Composition Law Research Articles

Composition Analysis and Identification of Ancient Glass Products

Ancient glass products are valuable evidences for studying the cultural exchanges between China and the West in ancient times. Because ancient glass is easily weathered by the influence of burial environment, its chemical composition changes, which affects the correct judgment of glass types. This paper mainly makes full use of the known sample data through the establishment of statistical models, classification models, correlation analysis models, and the combination of numbers and shapes, The important indexes affecting surface weathering are studied respectively; The chemical composition law, classification, correlation and difference of glass cultural relics have been established, and a high accuracy identification model of glass cultural relics has been established, which is of great significance to the identification of glass cultural relics.

A new parametrization for ideal classes in rings defined by binary forms, and applications

Abstract We give a parametrization of square roots of the ideal class of the inverse different of rings defined by binary forms in terms of the orbits of a coregular representation. This parametrization, which can be construed as a new integral model of a “higher composition law” discovered by Bhargava and generalized by Wood, was the missing ingredient needed to solve a range of previously intractable open problems concerning distributions of class groups, Selmer groups, and related objects. For instance, in this paper, we apply the parametrization to bound the average size of the 2-class group in families of number fields defined by binary n-ic forms, where n ≥ 3 {n\geq 3} is an arbitrary integer, odd or even; in the paper [A. Swaminathan, Most integral odd-degree binary forms fail to properly represent a square, preprint 2020], we applied it to prove that most integral odd-degree binary forms fail to primitively represent a square; and in the paper [M. Bhargava, A. Shankar and A. Swaminathan, The second moment of the size of the 2-Selmer group of elliptic curves, preprint 2021], joint with Bhargava and Shankar, we applied it to bound the second moment of the size of the 2-Selmer group of elliptic curves.

A composite adaptive robust control for nonlinear systems with model uncertainties

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.

Gradient free cooperative seeking of a moving source

In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum seeking with formation control in order to converge to the extrema faster by minimising the gradient estimation error. By formalising the relationship between the formation and the gradient estimation error, we provide a novel analysis to prove the convergence of the network to a bounded neighbourhood of the field’s time varying extrema. We assume the time-varying field satisfies the Polyak–Łojasiewicz inequality and the gradient is Lipschitz continuous at each iteration. Numerical studies and comparisons are provided to support the theoretical results.

Self-Disciplined Nonsmooth Coordination Control for Battery Energy Storage System in Autonomous DC Microgrids Toward Large-Signal Stability

For a Battery Energy Storage System (BESS)-based autonomous DC microgrid, owing to the coupling complexity between multiple control objectives under a hierarchical control framework, coordination control for large-signal stabilization is well-acknowledged as a non-trivial problem. This paper aims to present a self-disciplined nonsmooth coordination control strategy to address the multi-objective task within one framework. Firstly, a nonsmooth composite regulation law is designed to mitigate the increasing constant power loads (CPLs) by employing a feedforward compensation. Secondly, a dynamic droop strategy aiming for dynamic power allocation for state-of-charging (SOC) balancing of BESS is built based on a nonsmooth dynamic average consensus protocol with low communication cost. Then by utilizing a dynamic power allocation strategy and a large-signal stabilizer for each energy storage unit (ESU), both SOC dynamic balancing and system level large-signal stability can be ensured. Moreover, a fast performance recovery ability can be promised by bringing into two convergence rate coordination factors. Simulation and comparative experimental studies have demonstrated the efficacy of the proposed control strategy.

Multivariable Finite-Time Composite Neural Control via Prescribed Performance for Error Norm

This work investigates finite-time tracking control for a multi-input–multi-output plant with multisource uncertainties. A multivariable finite-time prescribed performance control scheme is proposed, where the norm of the tracking error vector is constrained with a prescribed bound. Due to the positiveness of the norm of the error vector, a novel error transformation is given to transform the “constrained” problem into an equivalent “unconstrained” problem. Meanwhile, the composite neural adaptive law is established to attenuate the effect of multisource uncertainties. The parametric perturbations are counteracted by neural adaptive terms. Time-varying uncertain control gains and external disturbances in the multivariable systems are compensated by adaptively estimating their bounds and applying the Lyapunov control design. To tackle the practical tracking problem, the aforementioned method is integrated into a dynamic-surface-based backstepping framework. Additionally, the practical quaternion-based attitude tracking problem is addressed, in which a quaternion-based form of error-norm constraint is constructed to express the generality and scalability of our proposed.

Reasoning over time into models with DataTime

Models at runtime have been initially investigated for adaptive systems. Models are used as a reflective layer of the current state of the system to support the implementation of a feedback loop. More recently, models at runtime have also been identified as key for supporting the development of full-fledged digital twins. However, this use of models at runtime raises new challenges, such as the ability to seamlessly interact with the past, present, and future states of the system. In this paper, we propose a framework called DataTime to implement models at runtime which capture the state of the system according to the dimensions of both time and space, here modeled as a directed graph where both nodes and edges bear local states (i.e., values of properties of interest). DataTime offers a unifying interface to query the past, present, and future (predicted) states of the system. This unifying interface provides (i) an optimized structure of the time series that capture the past states of the system, possibly evolving over time, (ii) the ability to get the last available value provided by the system’s sensors, and (iii) a continuous micro-learning over graph edges of a predictive model to make it possible to query future states, either locally or more globally, thanks to a composition law. The framework has been developed and evaluated in the context of the Intelligent Public Transportation Systems of the city of Rennes (France). This experimentation has demonstrated how DataTime can be used for managing data from the past, the present, and the future and facilitate the development of digital twins.

Event‐driven fault‐tolerant attitude control of spacecraft with finite‐time disturbance observer under input saturation

AbstractThis paper investigates the attitude stabilization problem for a bandwidth‐constrained spacecraft subjected to model uncertainty, external disturbances, actuator faults, and saturated input. The proposed attitude controller is developed by combining the disturbance observer with an event‐trigger technique to provide disturbance attenuation meanwhile respecting the constraint on the wireless control network. The proposed disturbance observer estimates the lumped disturbance within a finite time, and its output is then fed to the composite control law. The presented control scheme relaxes the use of a priori upper bound knowledge of disturbance and resolves the unwinding problem in the quaternion‐based attitude representation. The closed‐loop stability analysis under the proposed algorithm shows the uniformly ultimately bounded convergence of state trajectories. Moreover, the designed event trigger approach avoids the Zeno behavior. The numerical simulation with comparative analysis illustrates the efficacy of the proposed controller in terms of convergence time, steady‐state bound, rate of control update, and energy consumption.

МЕНЕДЖМЕНТ ПІДПРИЄМСТВА: СУТНІСТЬ ТА ЕЛЕМЕНТНИЙ СКЛАД

The article is devoted to generalization of views on the essence of management in modern economic conditions. The article presents various views on the content of this phenomenon. The author analyzes the essence of management through the prism of considering definitions by transforming historical views and approaches of modern researchers. The key features of modern management are considered, in particular: a rational combination of the market and government regulation; constant adjustment of the organization's goals; the important role of organizational culture; decentralized management structures; social responsibility to employees and society, etc. The economic, legal, socio-psychological, organizational, and technical aspects of management are also considered. Attention is paid to the laws of organization functioning (law of composition; law of proportionality; law of least; law of ontogeny) and the laws of organization development (law of synergy; law of self-preservation; law of awareness-order; law of unity of analysis and synthesis). The key principles of management are considered both in the historical context and in the modern economic environment. In particular, it is noted that for the formation, functioning and development of an organization, it is necessary to adhere to the basic principles of management: resistance to changes in the environment of the organization's functioning; cost-effectiveness of management; the main vector of management actions is the priority of the consumer and ensuring the long-term development of the organization. The author also describes the functionality of management, primarily through the implementation of general functions according to the formula 4 (planning, motivation, organization, control) + 2 (coordination and regulation) and specific functions (management of finance, personnel, trade and technological processes, labor and wage management, inventory management, etc.) Attention is also paid to the main methods of management. The expediency of a critical rethinking of the existing management principles is considered.

Dynamic Event-Triggered Adaptive Neural Output Feedback Control for MSVs Using Composite Learning

This paper investigates the control issue of marine surface vehicles (MSVs) subject to internal and external uncertainties without velocity information. Utilizing the specific advantages of adaptive neural network and disturbance observer, a classification reconstruction idea is developed. Based on this idea, a novel adaptive neural-based state observer with disturbance observer is proposed to recover the unmeasurable velocity. Under the vector-backstepping design framework, the classification reconstruction idea and adaptive neural-based state observer are used to resolve the control design issue for MSVs. To improve the control performance, the serial-parallel estimation model is introduced to obtain a prediction error, and then a composite learning law is designed by embedding the prediction error and estimate of lumped disturbance. To reduce the mechanical wear of actuator, a dynamic event triggering protocol is established between the control law and actuator. Finally, a new dynamic event-triggered composite learning adaptive neural output feedback control solution is developed. Employing the Lyapunov stability theory, it is strictly proved that all signals in the closed-loop control system of MSVs are bounded. Simulation and comparison results validate the effectiveness of control solution.

Enhanced Adaptive Control over Robotic Systems via Generalized Momentum Dynamic Extensions

Adaptive control and parameter estimation have been widely employed in robotics to deal with parametric uncertainty. However, these techniques may suffer from parameter drift, dependence on acceleration estimates and conservative requirements for system excitation. To overcome these limitations, composite adaptation laws can be used. In this paper, we propose an enhanced composite adaptive control approach for robotic systems that exploits the acceleration-free momentum dynamics and regressor extensions to offer faster parameter and tracking convergence while relaxing excitation conditions and providing a clear physical interpretation. The effectiveness of the proposed approach is validated through experimental evaluation on a 3-DoF robotic leg.

Mathematical Aspects of <i>SU</i> (2) and <i>SO</i>(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

Chemical composition and identification of glass products based on generalized linear model

Weathering will cause the proportion of chemical composition of ancient glass products to change, thereby affecting the classification judgment of glass type. In order to reasonably analyze the composition content of ancient glass products, this paper provides a reference for studying the content change trend of glass weathering by exploring whether the appearance of glass cultural relics affects the weathering trend and the weathering composition law. According to the relationship between glass surface weathering and ornamentation, color and glass type, a linear regression model is constructed, and in order to solve the problem of heteroscedasticity in the perturbation term, the OLS robust + standard error method is used to improve the model parameters. The results show that the ornaments are B and C and are more likely to weather, high potassium glass is easy to weather, the color is green is mostly unweathered glass, and the color is black There is a tendency to change to weathered glass. The lower the content of potassium oxide, iron oxide and alumina in high potassium, the easier it is to weather, the higher the silica content, the easier it is to weather, and the regularity of weathering and component content of lead barium compared with high potassium is not obvious.

Composite Terminal Guidance Law for Supercavitating Torpedoes with Impact Angle Constraints

A novel composite terminal guidance law with impact angle constraints is proposed for supercavitating torpedoes to intercept maneuvering warships. Based on an adaptive super-twisting algorithm and nonsingular terminal sliding mode (NTSM), the proposed guidance law can guarantee the finite-time convergence of line-of-sight (LOS) angle error and the LOS angular rate error. The new guidance law is a combination of finite-time stability theory, sliding mode control (SMC), tracking differentiator (TD), disturbance observer (DO), and dynamic surface control. A high-order sliding mode TD is used for denoising, tracking, and differentiating the measured target heading angle. A novel DO, with its finite-time stability proved, is designed to estimate the target lateral acceleration for feedforward compensation to attenuate chattering in control input. In the case of a first-order-lag autopilot, a new kind of tracking differentiator is adopted to compute the first-order time derivative of the virtual control command, which can improve the accuracy of dynamic surface control and avoid the “explosion of items” problem encountered with the backstepping control. Finally, numerical simulation results are presented to validate the effectiveness and superiority of the proposed TD, DO, and the composite guidance law.

A Composite Exponential Reaching Law Based SMC with Rotating Sliding Surface Selection Mechanism for Two Level Three Phase VSI in Vehicle to Load Applications

Voltage source inverters (VSIs) are an integral part of electrical vehicles (EVs) to enhance the reliability of the supply power to critical loads in vehicle to load (V2L) applications. The inherent properties of sliding mode control (SMC) makes it one of the best available options to achieve the desired voltage quality under variable load conditions. The intrinsic characteristic of robustness associated with SMC is generally achieved at the cost of unwanted chattering along the sliding surface. To manage this compromise better, optimal selection of sliding surface coefficient is applied with the proposed composite exponential reaching law (C-ERL). The novelty of the proposed C-ERL is associated with the intelligent mix of the exponential, power, and difference functions blended with the rotating sliding surface selection (RSS) technique for three phase two level VSI. Moreover, the proposed reaching law along with the power rate exponential reaching law (PRERL), enhanced exponential reaching law (EERL), and repetitive reaching law (RRL) were implemented on two level three phase VSI under variable load conditions. A comparative analysis strongly advocates the authenticity and effectiveness of the proposed reaching law in achieving a well-regulated output voltage with a high level of robustness, reduced chattering, and low %THD.

Prescribed‐time regulation of nonlinear uncertain systems with unknown input gain and appended dynamics

AbstractThe prescribed‐time stabilization problem for a general class of uncertain nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed‐time stabilization objective requires convergence of the state vector to the origin in a finite time interval that can be arbitrarily picked (i.e., “prescribed”) by the control system designer irrespective of the system's initial condition. The class of systems considered is allowed to have general nonlinear uncertain terms throughout the system dynamics as well as uncertain appended dynamics (that effectively generate a time‐varying non‐vanishing disturbance signal input into the nominal system). The control design is based on a nonlinear transformation of the time scale, dynamic high‐gain scaling, adaptation dynamics with temporal forcing terms, and a composite control law that includes two components. The first component in the composite control law is analogous to prior dynamic high‐gain scaling‐based control designs, but with a time‐dependent function in place of the unknown input gain, while the second component has a non‐smooth form with time‐dependent terms that ensure prescribed‐time convergence in spite of the unknown input gain and the disturbances. The efficacy of the proposed control design is illustrated through numerical simulation studies on two example systems (a “synthetic” fifth‐order system and a “real‐world” electromechanical system).

Composite adaptive finite‐time fuzzy control for switched nonlinear systems with preassigned performance

SummaryThis article investigates the composite adaptive fuzzy finite‐time prescribed performance control issue of switched nonlinear systems subject to the unknown external disturbance and performance requirement. First, by utilizing the compensation and prediction errors, the piecewise switched composite parameter update law is employed to improve the approximation accuracy of the unknown nonlinearity. Then, the improved fractional‐order filter and error compensation signal are introduced to cope with the influences caused by the explosive calculation and filter error, respectively. Meanwhile, the effect of the compound disturbances consisting of the unknown disturbances and approximation errors is reduced appropriately by designing the piecewise switched nonlinear disturbance observer. Moreover, stability analysis results prove that the proposed preassigned performance control scheme not only ensures that all states of the closed‐loop system are practical finite‐time bounded, but also that the tracking error converges to a preassigned area with a finite time. Ultimately, the simulation examples are given to demonstrate the effectiveness of the proposed control strategy.

Robust Voltage Regulation for DC–DC Converters via a Predictive GPIO-Based Control Approach

Performance degradations of DC-DC converters are caused by various complicated factors. In this brief, the output voltage regulation problem in the presence of input time-delay and load uncertainties is addressed by adopting an observer based composite control approach. Firstly, a predictive generalized proportional-integral observer (PGPIO) is constructed to have accurate state predictions as well as disturbance estimations. Then, by integrating the prediction information and choosing appropriate disturbance compensation gains, the adverse influences of the load disturbance can be effectively eliminated from the output voltage channel. Finally, a composite control law is obtained to realize a better voltage tracking performance. Rigorous stability and performance analysis are presented. To verify the feasibility of the designed controller, some experimental comparisons are illustrated. The comparative results show that a better disturbance rejection performance can be achieved even in the presence of time-delay.

COMPOSITE NEURAL NETWORK LEARNING FROM FRACTIONAL BACKSTEPPING

This paper focuses on parameter convergence and precise modeling for fractional-order nonlinear systems with functional uncertainties via using adaptive backstepping neural network control (ABNNC) and composite learning adaptive backstepping neural network control (CLABNNC). In the ABNNC design, a command filter is proposed, and the neural network approximation system is considered to deal with the unknown function, where an adaptation law is designed to ensure tracking errors converge to an arbitrarily small region near the origin under a strict persistent excitation condition that is too strict for the convergence of adaptive parameters. In order to relax this condition, a composite learning adaptation law is established by taking advantage of the tracking error and the prediction error to update the free parameter of the neural network system. The proposed CLABNNC method can not only ensure the convergence of tracking errors, but also achieve the accurate approximation of functional uncertainties under a weaker interval excitation condition. Finally, a numerical simulation example is put forward to demonstrate the effectiveness of our method.

Composite disturbance observer-based backstepping stabilisation for 3-DOF ship-borne platform with unknown disturbances

ABSTRACT A composite anti-disturbance stabilisation control scheme is presented for the ship-borne platform system with completely unknown disturbances. The completely unknown disturbances consist of external time-varying disturbances and norm-bounded unmodelled dynamics. The composite anti-disturbance control scheme is built through integrating the nonlinear disturbance observer and the robustifying term with the vectorial backstepping technique. The nonlinear disturbance observer is designed to provide the on-line estimations of external time-varying disturbances such that the disturbance compensation term is introduced into the control design. The robustifying term with the adaptive law is employed to attenuate norm-bounded unmodelled dynamics. On the basis of the vectorial backstepping technique, the composite anti-disturbance control law is derived. The composite anti-disturbance control structure consists of the outer layer with the nonlinear disturbance observer for external time-varying disturbance cancellation as well as the inner layer with the vectorial backstepping control together with the robustifying term for unmodelled dynamic attenuation. By means of the Lyapunov stability theory, it is proven that the composite anti-disturbance stabilisation controller can achieve the disturbance rejection and attenuation simultaneously. It is verified by illustrative simulations that the composite anti-disturbance stabilisation control scheme can effectively stabilise the ship-borne stabilisation platform.