Low-order System Research Articles

Predefined-time stabilisation of stochastic low-order nonlinear systems with asymmetric output constraint

This paper researches the predefined-time stabilisation problem for a class of stochastic low-order nonlinear systems with asymmetric output constraint whose nonlinearities satisfy high-order and low-order growth conditions. By introducing a novel nonlinear transformation and utilising the adding a power integrator technique, a continuous state feedback controller is designed. The proposed control scheme can guarantee that the output constraint will not be violated almost surely and the trivial solution of the closed-loop system is stochastic predefined-time stable. Finally, two simulation examples are provided to demonstrate the effectiveness of this control method.

Finite-time output feedback control for a class of stochastic low-order nonlinear systems with output function

This paper studies the problem of finite-time output feedback stabilisation for a class of stochastic low-order nonlinear systems with output function. Under the assumption that output function is continuous, by generalising the adding a power integrator technique, constructing a new implementable reduced-order observer and using the stochastic finite-time stability criterion, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee finite-time stability in probability of the closed-loop system. A simulation example is provided to verify the effectiveness of the proposed design method.

Using the check dam deposit for an individual event to document the sources and erosional loss of sediment-associated organic carbon from a small catchment on the Chinese Loess Plateau

Information on the sources and fate of organic carbon mobilized by soil erosion is crucial for understanding the impact of erosion on carbon (C) cycling. However, few studies have evaluated this in low-order stream systems. In this study, we adopted a novel approach, that used the sediment deposited behind a check dam constructed at the outlet of the Fengzigou catchment (0.91 km2) on the Chinese Loess Plateau by a single high magnitude storm event, to simplify the field sampling requirements. The total sediment-associated organic carbon (TOC) was fractionated into particulate organic carbon (POC) and mineral associated organic carbon (MOC). These results were combined with those from a sediment source tracing exercise. This made it possible to explore further the source and loss of the sediment-associated organic carbon. The results showed that the inter-gully areas contributed the most eroded TOC (52.3 ± 7.6 %) and, together with the gully walls, represented the main TOC source. The primary contributor of the POC fraction in the deposited sediment was the inter-gully areas (80.5 ± 12.6 %), whereas the gully walls were the main contributor of the MOC fraction (54.9 ± 10.2 %). The total output of sediment produced by the event was 1304 ± 48 t and the equivalent value for sediment-associated TOC was 2.94 ± 0.26 t, of which the POC fraction accounted for 27.6 ± 3.6 % and the MOC fraction 72.4 ± 9.8 %. The TOC lost (0.3 ± 0.02 t) through the mobilization and delivery processes was 10.2 ± 1.2 % of the TOC mobilized by erosion, and the lost carbon was dominated by the POC fraction (86.7 ± 8.8 %). The specific TOC output from the catchment associated with the event documented was 0.3 t km−2. This work demonstrates the potential for erosion-induced carbon redistribution to provide a source for atmospheric CO2 in the study area.

A comparative study of predicting high entropy alloy phase fractions with traditional machine learning and deep neural networks

Predicting phase stability in high entropy alloys (HEAs), such as phase fractions as functions of composition and temperature, is essential for understanding alloy properties and screening desirable materials. Traditional methods like CALPHAD are computationally intensive for exploring high-dimensional compositional spaces. To address such a challenge, this study explored and compared the effectiveness of random forests (RF) and deep neural networks (DNN) for accelerating materials discovery by building surrogate models of phase stability prediction. For interpolation scenarios (testing on the same order of system as trained), RF models generally produce smaller errors than DNN models. However, for extrapolation scenarios (training on lower-order systems and testing on higher order systems), DNNs generalize more effectively than traditional ML models. DNN demonstrate the potential to predict topologically relevant phase composition when data were missing, making it a powerful predictive tool in materials discovery frameworks. The study uses a CALPHAD dataset of 480 million data points generated from a custom database, available for further model development and benchmarking. Experiments show that DNN models are data-efficient, achieving similar performance with a fraction of the dataset. This work highlights the potential of DNNs in materials discovery, providing a powerful tool for predicting phase stability in HEAs, particularly within the Cr-Hf-Mo-Nb-Ta-Ti-V-W-Zr composition space.

Intelligent cooperative control for flexible landing on small celestial bodies

In view of the potential landing risks in small celestial body landing missions, the concept of flexible landing has been proposed in recent years. By employing a flexible lander with structural compliance to complex surface topography, the risks of rebound or overturning upon touchdown can be reduced. During flexible landing, the overall motion of the flexible lander is controlled by several nodes embedded in the flexible structure. Due to the flexible deformation, the motion among the nodes is intricately coupled, posing challenges to the control algorithm design. To address this problem, an intelligent cooperative control method for flexible landing is proposed in this paper. By decomposing the flexible internal force into a low-order principal term with specific physical interpretation and an unmodeled high-order residual term, the coupling relationship among the nodes is characterized. On this basis, the low-order dynamics system is reconstructed into a piecewise affine system, upon which a multi-node cooperative optimal controller is designed. A long-short-term memory recurrent neural network is further established to compensate for the unmodeled high-order term. Through the combination of the low-order principal control and the high-order intelligent compensation, a feasible approach for achieving flexible landing is obtained. Finally, the effectiveness of the proposed control method is verified via 433 Eros-based flexible landing simulations.

Approximating printed circuit heat exchangers dynamics in a sCO2 RCBC as a low-order system via an optimal time constant

The low-order approximation emerges as a promising method for capturing the dynamic behavior of Printed Circuit Heat Exchangers (PCHEs) in sCO2 Recompression Closed Brayton Cycles (RCBCs). However, two primary challenges hinder widespread adoption: concerns regarding feasibility and the determination of key parameters, such as the time constant. To address these challenges, this study first affirms the feasibility of approximating PCHE's dynamic behaviors with a low-order system. In specific, the validity of first-order approximation on the dynamics of high-temperature recuperator (HTR) with mild non-linear property variations is initially assumed. However, a discrepancy is noticed under various operating conditions by employing the same time constant after being compared with the reference model (SCOPE). Then, a novel concept of the optimal time constant, τop, is introduced to underscore the influence of operating conditions on parameter accuracy. Through extensive parameter sweeping, the impact of operating conditions on approximation error is evaluated from two perspectives. First, utilizing τop effectively reduces approximation errors to acceptable levels. The mean squared error remains below 2°C2 for mass flow rate fluctuations below 32.5 kg/s, and below 4°C2 for temperature variations below 40°C. Second, the optimal time constant is significantly influenced by mass flow rate, notably affected by geometry configuration, and minimally influenced by hot inlet temperature. Additionally, this study provides insights for design optimization and control strategy selection, as the findings highlight the trade-off between response speed and thermal performance, and the relatively rapid response of sCO2-PCHEs to temperature control, compared with mass flow rate control.

MODEL ORDER REDUCTION USING EIGEN SPECTRUM ANALYSIS AND ROUTH ARRAY METHOD

The author suggests a hybrid technique to reduce the high order dynamic systems. The suggested approach uses the Routh array method to obtain the coefficients of the numerator and the Eigen Spectrum Analysis of the original system to generate the denominator polynomial of the lower order system, which is preserved in the reduced model. This technique is easy and simple and generates stable reduced models if the original high- order system is stable. The suggested technique is illustrated with the help of the numerical example taken from the literature

Wave power calculation of a large periodic array of bottom-hinged paddle wave energy converters using Floquet–Bloch theory

In this study we consider a wave energy farm consisting of a large number of bottom-hinged paddles. The paddles are arranged in a doubly-periodic manner, with a finite number of identical rows and each row containing an infinite number of paddles. Each paddle is attached to its own damper and spring, allowing power to be generated through its pitching motion. Unlike previous studies into paddle arrays, we envisage compact arrays consisting of small devices arranged across a large number of rows. The mathematical analysis of this proposed configuration is best suited to methods that exploit the periodicity of the array. It is shown that the velocity potential everywhere within the array can be described by an expansion in terms of suitably-defined Floquet–Bloch eigenmodes and this allows the solution to the scattering problem involving waves incident upon the array to be determined by a simple low-order system of equations. The method used in this study is exact within the setting of linearised water waves and has all of the advantages of classical low-frequency multi-scale homogenisation without the low-frequency restriction. It may also be regarded as a natural extension of the well-known wide-spacing approximation without the large separation restriction. Although the focus of this paper is on the mathematical approach to the solution of the problem, we provide a range of results to illustrate the performance of this proposed wave energy converter concept.

Efficient strategy for topology optimization of stochastic viscoelastic damping structures

In this study, the dynamic topology optimization (TO) of stochastic viscoelastic damping structures (VDSs) is performed for the first time. However, the expensive computation cost seriously hinders the TO process. To address this problem, an efficient strategy is proposed. On the one hand, in the stochastic structural response analysis, a fully adaptive method based on direct probability integral method is presented to determine the number and locations of samples. Meanwhile, to improve the computational efficiency of structural response for each sample, a piecewise model-order reduction method based on Krylov subspace is adopted to generate the orthonormal basis and project the original large-scale system onto a low-order system. On the other hand, to overcome the optimization challenge arising from large number of design variables in the density-based topology method, a material-field series-expansion method is employed to describe the topology layout and significantly reduce the number of design variables. Moreover, the sensitivity of the optimization model is derived by the adjoint method and the method of moving asymptotes (MMA) is used to efficiently update the design variables. Some numerical examples comprehensively demonstrate the effectiveness and efficiency of the proposed strategy. The results indicate that the uncertainty of structural parameters greatly affect both the topology layout of VDS and vibration damping capacity.

Fast finite-time control for a class of stochastic low-order nonlinear system with uncertainties

This work explores the challenge of adaptive fast finite-time control for stochastic low-order nonlinear systems with uncertainties. It introduces an improved practical finite-time criterion that aims to achieve accelerated convergence. The criterion aims to extend to a larger range of stochastic nonlinear systems, accommodating state uncertainties and integrating Lyapunov functions with varying powers to ensure rapid convergence in the presence of uncertainties. The entire control design approach is based on the backstepping method. Specifically, fuzzy logic systems are employed in the recursive design of controllers and adaptive laws to address complex uncertain terms. Additionally, the desired magnitude target powers of the Lyapunov function in the criterion are effectively obtained by a clever overlapping selection of parameters. Finally, this study demonstrates the practical finite-time stability of stochastic low-order uncertain nonlinear systems and validates the effectiveness of the proposed approach through simulation example, highlighting its ability to achieve fast convergence.

Seasonal particulate organic carbon dynamics of the Kolyma River tributaries, Siberia

Abstract. Arctic warming is causing permafrost thaw and release of organic carbon (OC) to fluvial systems. Permafrost-derived OC can be transported downstream and degraded into greenhouse gases that may enhance climate warming. Susceptibility of OC to decomposition depends largely upon its source and composition, which vary throughout the seasonally distinct hydrograph. Most studies on carbon dynamics to date have focused on larger Arctic rivers, yet little is known about carbon cycling in lower-order rivers and streams. Here, we characterize the composition and sources of OC, focusing on less studied particulate OC (POC), in smaller waterways within the Kolyma River watershed. Additionally, we examine how watershed characteristics control carbon concentrations. In lower-order systems, we find rapid initiation of primary production in response to warm water temperatures during spring freshet, shown by decreasing δ13C-POC, in contrast to larger rivers. This results in CO2 uptake by primary producers and microbial degradation of mainly autochthonous OC. However, if terrestrially derived inorganic carbon is assimilated by primary producers, part of it is returned via CO2 emissions if the autochthonous OC pool is simultaneously degraded. As Arctic warming and hydrologic changes may increase OC transfer from smaller waterways to larger river networks, understanding carbon dynamics in smaller waterways is crucial.

Modeling of an all-solid-state battery with a composite positive electrode

All solid-state batteries are considered as the most promising battery technology due to their safety and high energy density. This study presents an advanced mathematical model that accurately simulates the complex behavior of all-solid-state lithium-ion batteries with composite positive electrodes. The partial differential equations of ionic transport and potential dynamics in the electrode and electrolyte are solved and reduced to a low-order system with Padé approximation. Moreover, the imperfect contact and the electrical double layers at the solid-solid interface are also taken into consideration. Subsequent experiments are conducted for the blocked cell and half-cells to extract parameters. Next, the parameterized model is validated with extensive experimental data from NCM811/LPSC/Li4.4Si batteries, illustrating the superior capability of predicting cell voltage with an average RMSE of 19.5 mV for the discharging/charging phases and 2.8 mV for the end of relaxation under a total of 15 conditions. From the simulations, it can be concluded that the limiting factors for battery performance are overpotentials caused by concentration polarization within positive particles and interface reactions. Finally, through a parameter sensitivity analysis, we offer strategic guidelines for optimizing battery performance, thus enhancing the development efficiency of ASSBs.

Identification of Low Order Systems in a Loewner Framework

This paper considers the problem of non-parametric identification of low-order models from time-domain experimental data using a combination of Caratheodory Fejer and Loewner-based interpolation, followed by a Loewner matrix Balanced Reduction (LBR) step. As we show in the paper, the Loewner matrix is an estimator for the trace norm of a system, playing a role similar to the one played by the Hankel matrix. However, utilizing Zolotarev numbers to establish decay rate bounds for singular values reveals that the decay of singular values in the Loewner matrix is considerably faster than that in the Hankel matrix. Thus, Loewner-based methods yield lower order systems, with the same error bound, than comparable ones based on Hankel matrices. The effectiveness of our method is demonstrated through a numerical example.

ПРОБЛЕМИ ТА ПЕРСПЕКТИВИ РОЗВИТКУ АВТОМАТИЗОВАНИХ СИСТЕМ УПРАВЛІННЯ ЦІЛЕВКАЗАННЯ

The justification of the need to improve the automated control process in the system of automatic targeting testing is presented. The modern Armed Forces of Ukraine use means of automation at all levels of command of the troops and managing the means of defeat. In parallel with the automation of the management process at all levels, the shadows of recent years indicate a shift of attention towards the lower management levels. The command systems at these levels collect, process and analyse information necessary to optimize the management of the actual combat assets. The specific fire task to combat crew, its transfer and delivery to the contractor is an important point in the process of such control. A central part of the task statement is targeting i.e. a brief, clear and understandable message about the location of the target and other information about it. The guaranteed transmission of target instruction from any level of control to the means of destruction is one of the directions of development and improvement of automated control systems for military purposes. The automated method for achieving the target-setting provides a minimum time for setting the firing task and carrying it out. However, in order for it to be revived, information on the full identification of targets at the different levels of control and sufficiently accurate information on the location of its forces and assets is necessary. In many cases, the dynamic properties of such control systems are described by high-order differential equations. The implementation of optimal speed in such cases faces a number of technical difficulties related to the need to calculate and implement the number of intervals of control action.The number of intervals is equal to the order of the differential equation of the system. In this case, it is advisable to move to a quasi-optimal control with the number of controls switching equal to three. Reducing the number of switches will not only simplify the functions of the microprocessor in such a control system, but also increase its reliability. Optimum system theory illuminates the way forward and points to unused reserves of existing automatic control systems. The development of mathematical theory is largely determined by the development of methods of synthesis of optimal systems. Bellman R. and Feldbaum O. first formulated and proved the theorem of n intervals or n switching by control systems. According to the n interval theorem, the number of switches can be reduced by replacing the n-order control system with an equivalent lower-order system. According to the hypothesis of Academician A.Y. Ishlinsky, a third-order system can be found for any n-order system. The paper presents a numerical experiment confirming the hypothesis of Academician A.Y. Ishlinsky about the possibility of presenting a high-order system equivalent to a third-order system. The problem of identifying the dynamics of technological processes is solved by acceleration curves. The use of direct numerical methods is limited in some cases by the inability to implement the input of the required form. In this case, object identification is carried out by a conventional differential equation of order 4. A type of differential equation of order 3 is also known. The values of the parameters at which the solutions of the differential equations of order 4 and order 3 are most closely related are found. To solve the problem, the Nelder-Mead method is used. The solution of the original differential equation is proposed to be found by the Runge-Kutt-Merson method. The obtained results make it possible to simplify the process of object management in the systems of automatic targeting testing. The numerical experiments carried out confirmed the conjecture of Academician A.Y. Ishlinsky that the n-order system can be represented by an equivalent system of order 3. Thus, to reduce the time required to collect, process and analyze information necessary for the management of combat assets.

Model based optimization of fertilization with treated wastewater reuse

Treated wastewater contains vital crop nutrients and offers the possibility for not only irrigation but also fertilization from a renewable source. The feasibility of replacing conventional chemical fertilizers with wastewater reuse is investigated, focusing on the implications of coupling irrigation and fertilization. We consider a multi-objective dynamic optimization problem of crop irrigation and fertigation with treated wastewater, with the objectives of maximizing crop production and minimizing environmental costs. A double modeling method is proposed that relies on both a modern complex crop model – the simulation model – and a low-order dynamical systems model – the control model – to solve efficiently the optimization problem, whilst maintaining a detailed representation of the system of study. Through a case study, we show that it is possible to achieve high levels of crop production. The maximum nutrient concentration of the reclaimed waters CNmax is a key parameter of the system performance: when CNmax is high enough, it is possible to substitute entirely conventional fertilization for irrigation with wastewater. However, when CNmax is small, our results highlight that meeting crop needs would require excessive irrigation, with the added risk of dilution of the nutrients already present in soil. We find that there is a maximum amount of nutrients that can be delivered efficiently to the soil-crop system and identify the conditions when wastewater irrigation is only be capable of providing a portion of the crop needs and should be complimented with other sources of fertilization. The double modeling method and the control model provide a means to estimate the key quantities to determine the best strategy to adopt for wastewater fertilization, as well as to obtain efficient and simple controls, that could be applied in practice.

An H1-Galerkin Space-Time Mixed Finite Element Method for Semilinear Convection–Diffusion–Reaction Equations

In this paper, the semilinear convection–diffusion–reaction equation is split into a lower-order system by introducing the auxiliary variable q=a(x)ux. An H1-Galerkin space-time mixed finite element method for the lower-order system is then constructed. The proposed method applies the finite element method to discretize the time and space directions simultaneously and does not require checking the Ladyzhenskaya–Babusˇka–Brezzi (LBB) compatibility constraints, which differs from the traditional mixed finite element method. The uniqueness of the approximate solutions u and q are proven. The L2(L2) norm optimal order error estimates of the approximate solution u and q are derived by introducing the space-time projection operator. The numerical experiment is presented to verify the theoretical results. Furthermore, by comparing with the classical H1-Galerkin mixed finite element scheme, the proposed scheme can easily improve computational accuracy and time convergence order by changing the basis function.

A Quantile-Conserving Ensemble Filter Framework. Part II: Regression of Observation Increments in a Probit and Probability Integral Transformed Space

Abstract Traditional ensemble Kalman filter data assimilation methods make implicit assumptions of Gaussianity and linearity that are strongly violated by many important Earth system applications. For instance, bounded quantities like the amount of a tracer and sea ice fractional coverage cannot be accurately represented by a Gaussian that is unbounded by definition. Nonlinear relations between observations and model state variables abound. Examples include the relation between a remotely sensed radiance and the column of atmospheric temperatures, or the relation between cloud amount and water vapor quantity. Part I of this paper described a very general data assimilation framework for computing observation increments for non-Gaussian prior distributions and likelihoods. These methods can respect bounds and other non-Gaussian aspects of observed variables. However, these benefits can be lost when observation increments are used to update state variables using the linear regression that is part of standard ensemble Kalman filter algorithms. Here, regression of observation increments is performed in a space where variables are transformed by the probit and probability integral transforms, a specific type of Gaussian anamorphosis. This method can enforce appropriate bounds for all quantities and deal much more effectively with nonlinear relations between observations and state variables. Important enhancements like localization and inflation can be performed in the transformed space. Results are provided for idealized bivariate distributions and for cycling assimilation in a low-order dynamical system. Implications for improved data assimilation across Earth system applications are discussed.

A Two-Stage Data-Driven Method for Estimating the System Inertia Utilizing Event-Driven PMU Measurements

With the increasing penetration level of renewable energy resources with less system inertia, accurate estimation of the power system inertia has become a critical issue for maintaining the frequency stability of the entire power system. To tackle out this challenging task, a two-stage data-driven method is proposed in this paper for estimating the system inertia from disturbed PMU measurements. First, by integrating its low-order system frequency response model with the first-order turbine model, analytical expressions of the frequency response under the steady-state and these transient oscillatory components are derived. Then, based on this parametric model, a two-stage estimation algorithm will be developed. At the first stage, system parameters of oscillatory components can be extracted from PMU measurements by Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). By utilizing frequency measurement data from PMUs and those estimated parameters from the ESPRIT algorithm, a weighted nonlinear least square approach is applied at the second stage to estimate physical parameters such as system inertia, damping coefficient, turbine time constant, and regulation coefficient. To validate the effectiveness of the proposed method, simulation studies of IEEE 39- bus system is investigated. Historical PMU measurements from various contingencies of Taiwan Power System will also be explored. All of these results demonstrated that the proposed method provides satisfactory performances with the mean relative error less than 10%. Comparisons with other existing methods are performed to demonstrate the advantage of the proposed method.

Formation of information decision support system in the diagnostics of management efficiency of enterprise’s financial and economic activity

The complexity management of financial and economic activity of the enterprise requires the search for qualitatively new approaches to the formation, systematization and analysis of information in order to identify and solve the problems of developing a strategy and tactics for the development of the enterprise. The purpose of the paper is the formation and justification of the structure of information support system’s formation concerning decisions in the diagnostics of financial and economic activity of the enterprise management efficiency, which is aimed at increasing the effectiveness of management decision-making of a strategic and tactical nature. The tasks of the information support system for diagnostics of financial and economic activity of the enterprise management efficiency have been determined, which allows to eliminate a number of causes of information uncertainty in the process of managing the enterprise's activities. It is proved that the system of information support for decision-making in the diagnosis of financial and economic activity of the enterprise management efficiency should be considered in the form of three interconnected subsystems, which are lower-order systems, namely: the financial and information system, the system of financial and information diagnostics and the system of detected financial problems. The author proposed a comprehensive functionality of all components of the information support system for decision-making support in the diagnosis of the management of the financial and economic activities of the enterprise, which will increase the validity and effectiveness of the management decisions made, taking into account the influence of the instability of the external and internal environment of its functioning.

An effective controller design strategy for higher order systems

The recent methods that guarantee the stability of the reduced-order models are Mihailov stability, improved Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization. Further, these methods could overcome the limitations such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. This research emphasizes the design of the proposed compensating algorithm by using an additional open loop zero for the stable reduced-order models of large-scale single-input single-output linear time-invariant continuous time systems. The results of the proposed algorithm are compared with the existing compensating methods and the design is validated and illustrated numerically.