Illustrative Simulation Research Articles

Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to the S2 star orbit

This study provides a comprehensive analytical investigation of the bound and unbound motion of magnetized particles orbiting a Schwarzschild black hole immersed in an external asymptotically uniform magnetic field, which includes all conceivable types of bounded and unbounded orbits. In particular, for planetary orbits, we perform a comparative analysis of our findings with the observed position of the S2 star carrying magnetic dipole moment around Sagittarius A*. We found maximum and minimum values for the parameter of magnetic interaction between the magnetic dipole of the star and the external magnetic field, as well as the energy and angular momentum of the S2 star. As a result, we obtain estimations of the magnetic dipole of the star in the order of 106 G·cm3. Additionally, we explore deflecting trajectories akin to gravitational Rutherford scattering. In obtaining the solutions for the orbital equations, we articulate the elliptic integrals and Jacobi elliptic functions, and illustrative figures and simulations augment our study. Published by the American Physical Society 2024

Tobit Kalman fusion filtering under dynamic event-triggering protocol with token bucket specification

This paper addresses the multi-sensor fusion filtering problem for a class of linear discrete time-varying systems with censored measurement, described by the Tobit model, and scheduled by dynamic event-triggering protocols with token bucket specification. A dynamic event-triggering mechanism is first used to determine whether to transmit measurements under the token bucket specification, allowing transmission only if there are sufficient tokens and if the event-triggering condition is satisfied. Next, two indicator variables are denoted to represent the combined impact of the dynamic event-triggering protocol and the token bucket specification. A local Tobit Kalman filtering algorithm is then designed for each node by minimizing the trace of the filtering error covariance matrix under censoring and information transmission protocols' influence. Subsequently, all local estimates from each node are transmitted to the fusion center, where global estimates are generated using a federal fusion rule. The global estimates with suitable weights are sent back to every node for predictions at subsequent time instants. Finally, an illustrative simulation example is used to evaluate performance of this fused filtering scheme proposed in this paper.

Active disturbance rejection control for spacecraft relative motion in libration point orbits subject to actuator saturation and time-delays

This paper proposes a novel active disturbance rejection control (ADRC) scheme to achieve the spacecraft relative pose synchronization in the libration orbits under the constrations of the actuator saturation and time-delays. The relative kinematics and dynamics between two spacecraft are modeled using dual quaternions to avoid singularity. A set of dimensionless variables is introduced to improve computational accuracy. An extended state observer, consisting of a time-delay predictor and an anti-windup compensator, is designed to address actuator saturation and communication time delays. A composite controller is then proposed, based on the designed observer, to mitigate the impact of total disturbances. Finally, two illustrative numerical simulations, including a spacecraft close rendezvous and docking scenario and a formation flying scenario, are provided to verify the effectiveness of the proposed ADRC scheme.

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.

Synchronization control of cyber–physical systems with time-varying dynamics under denial-of-service attacks

In this paper, the problem of synchronization control of cyber–physical systems with time-varying dynamics under Denial-of-Service attacks is studied. The communication channels of the synchronization protocol between the subsystems in the cyber–physical systems may be injected into DoS attacks. To counteract the adverse effects of these attacks on synchronization, a target reference model is initially created for each subsystem to mimic its standard operational dynamics. Subsequently, utilizing this reference model, an adaptive compensator is proposed. The unified synchronization protocol guarantees that the synchronization error remains minimal through the adjustment of specific parameters, even under DoS attacks. To showcase the efficiency of this approach, an illustrative numerical simulation example is conducted.

Mixed deterministic and stochastic disturbances in a discrete-time Nash game

This paper considers a discrete-time non-cooperative M-players linear affine quadratic game of pre-specified fixed duration, affected by stochastic noise and deterministic disturbances. The last one is seen as a pernicious fictitious player looking to maximise the expected cost functions of each player. Inspired in the discrete-time robust dynamic programming, sufficient conditions for the existence of a type of robust feedback NE are given in the solution of a set of discrete-time difference equations. A formal induction proof is provided for the closed form of the obtained robust set of strategies. Two illustrative simulation examples are included, one related to the problem of coordination of a two-echelon supply chain with uncertain seasonal demand. The goal of the agents is to reduce the expected cost of storage while satisfying a partially known demand. The second example is related to a game of government debt stabilisation. Comparing the simulation with the standard Nash strategy, the robust one achieves a better performance.

Unscented recursive three-step filter based unbiased minimum-variance estimation for a class of nonlinear systems

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

Self-Triggered Impulsive Control for Lyapunov Stability of Nonlinear Systems in Discrete Time.

This article studies Lyapunov stability for nonlinear systems based on discrete-time self-triggered impulsive control (STIC). With the help of comparison approach, some Lyapunov-based sufficient conditions guaranteeing nonZeno behavior and global asymptotic stability of nonlinear systems under STIC are derived. Different from the existing self-triggered mechanisms using implicit expressions to compute the next impulse instant, which may result in computational burden, we propose a novel discrete-time self-triggered mechanism (STM) by which the next impulse instant can be predicted directly by the information of the comparison system. Moreover, the resulting algorithm is easy to be implemented. It is shown that the designed STIC strategy can not only achieve a tradeoff between computational complexity, communication resource usage and control performance, but also has strong robustness and flexibility. Finally, an illustrative simulation is provided showing the effectiveness of the results.

Zeroing neural network based on the equation AXA = A

According to available scientific research, there is no information that Zeroing Neural Network (ZNN) models for calculating the matrix inverse and generalized inverses have been studied on the basis of Penrose equations. Our intention is to present a new ZNN design which defined on the Penrose matrix equations and whose intention is to find the time-variant matrix inverse and pseudoinverse. We propose a novel Zeroing function (ZF) based on the first Penrose equation AXA=A. The initiated ZNN design for computing the time-varying inverse and the pseudoinverse is defined and investigated. An explicit form of the defined model is also proposed. The convergence properties of the proposed explicit dynamics are investigated in both the time-invariant and time-varying case. Illustrative simulation results are given in order to verify the obtained theoretical results.

NANO.PTML model for read-across prediction of nanosystems in neurosciences. computational model and experimental case of study

Neurodegenerative diseases involve progressive neuronal death. Traditional treatments often struggle due to solubility, bioavailability, and crossing the Blood-Brain Barrier (BBB). Nanoparticles (NPs) in biomedical field are garnering growing attention as neurodegenerative disease drugs (NDDs) carrier to the central nervous system. Here, we introduced computational and experimental analysis. In the computational study, a specific IFPTML technique was used, which combined Information Fusion (IF) + Perturbation Theory (PT) + Machine Learning (ML) to select the most promising Nanoparticle Neuronal Disease Drug Delivery (N2D3) systems. For the application of IFPTML model in the nanoscience, NANO.PTML is used. IF-process was carried out between 4403 NDDs assays and 260 cytotoxicity NP assays conducting a dataset of 500,000 cases. The optimal IFPTML was the Decision Tree (DT) algorithm which shown satisfactory performance with specificity values of 96.4% and 96.2%, and sensitivity values of 79.3% and 75.7% in the training (375k/75%) and validation (125k/25%) set. Moreover, the DT model obtained Area Under Receiver Operating Characteristic (AUROC) scores of 0.97 and 0.96 in the training and validation series, highlighting its effectiveness in classification tasks. In the experimental part, two samples of NPs (Fe3O4_A and Fe3O4_B) were synthesized by thermal decomposition of an iron(III) oleate (FeOl) precursor and structurally characterized by different methods. Additionally, in order to make the as-synthesized hydrophobic NPs (Fe3O4_A and Fe3O4_B) soluble in water the amphiphilic CTAB (Cetyl Trimethyl Ammonium Bromide) molecule was employed. Therefore, to conduct a study with a wider range of NP system variants, an experimental illustrative simulation experiment was performed using the IFPTML-DT model. For this, a set of 500,000 prediction dataset was created. The outcome of this experiment highlighted certain NANO.PTML systems as promising candidates for further investigation. The NANO.PTML approach holds potential to accelerate experimental investigations and offer initial insights into various NP and NDDs compounds, serving as an efficient alternative to time-consuming trial-and-error procedures.

CBDC and the Banking System

Abstract This paper examines the potential impact a central bank digital currency (CBDC) on banks’ balance sheets. We first analyze the possible implications of the introduction of a CBDC for the banking system and the economy as a whole. Our analysis indicates that the impact of a CBDC depends on a number of design choices and on how credit institutions re-optimize their balance sheets in response to the outflow of deposits caused by the substitution of private money with public digital money. We then present a series of illustrative simulations on the impact of a CBDC on the funding structure and profitability of credit institutions using data on Italian banks between June 2021 and March 2023. The analysis suggests that the overall impact on banks’ funding could be manageable in the presence of individual holding limits and in an environment characterized by ample liquidity and stable funding for credit institutions. The cost of covering the reduction of deposits would be relatively higher for intermediaries with low excess reserves and for those that may need to issue long-term liabilities to maintain stable funding levels above regulatory requirements.

Gradient neural network model for the system of two linear matrix equations and applications

In this paper, the new type of Gradient Neural Network (GNN) model is proposed for the following linear system of matrix equations: AX=C,XB=D. The convergence analysis of given models is shown. The model is applied for the computation of the regular matrix inverse, as well as Moore-Penrose and Drazin generalized inverses. Some illustrative examples and simulations are given to verify theoretical results.

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov–Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

Forecast Uncertainties Real-Time Data-Driven Compensation Scheme for Optimal Storage Control

This study introduces a real-time data-driven battery management scheme designed to address uncertainties in load and generation forecasts, which are integral to an optimal energy storage control system. By expanding on an existing algorithm, this study resolves issues discovered during implementation and addresses previously overlooked concerns, resulting in significant enhancements in both performance and reliability. The refined real-time control scheme is integrated with a day-ahead optimization engine and forecast model, which is utilized for illustrative simulations to highlight its potential efficacy on a real site. Furthermore, a comprehensive comparison with the original formulation was conducted to cover all possible scenarios. This analysis validated the operational effectiveness of the scheme and provided a detailed evaluation of the improvements and expected behavior of the control system. Incorrect or improper adjustments to mitigate forecast uncertainties can result in suboptimal energy management, significant financial losses and penalties, and potential contract violations. The revised algorithm optimizes the operation of the battery system in real time and safeguards its state of health by limiting the charging/discharging cycles and enforcing adherence to contractual agreements. These advancements yield a reliable and efficient real-time correction algorithm for optimal site management, designed as an independent white box that can be integrated with any day-ahead optimization control system.

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.

Older Adult Stair and Walking Speeds from Controlled Trials as Inputs into Simulations of Retirement Home Evacuation

This work aims to add to the current database of human movement data, specifically, 3-stair descent speeds from controlled trials of typically aging older adults (n=212, aged 60-99) with and without mobility impairments. Additionally, to explore the impacts of model input parameters, stair and walking speeds obtained from controlled trials are used to simulate first-iteration Canadian retirement home egress scenarios with Pathfinder. Analysis of descending stair speeds reveal interesting trends and key inter-population variations. Moreover, when the stair and horizontal walking speeds determined from these controlled trials are used as inputs into the illustrative egress simulations, a difference in predicted egress outcomes are seen compared to when model defaults are used. Together, the findings indicate important egress considerations for a vulnerable population.

Adaptive Critic Learning-Based Optimal Bipartite Consensus for Multiagent Systems With Prescribed Performance.

Developing a distributed bipartite optimal consensus scheme while ensuring user-predefined performance is essential in practical applications. Existing approaches to this problem typically require a complex controller structure due to adopting an identifier-actor-critic framework and prescribed performance cannot be guaranteed. In this work, an adaptive critic learning (ACL)-based optimal bipartite consensus scheme is developed to bridge the gap. A newly designed error scaling function, which defines the user-predefined settling time and steady accuracy without relying on the initial conditions, is then integrated into a cost function. The backstepping framework combines the ACL and integral reinforcement learning (IRL) algorithm to develop the adaptive optimal bipartite consensus scheme, which contributes a critic-only controller structure by removing the identifier and actor networks in the existing methods. The adaptive law of the critic network is derived by the gradient descent algorithm and experience replay to minimize the IRL-based residual error. It is shown that a compute-saving learning mechanism can achieve the optimal consensus, and the error variables of the closed-loop system are uniformly ultimately bounded (UUB). Besides, in any bounded initial condition, the evolution of bipartite consensus is limited to a user-prescribed boundary under bounded initial conditions. The illustrative simulation results validate the efficacy of the approach.

A Novel Accelerated Multistage Learning Control Mechanism via Virtual Performance Reduction.

This study uses a multistage learning mechanism concept to investigate the accelerated learning control for stochastic systems. In this mechanism, the learning iterations are divided into successive stages, with each stage comprising several iterations. The learning gain is constant in each stage to accelerate the learning process and decreases it from one stage to another to eliminate the noise effect asymptotically. The critical issue is determining the switching iteration when a new stage starts. This study resolves this issue by calculating a virtual performance index of the mean-squared input error and its estimated upper bound. Specifically, the ideal, practical, and improved multistage learning control schemes are proposed to determine the switching iteration and generate the learning gain sequence. The ideal scheme achieves the best performance at the cost of a large computation burden, and the practical scheme saves computation cost, but the performance is not excellent. The improved scheme significantly approximates the best performance by introducing additional stretching parameters to the performance index. Illustrative simulations are provided to verify the theoretical results.

EXPLORING THE IMPACT OF PTH THERAPY ON BONE REMODELING: A MATHEMATICAL INVESTIGATION

The regulatory influence of the parathyroid hormone (PTH) is exerted on bone, which serves as a vital reservoir of calcium within the body. While various aspects of bone growth, turnover, and mechanisms operate independently of gonadal hormones, a crucial role is assumed by sex steroids, particularly estrogen, in maintaining bone equilibrium in adults. In order to unravel the underlying mechanisms of bone remodeling mediated by PTH, a distinguished mathematical model of this intricate process is presented. Subsequently, the temporal effects of Plasma PTH and PTH external dosages are investigated using the proposed mathematical model. Among the limited repertoire of approved and accessible anabolic treatments for severe osteoporosis, daily injections of PTH stand out. This pharmaceutical marvel possesses a unique dual action, capable of acting either anabolically or catabolically, contingent upon the mode of administration. The study aims to accurately predict osteogenic responses to introduced and endogenous PTH, incorporating factors such as [Formula: see text]-[Formula: see text], [Formula: see text], and bisphosphonates in osteoblast–osteoclast signaling, as well as considering PTH’s influence on the gland and the regulatory roles of [Formula: see text], [Formula: see text], and [Formula: see text] in osteoblast apoptosis and bone volume effects. Through diverse methods including illustrative depictions, numerical simulations, sensitivity analysis, and stability analysis, this work seeks to comprehend how PTH therapy impacts bone volume, enhancing its therapeutic relevance.

Dynamics and optimal therapy of a stochastic HTLV‐1 model incorporating Ornstein–Uhlenbeck process

As the prevalence of viral infection in body, human T‐cell leukemia virus type 1 (HTLV‐1) is receiving increasing attention. Research on the corresponding virus models is of great significance to tackle the challenges of understanding HTLV‐1 development and treatment. This paper focuses on the dynamic analysis for a stochastic model with nonlinear cytotoxic T lymphocyte (CTL) response, which is driven by Ornstein–Uhlenbeck (OU) process to model the progression of HTLV‐1 in vivo. Rich dynamic behaviors such as the extinction of infected CD4+ T cells (ITCs), stationary distribution (SD), probability density, and finite‐time stability (FTS) of the model are established to reveal the interaction of cell populations. The optimal therapeutic strategy based on the cost‐benefit viewpoint is further obtained. Finally, illustrative numerical simulations are represented to corroborate the effectiveness of treatment and the ambient perturbation's impact that strengthening the noise strength can lead to rapid virus clearance.