eliminate the effects of the adjacent region by bending the terminal parts of each coil reversely to the ferrite layer for shielding. Compared to traditional planar couplers, this structure array can generate a uniform magnetic field over various air gaps. A 100 W laboratory prototype was built to verify the feasibility of the proposed system. The experimental results show that the proposed system achieved a constant output voltage, and the output pulsation was within ±2.3% in the dynamic powering process. The average efficiency was about 88.29%, with a 200 mm transfer distance. When the air gap varied from 20 mm to 30 mm, the system could still retain constant voltage output characteristics.

An efficient Volterra series approach for identifying nonlinear system vibration responses to an excitation

This paper focuses on the issue of nonlinear vibration responses identification of nonlinear systems. An efficient algorithm is presented, in which the nonlinear vibration system under studied is decomposed into a multiple-input/single-output (MISO) linear system with a series of power characterized inputs based on Volterra series, and the nonlinear output responses of different orders are identified by taking power spectra operation to the input and output data, revealing the contributions of each order nonlinearity to the output of the system. Compared to the existing method, the input signal of the system required in the presented approach need not remain unchanged in waveform and adjustable in magnitude. To verify the approach, a classic Duffing–Van der Pol oscillator was simulated, obtaining results very close to the fourth order Runge–Kutta method. Finally, an experiment analysis was carried out, in which the vibration transmission properties of a bolt connection were tested when the bolt was tight and loose, respectively. The results proved that the approach is effective in identifying nonlinear vibration frequency responses.

Interval observer-based consensus tracking for multi-agent systems under Markovian switching topologies with stealthy attack

This article investigates the bounded consensus tracking problem for uncertain linear multi-agent systems (MASs) under Markovian switching topologies in the presence of unknown but bounded disturbances and stealthy attacks. First, a class of interval observers (IOs) is designed to estimate confidence bounds of agents states and stealthy attack signals. The stealthy attack is considered as that the output information is modified by the malicious attacker. Second, distributed control protocols under Markovian switching topologies are proposed for the MASs based on the designed IOs to achieve bounded consensus. The mean-square error bounds depend on the error bounds of disturbances. After rigorous mathematical proofs, some sufficient conditions are acquired for achieving control goals. Simulations are provided to validate the effectiveness of the proposed IOs and control protocols.

A Comprehensive Review of Artificial Intelligence and Machine Learning in Control Theory

Abstract: Traditional control methods, such as proportional-integral-derivative (PID) controllers and linear-quadratic regulators (LQRs), have proven effective for linear and well-modeled systems. However, these methods often perform poorly in nonlinear, complex and dynamic environments. The paper aims to investigate the modern control systems by integrating artificial intelligence (AI) techniques, such as machine learning (ML), reinforcement learning (RL), deep learning, and fuzzy logic, to enhance their adaptive, robust, and predictive capabilities. And it reviews the literature and analyzes AI integration in control systems. The proposed strategies include supervised learning for trajectory optimization and fault detection, reinforcement learning for optimal control in dynamic environments, neural networks for complex nonlinear function approximation, and fuzzy logic for handling uncertainty and imprecise inputs. AI techniques significantly enhance the ability to tackle nonlinear problems and dynamic changes, demonstrating superior performance in applications like self-driving cars adapting to various road conditions and optimal energy distribution in smart grids. Despite the challenges of computational complexity, scalability, and the safety and reliability in the implementation of interpretable AI models, this paper suggests that hybrid approaches combining traditional control and AI techniques, along with the evolution of interpretable AI and convergence with quantum control, hold great promise for advancing AI-driven control systems.

Seasonal Prediction Model for Airborne Pollen Content in Beijing Urban Area

Airborne pollen is considered to be one of the air pollutants that can cause allergic reactions in humans, leading to the occurrence or aggravation of a series of allergic diseases. The latest study showed that the positive rate of pollen allergens in allergic rhinitis patients in urban areas of Beijing exceeded 80%. Accurate prediction of pollen content could provide more effective assistance to susceptible populations. Based on the measured data from multiple stations in the urban area of Beijing during the pollen season from 2021 to 2022, the spatiotemporal distribution characteristics of pollen content were analyzed. The results showed that the main meteorological factors affecting spring pollen content in the urban area of Beijing were daily average wind speed, 3-day average temperature, water vapor pressure, daily average, temperature, and accumulated temperature. The main meteorological factors affecting autumn pollen content were 3-day average temperature, water vapor pressure, minimum surface temperature, and daily average temperature. In addition, it was found that there was a consistent spatial correlation between the current air pollen content and meteorological elements in the urban area of Beijing, but this correlation had significant seasonal differences. Furthermore, the Granger causality test method was applied to select the main meteorological factors that affected airborne pollen content in the urban area of Beijing, and two prediction models for air pollen content in the Beijing urban area for different seasons were established based on the support vector machine method （SVM） and multiple linear regression theory. The test of the prediction results for 2023 showed that both the SVM model considering seasonal differences and the multiple linear regression model could predict the daily distribution trend of pollen content well. The overall correlation coefficients between the predicted pollen content and the measured values were 0.693 and 0.636 （P <0.01）, respectively. Additionally, both models had good predictive ability for several severe content pollen pollution events within the year. In the spring of 2023, the prediction accuracy of the SVM model and linear model were 61.2% and 60.1%, respectively. During autumn, the prediction accuracy was 68.1% and 66.7%, respectively. The performance was better than that of existing business models, especially in the cross-level error improvement of heavy pollution event prediction. The research results provide reference value for further improving the prediction technology of airborne pollen content in the Beijing area.

Method for Constructing a Compact Component Mode Synthesis Model for Analyzing Nonlinear Normal Modes of Structures with Localized Nonlinearities

Abstract Nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations, especially for systems with numerous degrees-of-freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis (CMS) technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. The proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the CMS modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with a significant reduction in computational costs.

CONECTANDO CONCEITOS: O IMPACTO DOS MAPAS MENTAIS DIGITAIS DINÂMICOS NA APRENDIZAGEM DE SISTEMAS LINEARES

Traditional teaching methods tend to emphasize verbal and linear learning, focusing on isolated information rather than identifying relationships between concepts. However, building meaningful understanding requires visualizing these conceptual interconnections. The shift from a linear approach to integrated network models, such as mind maps, facilitates this knowledge organization, allowing students to develop a deeper understanding of concepts. With the advent of distance learning, additional challenges arise in the production of teaching materials, requiring critical reflection on the potentialities and challenges of digital technologies in pedagogical practice. Therefore, this research investigates the effectiveness of using dynamic digital mind maps (DDMM) in learning Electrical Engineering, focusing on the Linear Systems course. The study aims to evaluate, through a data collection instrument, how mind maps can assist students in understanding mathematical and abstract concepts, highlighting two perspectives: how students learn, and their perceptions of meaningful learning based on Digital Educational Resources. The experience emphasized a lesson plan for knowledge construction in the face of the challenges of 21st-century engineering education, developing competencies and skills for solving real and interdisciplinary problems.

A cloud-edge framework for energy-efficient event-driven control: an integration of online supervised learning, spiking neural networks and local plasticity rules

Abstract This paper presents a novel cloud-edge framework for addressing energy constraints in complex control systems. Our approach centers around a learning-based controller using Spiking Neural Networks (SNN) on physical plants. By integrating a biologically plausible learning method with local plasticity rules, we harness the energy efficiency, scalability of the newtwork, and low latency of SNNs. This design replicates control signals from a cloud-based controller directly on the plant, reducing the need for constant plant-cloud communication. The plant updates weights only when errors surpass predefined thresholds, ensuring efficiency and robustness in various conditions. Applied to linear workbench systems and satellite rendezvous scenarios, including obstacle avoidance, our architecture dramatically lowers normalized tracking error by 96% with increased network size. The event-driven nature of SNNs minimizes energy consumption, utilizing only about 11.1 × 104 pJ (0.3% of conventional computing requirements). The results demonstrate the system’s adjustment to changing work environments and its efficient use of energy resources, with a moderate increase in energy consumption of 37% for dynamic obstacles, compared to non-obstacle scenarios.

Machine Learning Model for the Prediction of Hubbard U Parameters and Its Application to Fe-O Systems.

Without incurring additional computational cost, the Hubbard model can prevalently address the electron self-interaction problems of the local or semilocal exchange-correlation functions within density functional theory. However, determining the value of the Hubbard parameter, U, promptly, efficiently, and accurately has been a long-standing challenge. Here, we develop a method for predicting the Hubbard U of iron oxides by establishing a potential relationship through machine learning fitting of structural fingerprints and the U evaluated by the linear response-constrained density functional theory method. This method performs well in calculating the properties of wüstite, hematite, and magnetite, aligning with experimental measurements or more costly hybrid functional results. Using this method, we redefine the convex hulls of the Fe-O system at 0, 50, and 100 GPa; the obtained results are in good agreement with experimental observations. We also provide insights into the debates surrounding the high-pressure phases of Fe2O3 and Fe3O4.

Theoretical Evaluation of Complex Dielectric Constant for Gamma Relaxation of Poly(methyl methacrylate), A Study of Quantum Chemistry and Linear Response Theory.

It is widely accepted that the γ relaxation of poly(methyl methacrylate) (PMMA) arises from the hindered rotational motion of the side chain around the C-C bond, which links to the main chain. However, the physical model to explain this process has been unknown. The hybrid density functional theory calculation showed that the PMMA intramolecular hindered rotation has an activation energy of 6.53 kcal/mol. This activation energy causes the friction coefficient to the intramolecule to hinder rotation. The qualitative value of the friction coefficient was evaluated on the basis of linear response theory by using the calculated value of the activation energy. The Lorentz model is adopted to calculate the complex dielectric constant of the γ relaxation using the calculated value of the friction coefficient. The calculated value of the complex dielectric constant agreed reasonably well with experimental results.

Minimum-Time Control of a Linear System With Input Saturation: A Practical Approach

Abstract A simple algorithm is presented to find near-minimum-time control inputs for a controllable continuous-time linear time-invariant system with any number of states and inputs. The well-known digital deadbeat control algorithm is modified to satisfy input constraints, and the design issue is the selection of sampling period to minimize the time required to reach the desired final state. During each sampling period, the input required to place all the poles at the origin of z-plane (deadbeat control) via state feedback is computed. If the infinity norm of the deadbeat input exceeds the input constraint, the input is found by placing the poles as close to the origin as possible. A sufficient condition for the system stability is developed. Numerical examples illustrate that this algorithm can lead to true time-optimal control or near time-optimal control.

Constrained solutions of generalized coupled discrete-time periodic matrix equations with application in state observer design for linear periodic systems

PurposeIt is desired to provide a diversified iterative scheme for solving the constrained solutions of the generalized coupled discrete-time periodic (GCDTP) matrix equations from the perspective of optimization.Design/methodology/approachThe paper considers generalized reflexive solutions of the GCDTP matrix equations by applying the Jacobi gradient-based iterative (JGI) algorithm, which is an extended variant of the gradient-based iterative (GI) algorithm.FindingsThrough numerical simulation, it is verified that the efficiency and accuracy of the JGI algorithm are better than some existing algorithms, such as the GI algorithm in Hajarian, the RGI algorithm in Sheng and the AGI algorithm in Xie and Ma.Originality/valueIt is the first instance in which the GCDTP matrix equations are solved applying the JGI algorithm.

DUALITY: DETECTABILITY VERSUS STABILIZABILITY IN THE STOCHASTIC CONTEXT

The aim of this paper is to extend to the stochastic framework the well known duality relation between the detectability property and the stabilizability property of a finite dimensional, linear time invariant, deterministic system. We consider continuous time linear stochastic systems having the state space representation described by a system of Itˆo differential equations with periodic coefficients possibly subject to some stochastic perturbations modeled by a standard homogeneous Markov process with a finite number of states. It will be seen that in the case when the given system is affected by jump Markov perturba tions a state space representation of the dual triple may be rigorously defined if and only if the transition probability matrix of the Markov process is double stochastic (in the sense that the sums of all elements from its each row and each column are equal 1).

Capabilities and limitations of smoothed particle hydrodynamics for the simulation of two‐phase flow instabilities

AbstractSmoothed particle hydrodynamics (SPH) is a mesh‐free, Lagrangian particle‐based method that is able to simulate multiphase flows in an economical manner. However, its ability to capture the flow regimes and regime transitions in two phase (liquid‐gas) internal flows, such as pipe or channel flows is not yet generally established. To address this lack in understanding, we first examine a laminar rising bubble case in order to evaluate the fluid‐fluid interface representation and transient interface evolution by the solver. With a focus towards the transition mechanism from a stratified flow regime to a slug flow regime, we investigate the Kelvin–Helmholtz instability (KHI) both qualitatively and quantitatively, initially focusing on a low density ratio () and then extending it to a high density ratio (). For the low density ratio, we conduct an analysis of the temporal evolution and demonstrate that the SPH solver captures the initial exponential growth in qualitative agreement with inviscid linear stability theory (LST) and reference numerical data for shear‐dominated flow with Richardson number . By conducting eight additional simulations for various for the high density ratio, we demonstrate that the numerically obtained parameter value for instability is around , which is in reasonable agreement with the theoretically expected value of . Based on the SPH results obtained for the range , we suggest a simple parameterization of the reduction of the effective growth rate proportional to .