Initial State Of System Research Articles

Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions

The Helmholtz oscillator is a nonlinear mixed‐parity oscillator that models the asymmetric vibrations of many engineering and scientific systems. This paper investigated a general and completely integrable form of the Helmholtz oscillator and derived its exact periodic solution from the first integral of the governing differential equation. The considered Helmholtz oscillator has general linear and nonlinear stiffness constants, is subject to a constant force, and has arbitrary initial conditions. Its exact time period was derived in terms of the complete elliptic integral of the first kind, while the exact displacement was derived in terms of the Jacobi elliptic sine function. The validity of the exact solutions was verified for various combinations of the system parameters and initial conditions by comparing with numerical solutions. The exact solutions and numerical solutions were found to match perfectly. Furthermore, the exact solution was applied to analyze the vibration response of real‐world systems that could be modeled as Helmholtz oscillators. The present exact solutions provide benchmark solutions that could be used to determine the accuracy of new and existing approximate solutions for the Helmholtz oscillator.

Fixed-time nonsingular terminal sliding mode control for trajectory tracking of uncertain robot manipulators

Fixed-time nonsingular terminal sliding mode control for trajectory tracking of uncertain robot manipulators

Prescribed time group output consensus for multiagent system via an observer-based approach

This paper deals with the problem of prescribed-time group output consensus for multi-agent systems via an observer-based approach. Distributed observers are designed to estimate the output information when the agents’ states are not easy to measure or unavailable. The multi-agent systems can achieve group output consensus within a user-preset time, which is independent of the system parameters and initial states. By using algebraic graph theory, Lyapunov stability and matrix theory, sufficient conditions with designed parameters are given to realise prescribed time group output consensus. Finally, a numerical example is conducted to verify the results.

Synchronous behaviors of three coupled liquid crystal elastomer-based spring oscillators under linear temperature fields.

Self-oscillating coupled systems possess the ability to actively absorb external environmental energy to sustain their motion. This quality endows them with autonomy and sustainability, making them have application value in the fields of synchronization and clustering, thereby furthering research and exploration in these domains. Building upon the foundation of thermal responsive liquid crystal elastomer-based (LCE-based) spring oscillators, a synchronous system comprising three LCE-based spring oscillators interconnected by springs is established. In this paper, the synchronization phenomenon is described, and the self-oscillation mechanism is revealed. The results indicate that by varying system parameters and initial conditions, three synchronization patterns emerge, namely, full synchronous mode, partial synchronous mode, and asynchronous mode. For strongly interacting systems, full synchronous mode always prevails, while for weak interactions, the adjustment of initial velocities in magnitude and direction yields the three synchronization patterns. Additionally, this study explores the impact of several system parameters, including LCE elasticity coefficient and spring elasticity coefficient, on the amplitude, frequency, and synchronous mode of the system. The findings in this paper can enhance our understanding of the synchronization behavior of multiple mutually coupled LCE-based spring oscillators, with promising applications in energy harvesting, soft robotics, signal monitoring, and various other fields.

The role of initial system–environment correlations with a spin environment

Open quantum systems are a subject of immense interest as their understanding is crucial in the implementation of modern quantum technologies. In the study of their dynamics, the role of the initial system–environment correlations is commonly ignored. In this work, to gain insights into the role of these correlations, we solve an exactly solvable model of a single two-level system interacting with a spin environment, with the initial system state prepared by a suitable unitary operation. By solving the dynamics exactly for arbitrary system–environment coupling strength while taking into account the initial system–environment correlations, we show that the effect of the initial correlations is, in general, very significant and nontrivial. To further highlight the importance of the initial system–environment correlations, we also extend our study to investigate the dynamics of the entanglement between two two-level systems interacting with a common spin environment.

Fault-tolerant controller based on artificial intelligence combined with terminal sliding mode and pre-described performance function applied on ship dynamic position stabilization systems

The presented study, develops an intelligent fault-tolerant controller to automatically control and maintain the position of a ship. The controller possesses the capabilities of holding the ship steady at a fixed position, automatically transferring the ship from one point to another, and tracking a target in the presence of various disturbances, uncertainties in the ship model, and thruster faults. A backstepping control approach based on the Terminal Sliding Mode method is employed to improve the accuracy of the controller. The aforesaid method guarantees time-limited convergence without relying on the initial conditions of system. A pre-described performance function (PPF) is utilized to ensure the performance in transient states and the calculations, which leads to the specific equations achievement for the study, which guarantees the system's stability. Environmental disturbances, uncertainties, and thruster faults are estimated using a Radial Basis Neural Network, allowing the controller to adapt to changes in the ship's environment and system uncertainties. The designed controller is proven to ensure the tracking error remains within a predefined range and can stabilize the ship system within a constant time without being influenced by the initial conditions. This stability is achieved in the presence of environmental disturbances, model uncertainties, and thruster faults, and the tracking error converges to a neighborhood near the origin. The controller is verified using a ship mode in the MATLAB environment, and the results show that the designed controller effectively controls the ship's position. The theoretical findings are successfully verified through these simulation tests.

Firms’ corporate social irresponsibility behaviors during interplay with consumers in evolutionary game models

We employ an evolutionary game model to investigate the interaction between firms’ engagement in corporate social irresponsibility (CSI) behaviors (without violating laws) and consumers’ perception of corporate social responsibility (CSR) within a consumer market. The core paradox revolves around the trade-off between firms benefiting from pursuing economic performance without adhering to social responsibility and the maximization of social welfare achieved when firms are socially responsible, and consumers possess strong CSR perception. Through an asymmetric two-population evolutionary game model, we identify two distinct scenarios of evolutionary stable strategies based on different industrial environments. Additionally, the evolution of a healthy market is contingent upon an increase in consumers’ bargaining power, although it is also influenced by the initial states of the two-group system, resulting in path dependence as a significant feature of the system’s evolutionary equilibrium. Furthermore, we observe that the added willingness to pay for CSR, while not impacting the evolutionary outcomes, could increase the likelihood of a healthy market when consumers’ bargaining power is high. These findings underscore the diverse dynamics of firms’ CSI behaviors, which depend on transaction costs, industrial structure, and consumers’ willingness to pay, offering valuable insights from a micro perspective.

Dynamics of quantum coherence and correlations in a transverse Ising spin chain environment

In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.

Design and FPGA implementation of a hyperchaotic conservative circuit with initial offset-boosting and transient transition behavior based on memcapacitor

A charge-controlled memcapacitive conservative chaotic circuit with trigonometric function terms is constructed in this paper. By analyzing the characteristics of the infinite equilibrium point and the divergence of the system, it is proved that the system is conservative. Under the influence of system parameters, hyperchaotic and chaotic characteristics can be switched to each other. With the increase of parameters and initial values, the Lyapunov exponent is also greatly improved. In addition, the transient chaos phenomenon accompanied by the internal crisis is also found, which leads to the sudden change of the orbit state of the attractor, and different types of coexisting attractors in different regions of the basins are also found. Through further analysis of the phase diagram, bifurcation diagram and time-domain waveform, it is found that there are three initial offset-boosting behaviors with different characteristics in the system. Finally, the spectral entropy (SE) algorithm is used to compare the memcapacitive circuit complexity under different initial conditions and system parameters. We find that the SE complexity distribution map is consistent with the Lyapunov exponent trajectory, which further reflects the influence of system parameters and initial conditions on the dynamic characteristics of the system. On the platform of Cyclone IV E series, the FPGA main chip of EP4CE10F17C8N is used to complete the hardware implementation of the system. The FPGA implementation results are consistent with numerical simulation, and verify the realistic feasibility of the memcapacitive conservative chaotic circuit in practical application.

Robust fixed-time fault-tolerant control for unmanned marine vehicles via integral terminal sliding mode technique

In this paper, a novel fixed-time fault-tolerant control (FTC) scheme is proposed for unmanned marine vehicles (UMVs) with dynamics uncertainties and ocean disturbances. By introducing a high-order integral term, a fixed-time integral terminal sliding mode (ITSM) with faster convergence rate is proposed, which mitigates the effect of the initial system state on the convergence time successfully. Furthermore, based on the online estimation information from the adaptive mechanism, the effects of thruster faults, dynamics uncertainties, and ocean disturbances can be compensated by designing an adaptive fixed-time fault-tolerant controller. Compared to the existing results, the proposed FTC strategy ensures stability in a fixed-time framework. Finally, the comparison simulations of a floating production ship have demonstrated the efficacy of the proposed scheme.

Event-triggered adaptive control for nonlinear systems using time-receding horizons without initial dependence

This paper investigates the full-state constraint event-triggered adaptive control for a class of uncertain strict-feedback systems. The lack of information on the coupling dynamics of virtual variables in backstepping increases the complexity of feedback design. Given this, the requirements of shaping system performance constraints, eliminating initial dependence, and reducing data transfer costs together give rise to an interesting and challenging problem. Constructing the time-receding horizon (TRH) and stitching it with the quadratic Lyapunov function (QLF) is the key to constrained tracking. Specifying TRHs as a set of smooth bounds with fixed-time convergence and forcing the system to stabilize within the constrained region before the prescribed settling time provide a sufficient condition for practical finite-time stability (PFS). For relaxing the initial dependence, a tuning function is designed to match the performance constraints under arbitrary system initial conditions. A dual-channel event-triggered mechanism (ETM) is developed to automatically adjust the controller and estimator data flow updates with less transmission burden. By combining a specific inequality with backstepping, uncertainties are overcome without the “complexity explosion” in recursion steps. Finally, simulations demonstrate the effectiveness of the proposed method.

Identifying winner-takes-all emergence in random nanowire networks: an inverse problem.

Random nanowire networks (NWNs) are interconnects that enable the integration of nanoscopic building blocks (the nanowires) in a disorganized fashion, enabling the study of complex emergent phenomena in nanomaterials and built-in fault-tolerant processing functionalities; the latter can lead to advances in large-scale electronic devices that can be fabricated with no particular array/grid high-precision pattern. However, when various nanowires are assembled to form an intricate network, their individual features are somehow lost in the complex NWN frame, in line with the complexity hallmark "the whole differs from the sum of the parts". Individual nanowire materials and geometrical features can only be inferred indirectly by attempting to extract information about their initial conditions from a response function measurement. In this work, we present a mathematical framework that enables inference of the intrinsic properties of highly complex/intricate systems such as random NWNs in which information about their individual parts cannot be easily accessed due to their network formation and dynamical conductance behaviour falling in the category of memristive systems. Our method, named misfit minimization, is rooted in nonlinear regression supervised learning approaches in which we find the optimum parameters that minimize a cost function defined as the square least error between conductance evolution curves taken for a target NWN system and multiple configurational NWN samples composing the training set. The optimized parameters are features referent to the target NWN system's initial conditions obtained in an inverse fashion: from the response output function, we extract information about the target system's initial conditions. Accessing the nanowire individual features in a NWN frame, as our methodology allows, enables us to predict the conduction mechanisms of the NWN subjected to a current input source; these can be via a "winner-takes-all" energy-efficient scheme using a single conduction pathway composed of multiple nanowires connected in series or via multiple parallel conduction pathways. Predicting the conduction mechanism of complex and dynamical systems such as memristive NWNs is critical for their use in next-generation memory and brain-inspired technologies since their memory capability relies on the creation of such pathways activated and consolidated by the input current signal.

A New Memristive System with Extreme Multistability and Hidden Chaotic Attractors and with Application to Image Encryption

Chaotic systems have proven highly beneficial in engineering applications. Pseudo-random numbers produced by chaotic systems have been used for secure communication, notably image encryption. Specific characteristics can increase the chaotic behavior of the system by adding complexity and nonlinearity. The three most well-known characteristics are memristive properties, multistability (coexisting attractors), and hidden attractors. These characteristics strengthen the produced time series’ unpredictability and randomness, strengthening an encryption algorithm’s resistance to many attacks. This study introduces a unique four-dimensional chaotic system with extreme multistability with respect to three initial conditions (including the memristor initial condition) and all previously known properties. It is rare to find an extreme multistable system like this. This system is coupled with a quadratic flux-controlled memristor based on the well-known Sprott J system. This system has a line of unstable equilibrium points with hidden attractors. The memristor displays the characteristic pinched hysteresis loops, where the area inside a loop and the voltage frequency are inversely related. A comprehensive dynamical analysis thoroughly examines all system characteristics and initial conditions. The numerical findings are carefully verified, and an analog circuit is successfully built and simulated. The chaotic sequences generated by this system are combined with deoxyribonucleic acid (DNA) operations and the global bit scrambling (GBS) technique to create an image encryption algorithm that has strong resistance to a variety of potential attacks, including noise, statistical, exhaustive, differential, and cropping attacks.

Superconductivity coupling of harmonic resonant oscillators: Homogeneous and heterogeneous extreme multistability with multi-scrolls.

Understanding and characterizing multistabilities, whether homogeneous or heterogeneous, is crucial in various fields as it helps to unveil complex system behaviors and provides insights into the resilience and adaptability of these systems when faced with perturbations or changes. Homogeneous and heterogeneous multistabilities refer, respectively, to situation in which various multiple stable states within a system are qualitatively similar or distinct. Generating such complex phenomena with multi-scrolls from inherent circuits is less reported. This paper aims to investigate extreme multistability dynamics with homogeneous and heterogeneous multi-scrolls in two coupled resonant oscillators through a shunted Josephson junction. Analysis of equilibrium points revealed that the system supports both hidden and self-excited attractors. Various dynamical tools, including bifurcation diagrams, spectrum of Lyapunov exponents, and phase portraits, are exploited to establish the connection between the system parameters and various complicated dynamical features of the system. By tuning both system parameters and initial conditions, some striking phenomena, such as homogeneous and heterogeneous extreme multistability, along with the emergence of multi-scrolls, are illustrated. Furthermore, it is observed that one can readily control the number of scrolls purely by varying the initial conditions of the investigated system. A multi-metastable phenomenon is also captured in the system and confirmed using the finite-time Lyapunov exponents. Finally, the microcontroller implementation of the system demonstrates strong alignment with the numerical investigations.

Fixed time control of free-flying space robotic manipulator with full state constraints: a barrier-Lyapunov-function term free approach

Space robotic manipulator (SRM) should be always performed in the given workspace for safety concern. This requires the system states such as rotation of each joint, attitude of base, and their velocities to be always constrained in the given regions. In this article, a new sliding mode control scheme based on a fixed time disturbance observer is proposed to realize the fixed time coordinate motion control of SRM with full-state constraints. Firstly, the tracking error and error velocity at the novel sliding manifold can converge to the equilibrium within a fixed time without violating their state constraints. Then, the control law based on the fixed time disturbance observer is designed to achieve the sliding manifold within a fixed time, which simultaneously satisfies the state constraints during the approaching stage. Unlike the most existing state constraint control schemes, the proposed controller does not include any Barrier Lyapunov Function (BLF) terms of system states, and therefore the risk of controller outputting inappropriately high control commands is eliminated. Moreover, the proposed control scheme is compatible to the initial system states violating their constraints, which thereby removes the assumption of feasible initial states. Furthermore, the proposed sliding manifold solves the singularity issue by a continuously varying power of tracking error, which thereby does not need an additional switch mechanism of manifold compared to the conventional fixed time controllers. The stability of the proposed control scheme is proven by using the Lyapunov theory, and the effectiveness is verified by numerical simulations.

Predefined‐time tracking control of a class of nonlinear systems via a novel C∞ performance function

AbstractIt is well‐known that the finite‐time and the fixed‐time control can ensure the finite‐time and the fixed‐time stabilities of systems, respectively. Therein the finite convergence time depends on both the initial conditions of systems and the controller design parameters, and the fixed convergence time only depends on the controller design parameters. The recently reported predefined‐time control removes the above limitations. Nevertheless, the existing predefined‐time control methods either require sliding modes, or suffer from the high‐gain control problem at the predefined time, or cannot be applied to high‐order systems. This article develops an alternative predefined‐time tracking control scheme of a class of nonlinear systems by introducing a novel performance function which reaches its terminal value at a predefined time. The developed predefined‐time tracking control scheme has higher compatibility, does not cause the high‐gain control problem at the predefined time and is applicable to arbitrary order systems. Theoretical analyses and simulations verify the effectiveness of our developed predefined‐time tracking control scheme.

Experimental study of the depressurization phenomena of supercritical carbon dioxide system

Depressurization accidents pose a significant safety concern for supercritical carbon dioxide (S–CO2) nuclear and power systems. However, due to the limited availability of system-level experiments, clear understandings of the phenomena associated with S–CO2 depressurization accidents are lacking. To address this gap, this paper conducted a series of experiments on a S–CO2 system to investigate the characteristics of depressurization accidents. Several key phenomena, including flash evaporation, transcritical transient heat transfer, fluid-thermo-structure coupling effect, and the fluid field changes in containment vessel, were identified and analyzed. Furthermore, the impact of break size and location, containment vessel, and initial system conditions on depressurization accidents was investigated. The acquired results provide crucial groundwork for establishing a Phenomenon Identification Ranking Table (PIRT) tailored to depressurization accidents in S–CO2 nuclear and power systems. This will significantly enhance the design and safety analysis of these systems.

Data assimilation for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS 2.0.0-beta): ensemble of 3D ensemble-variational (En-3DEnVar) assimilations

Abstract. An ensemble of 3D ensemble-variational (En-3DEnVar) data assimilations is demonstrated with the Joint Effort for Data assimilation Integration (JEDI) with the Model for Prediction Across Scales – Atmosphere (MPAS-A) (i.e., JEDI-MPAS). Basic software building blocks are reused from previously presented deterministic 3DEnVar functionality and combined with a formal experimental workflow manager in MPAS-Workflow. En-3DEnVar is used to produce an 80-member ensemble of analyses, which are cycled with ensemble forecasts in a 1-month experiment. The ensemble forecasts approximate a purely flow-dependent background error covariance (BEC) at each analysis time. The En-3DEnVar BECs and prior ensemble-mean forecast errors are compared to those produced by a similar experiment that uses the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter (EAKF). The experiment using En-3DEnVar produces a similar ensemble spread to and slightly smaller errors than the EAKF. The ensemble forecasts initialized from En-3DEnVar and EAKF analyses are used as BECs in deterministic cycling 3DEnVar experiments, which are compared to a control experiment that uses 20-member MPAS-A forecasts initialized from Global Ensemble Forecast System (GEFS) initial conditions. The experimental ensembles achieve mostly equivalent or better performance than the off-the-shelf ensemble system in this deterministic cycling setting, although there are many obvious differences in configuration between GEFS and the two MPAS ensemble systems. An additional experiment that uses hybrid 3DEnVar, which combines the En-3DEnVar ensemble BEC with a climatological BEC, increases tropospheric forecast quality compared to the corresponding pure 3DEnVar experiment. The JEDI-MPAS En-3DEnVar is technically working and useful for future research studies. Tuning of observation errors and spread is needed to improve performance, and several algorithmic advancements are needed to improve computational efficiency for larger-scale applications.

The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete‐time nonlinear objects

SummaryIn this work, an adaptive multiple model pre‐assigned exponential convergence control scheme based on the time varying exponential function is demonstrated for a class of discrete‐time nonlinear systems. For coping with the noncausality problem from previous adaptive backstepping design method of nonlinear discrete‐time systems, a first‐order recursive filter is used in controller design procedures and the n‐step prediction model is not needed, thereby reducing the computational burden effectively. The time varying function is employed to force all states variables to convergence to zero with a pre‐defined rate which does not rely on the initial conditions of systems. In addition, the multiple model set is constructed to address unknown parameters problem and further the second level adaptive algorithm of unknown parameters is developed. A characteristic feature of the second‐level multi‐model adaptation algorithm is that it dynamically adapts to time changes in the identified model (it uses identification information better than the switching multiple model control). In a unified framework of second level adaption, a first‐order recursive filter and backstepping technique, a pre‐assigned exponential convergence controller is presented. Finally, the results about discrete‐time pre‐assigned exponential convergence method are compared with other methods using two case studies.

Non‐singular fixed‐time fuzzy adaptive control for nonlinear systems subject to actuator faults

AbstractThis paper proposes a non‐singular fixed‐time fault‐tolerant adaptive tracking control method for a kind of multi‐input and multi‐output nonlinear system, which is in form of non‐strict feedback and is subject to actuator faults. The major contribution, compared to other practical fixed‐time fault‐tolerant control methods, is that the fixed time can be calculated precisely. By applying fuzzy logic systems, the identification of unknown nonlinearities is achieved, and by the boundness of fuzzy basis functions, the algebraic loop problem is avoided. Based on the fixed‐time stability theory, the practical fixed‐time fault‐tolerant adaptive tracking control method is proposed with adaptive back‐stepping control technology, in which the control singular problem is overcome by applying the adding power integration method. By the Lyapunov function theory, the practical fixed‐time stability of the closed‐loop system is theoretically proved. And even in the case of unknown actuator faults, the tracking error of the controlled system for the given command signal can still converge to a small neighbourhood of zero within a fixed time, regardless of the system initial state. Finally, the proposed control method is successfully implemented on a multi‐motor control platform, proving its effectiveness, and multiple comparative simulations are carried out, demonstrating its superiority.