PCLOS based fractional-order sliding mode stochastic path following control for underactuated marine vehicles with multiple disturbances and constraints.

This paper investigates the stochastic path following control of underactuated marine vehicles (UMVs) subject to multiple disturbances and constraints. Firstly, the complex marine environment in which UMVs navigate typically contains stochastic components, thus the multiple disturbances are categorized as slow-varying deterministic disturbances and stochastic disturbances. Secondly, a position-constrained line-of-sight (PCLOS) based fractional-order sliding mode stochastic (FSMS) control strategy is established to achieve path following control of UMVs. A PCLOS guidance law based on universal barrier Lyapunov function is proposed to ensure that the position errors remain within the constraint ranges, which is versatile for systems with symmetric constraints or without constraints. An FSMS controller based on fractional-order theory and sliding mode control is designed to improve the dynamic response speed of the system and effectively attenuate chattering phenomenon. A stochastic disturbance observer is developed to estimate the slow-varying deterministic disturbances in the stochastic system, and auxiliary dynamic compensators are used to mitigate the impact of input constraints. Lastly, theoretical analysis indicates that the closed-loop system is stable and the position constraint requirements are satisfied. Comparative simulations illustrate the effectiveness of the proposed control strategy.

Complete synchronization of discrete-time fractional-order BAM neural networks with leakage and discrete delays.

This paper concerns complete synchronization (CS) problem of discrete-time fractional-order BAM neural networks (BAMNNs) with leakage and discrete delays. Firstly, on the basis of Caputo fractional difference theory and nabla l-Laplace transform, two equations about the nabla sum are strictly proved. Secondly, two extended Halanay inequalities that are suitable for discrete-time fractional difference inequations with arbitrary initial time and multiple types of delays are introduced. In addition, through applying Caputo fractional difference theory and combining with inequalities gained from this paper, some sufficient CS criteria of discrete-time fractional-order BAMNNs with leakage and discrete delays are established under adaptive controller. Finally, one numerical simulation is utilized to certify the effectiveness of the obtained theoretical results.

Dynamic Effects Analysis in Fractional Memristor-Based Rulkov Neuron Model.

Mathematical models such as Fitzhugh-Nagoma and Hodgkin-Huxley models have been used to understand complex nervous systems. Still, due to their complexity, these models have made it challenging to analyze neural function. The discrete Rulkov model allows the analysis of neural function to facilitate the investigation of neuronal dynamics or others. This paper introduces a fractional memristor Rulkov neuron model and analyzes its dynamic effects, investigating how to improve neuron models by combining discrete memristors and fractional derivatives. These improvements include the more accurate generation of heritable properties compared to full-order models, the treatment of dynamic firing activity at multiple time scales for a single neuron, and the better performance of firing frequency responses in fractional designs compared to integer models. Initially, we combined a Rulkov neuron model with a memristor and evaluated all system parameters using bifurcation diagrams and the 0-1 chaos test. Subsequently, we applied a discrete fractional-order approach to the Rulkov memristor map. We investigated the impact of all parameters and the fractional order on the model and observed that the system exhibited various behaviors, including tonic firing, periodic firing, and chaotic firing. We also found that the more I tend towards the correct order, the more chaotic modes in the range of parameters. Following this, we coupled the proposed model with a similar one and assessed how the fractional order influences synchronization. Our results demonstrated that the fractional order significantly improves synchronization. The results of this research emphasize that the combination of memristor and discrete neurons provides an effective tool for modeling and estimating biophysical effects in neurons and artificial neural networks.

Efficient DC motor speed control using a novel multi-stage FOPD(1 + PI) controller optimized by the Pelican optimization algorithm.

This paper introduces a novel multi-stage FOPD(1 + PI) controller for DC motor speed control, optimized using the Pelican Optimization Algorithm (POA). Traditional PID controllers often fall short in handling the complex dynamics of DC motors, leading to suboptimal performance. Our proposed controller integrates fractional-order proportional-derivative (FOPD) and proportional-integral (PI) control actions, optimized via POA to achieve superior control performance. The effectiveness of the proposed controller is validated through rigorous simulations and experimental evaluations. Comparative analysis is conducted against conventional PID and fractional-order PID (FOPID) controllers, fine-tuned using metaheuristic algorithms such as atom search optimization (ASO), stochastic fractal search (SFS), grey wolf optimization (GWO), and sine-cosine algorithm (SCA). Quantitative results demonstrate that the FOPD(1 + PI) controller optimized by POA significantly enhances the dynamic response and stability of the DC motor. Key performance metrics show a reduction in rise time by 28%, settling time by 35%, and overshoot by 22%, while the steady-state error is minimized to 0.3%. The comparative analysis highlights the superior performance, faster response time, high accuracy, and robustness of the proposed controller in various operating conditions, consistently outperforming the PID and FOPID controllers optimized by other metaheuristic algorithms. In conclusion, the POA-optimized multi-stage FOPD(1 + PI) controller presents a significant advancement in DC motor speed control, offering a robust and efficient solution with substantial improvements in performance metrics. This innovative approach has the potential to enhance the efficiency and reliability of DC motor applications in industrial and automotive sectors.

Smart waterborne disease control for a scalable population using biodynamic model in IoT network.

We propose a biodynamic model for managing waterborne diseases over an Internet of Things (IoT) network, leveraging the scalability of LoRa IoT technology to accommodate a growing human population. The model, based on fractional order derivatives (FOD), enables smart prediction and control of pathogens that cause waterborne diseases using IoT infrastructure. The human-pathogen-based biodynamic FOD model utilises epidemic parameters (SVIRT: susceptibility, vaccination, infection, recovery, and treatment) transmitted over the IoT network to predict pathogenic contamination in water reservoirs and dumpsites in Iji-Nike, Enugu, the study community in Nigeria. These pathogens contribute to person-to-person, water-to-person, and dumpsite-to-person transmission of disease vectors. Five control measures are proposed: potable water supply, treatment, vaccination, adequate sanitation, and health education campaigns. A stable disease-free equilibrium point is found when the effective reproduction number of the pathogens, R0eff<1 and unstable if R0eff>1. While other studies showed a 98.2% reduction in infections when using IoT alone, this paper demonstrates that combining the SVIRT epidemic control parameters (such as potable water supply and health education campaign) with IoT achieves a 99.89% reduction in infected human populations and a 99.56% reduction in pathogen populations in water reservoirs. Furthermore, integrating treatment with sanitation results in a 99.97% reduction in infected populations. Finally, combining these five control strategies nearly eliminates infection and pathogen populations, demonstrating the effectiveness of multifaceted approaches in public health and environmental management. This study provides a blueprint for governments to plan sustainable smart cities for a growing population, ensuring potable water free from pathogenic contamination,in line with the United Nations Sustainable Development Goals #6 (Clean Water and Sanitation) and #11 (Sustainable Cities and Communities).

A fractional-order model for optimizing combination therapy in heterogeneous lung cancer: integrating immunotherapy and targeted therapy to minimize side effects.

This research presents a novel approach to address the complexities of heterogeneous lung cancer dynamics through the development of a Fractional-Order Model. Focusing on the optimization of combination therapy, the model integrates immunotherapy and targeted therapy with the specific aim of minimizing side effects. Notably, our approach incorporates a clever fusion of Proportional-Integral-Derivative (PID) feedback controls alongside the optimization process. Unlike previous studies, our model incorporates essential equations accounting for the interaction between regular and mutated cancer cells, delineates the dynamics between immune cells and mutated cancer cells, enhances immune cell cytotoxic activity, and elucidates the influence of genetic mutations on the spread of cancer cells. This refined model offers a comprehensive understanding of lung cancer progression, providing a valuable tool for the development of personalized and effective treatment strategies. the findings underscore the potential of the optimized treatment strategy in achieving key therapeutic goals, including primary tumor control, metastasis limitation, immune response enhancement, and controlled genetic mutations. The dynamic and adaptive nature of the treatment approach, coupled with economic considerations and memory effects, positions the research at the forefront of advancing precision and personalized cancer therapeutics.

The application of fractional calculus in economic growth modelling: An approach based on regression analysis.

This paper establishes a fractional-order economic growth model to model the gross domestic product (GDP). The fractional-order model consists of a differential equation of integer and fractional orders, where the GDP is a function of several exploratory variables. An empirical application is adopted using Malaysia's GDP data from 1956 to 2018, incorporating exploratory variables such as total population, crude death rate, production of logs, gross fixed capital formation, exports of goods and services, general government final consumption expenditure, private final consumption expenditure, and the impact of investment. Extensive comparisons were carried out to evaluate the modelling performance of the full and reduced fractional-order multiple linear regression models with the benchmark models, namely full and reduced integer-order multiple linear regression models. Results indicate that the reduced fractional-order model with six exploratory variables, excluding the crude death rate and production of logs, predominates other models for the in-sample model fitting based on the Akaike information criterion, coefficient of determination and other criteria. Furthermore, the fractional-order model offers the best-of-sample forecasts evaluated based on the root mean square forecast error and mean absolute forecast error. The application of the Diebold-Mariano test also serves to confirm the superior performance of the suggested fractional-order model, revealing a significant difference in forecasting ability between the fractional-order and integer-order models.

Finite-time cluster synchronization of multi-weighted fractional-order coupled neural networks with and without impulsive effects.

In this paper, finite-time cluster synchronization (FTCS) of multi-weighted fractional-order neural networks is studied. Firstly, a FTCS criterion of the considered neural networks is obtained by designing a new delayed state feedback controller. Secondly, a FTCS criterion for the considered neural networks with mixed impulsive effects is given by constructing a new piecewise controller, where both synchronizing and desynchronizing impulses are taken into account. It should be noted that it is the first time that finite-time cluster synchronization of multi-weighted neural networks has been investigated. Finally, numerical simulations are given to show the validity of the theoretical results.

Fractional-Order Boosted Hybrid Young's Double-Slit Experimental Optimizer for Truss Topology Engineering Optimization.

Inspired by classical experiments that uncovered the inherent properties of light waves, Young's Double-Slit Experiment (YDSE) optimization algorithm represents a physics-driven meta-heuristic method. Its unique search mechanism and scalability have attracted much attention. However, when facing complex or high-dimensional problems, the YDSE optimizer, although striking a good balance between global and local searches, does not converge as fast as it should and is prone to fall into local optimums, thus limiting its application scope. A fractional-order boosted hybrid YDSE, called FYDSE, is proposed in this article. FYDSE employs a multi-strategy mechanism to jointly address the YDSE problems and enhance its ability to solve complex problems. First, a fractional-order strategy is introduced into the dark edge position update of FYDSE to ensure more efficient use of the search potential of a single neighborhood space while reducing the possibility of trapping in a local best. Second, piecewise chaotic mapping is constructed at the initial stage of the population to obtain better-distributed initial solutions and increase the convergence rate to the optimal position. Moreover, the low exploration space is extended by using a dynamic opposition strategy, which improves the probability of acquisition of a globally optimal solution. Finally, by introducing the vertical operator, FYDSE can better balance global exploration and local exploitation and explore new unknown areas. The numerical results show that FYDSE outperforms YDSE in 11 (91.6%) of cec2022 sets. In addition, FYDSE performs best in 8 (66.6%) among all algorithms. Compared with the 11 methods, FYDSE obtains the optimal best and average weights for the 20-bar, 24-bar, and 72-bar truss problems, which proves its efficient optimization capability for difficult optimization cases.

A novel fractional-order memristive Hopfield neural network for traveling salesman problem and its FPGA implementation.

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

Navigating the Fractional Calcium Dynamics of Orai Mechanism in Polar Dimensions.

Calcium plays a crucial role as a second messenger in neuronal signal transduction pathways. The influx of calcium ions through various physicochemical gating channels activates neuronal calcium signaling. The Endoplasmic Reticulum (ER) is a significant intracellular structure that sequesters calcium and controls signaling through SERCA, IPR, and leak channel mechanisms. Disruption of calcium dynamics can trigger intrinsic dyshomeostasis, cell damage, and apoptosis. The present study articulates a Caputo fractional time derivative in the polar coordinate dimensions to investigate the role of nonlocal calcium-free ions in the neuron through the Orai channel, and ER fluxes, incorporating various physiological parameters. The solution was obtained through the hybrid integral transform technique for analytical form. The closed form was generated using Green's function in terms of Mainardi and Wright's functions. Our simulation uncovered the calcium concentration bandwidth of interaction with different neuronal parameters. Parameters and calcium ion synergy show normal and Alzheimer's disease-impacted interaction through different illustrations. Our simulation reveals that S100B and BAPTA have significant calcium-controlling behavior.

Generalised Neuronal Calcium Dynamics of Membrane and ER in the Polar Dimension.

Calcium ions are the second messenger playing as regulators for various cellular activities. Its spatiotemporal control is critical for various brain functions, including neuroplasticity, apoptosis, and cell death. The Endoplasmic Reticulum (ER) plays an important role in determining these spatiotemporal calcium dynamics. Stromal interaction molecule (STIM) - Orai channel on the membrane generates additional calcium flow, whereas other membrane fluxes contribute to cytosolic flux. Due to their anomalous character, we used the Caputo fractional differential operator to mimic these interactions in polar coordinates. Solutions were generated using hybrid integral transform methods to control the analytical approach. Using Green's function yielded a closed-form solution for Mittag-Leffler-type functions. This work emphasizes the significant relationship between calcium and various buffer levels in neurons. The differential transition simulation of a time derivative with space across different parameters indicated a decrease in calcium concentration. Anomalously low buffer levels exhibited the impact of Alzheimer's disease on calcium higher concentration, leading to the death of neurons. Additionally, the research introduces a method involving S100B, BAPTA, and calmodulin buffers to uphold optimal calcium levels within the neuronal cytosol. The applicability of this model with different buffer properties and parameters and memory impacts the calcium concentration with the neurological disorder.

Hyperspectral Characteristics and SPAD Estimation of Wheat Leaves under CO2 Microleakage Stress.

To non-destructively and rapidly monitor the chlorophyll content of winter wheat leaves under CO2 microleakage stress, and to establish the quantitative relationship between chlorophyll content and sensitive bands in the winter wheat growing season from 2023 to 2024, the leakage rate was set to 1 L/min, 3 L/min, 5 L/min, and 0 L/min through field experiments. The dimensional reduction was realized, fractional differential processing of a wheat canopy spectrum was carried out, a multiple linear regression (MLR) and partial least squares regression (PLSR) estimation model was constructed using a SPA selection band, and the model's accuracy was evaluated. The optimal model for hyperspectral estimation of wheat SPAD under CO2 microleakage stress was screened. The results show that the spectral curves of winter wheat leaves under CO2 microleakage stress showed a "red shift" of the green peak and a "blue shift" of the red edge. Compared with 1 L/min and 3 L/min, wheat leaves were more affected by CO2 at 5 L/min. Evaluation of the accuracy of the MLR and PLSR models shows that the MLR model is better, where the MLR estimation model based on 1.1, 1.8, 0.4, and 1.7 differential SPAD is the best for leakage rates of 1 L/min, 3 L/min, 5 L/min, and 0 L/min, with validation set R2 of 0.832, 0.760, 0.928, and 0.773, which are 11.528, 14.2, 17.048, and 37.3% higher than the raw spectra, respectively. This method can be used to estimate the chlorophyll content of winter wheat leaves under CO2 trace-leakage stress and to dynamically monitor CO2 trace-leakage stress in crops.

Wavelet Collocation Method for HIV-1/HTLV-I Co-Infection Model Using Hermite Polynomial.

In this study, the dynamic behavior of fractional order co-infection model with human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) is analyzed using operational matrix of Hermite wavelet collocation method. Also, the uniqueness and existence of solutions are calculated based on the fixed point hypothesis. For the fractional order co-infection model, its positivity and boundedness are demonstrated. Furthermore, different types of Ulam-Hyres stability are also discussed. The numerical solution of the model are obtained by using the operational matrix of the Hermite wavelet approach. This scheme is used to solve the system of nonlinear equations that are very fruitful and easy to implement. Additionally, the stability analysis of the numerical scheme is explained. The mathematical model taken in this work incorporates the biological characteristics of both HIV-1 and HTLV-I. After that all the equilibrium points of the fractional order co-infection model are found and their existence conditions are explored with the help of the Caputo derivative. The global stability of all equilibrium points of this model are determined with the help of Lyapunov functions and the LaSalle invariance principle. Convergence analysis is also discussed. Hermite wavelet operational matrix methods are more accurate and convergent than other numerical methods. Lastly, variations in model dynamics are found when examining different fractional order values. These findings will be valuable to biologists in the treatment of HIV-1/HTLV-I.

Sliding mode tracking control of a class of fractional-order nonstrict-feedback nonlinear systems.

Since the Leibniz rule for integer-order derivatives of the product of functions, which includes a finite number of terms, is not true for fractional-order (FO) derivatives of that, all sliding mode control (SMC) methods introduced in the literature involved a very limited class of FO nonlinear systems. This article presents a solution for the unsolved problem of SMC of a class of FO nonstrict-feedback nonlinear systems with uncertainties. Using the Leibniz rule for the FO derivative of the product of two functions, which includes an infinite number of terms, it is shown that only one of these terms is needed to design a SMC law. Using this point, an algorithm is given to design the controller for reference tracking, that significantly reduces the number of design parameters, compared to the literature. Then, it is proved that the algorithm has a closed-form solution which presents a straightforward tool to the designer to obtain the controller. The solution is applicable to the systems with a mixture of integer-order and FO dynamics. Stability and finite-time convergence of the offered control law are also demonstrated. In the end, the availability of the suggested SMC is illustrated through a numerical example arising from a real system.

Fractional-order state space reconstruction: a new frontier in multivariate complex time series.

This paper presents a novel approach to the phase space reconstruction technique, fractional-order phase space reconstruction (FOSS), which generalizes the traditional integer-order derivative-based method. By leveraging fractional derivatives, FOSS offers a novel perspective for understanding complex time series, revealing unique properties not captured by conventional methods. We further develop the multi-span transition entropy component method (MTECM-FOSS), an advanced complexity measurement technique that builds upon FOSS. MTECM-FOSS decomposes complexity into intra-sample and inter-sample components, providing a more comprehensive understanding of the dynamics in multivariate data. In simulated data, we observe that lower fractional orders can effectively filter out random noise. Time series with diverse long- and short-term memory patterns exhibit distinct extremities at different fractional orders. In practical applications, MTECM-FOSS exhibits competitive or superior classification performance compared to state-of-the-art algorithms when using fewer features, indicating its potential for engineering tasks.

Stability and synchronization of fractional-order reaction-diffusion inertial time-delayed neural networks with parameters perturbation.

This study is centered around the dynamic behaviors observed in a class of fractional-order generalized reaction-diffusion inertial neural networks (FGRDINNs) with time delays. These networks are characterized by differential equations involving two distinct fractional derivatives of the state. The global uniform stability of FGRDINNs with time delays is explored utilizing Lyapunov comparison principles. Furthermore, global synchronization conditions for FGRDINNs with time delays are derived through the Lyapunov direct method, with consideration given to various feedback control strategies and parameter perturbations. The effectiveness of the theoretical findings is demonstrated through three numerical examples, and the impact of controller parameters on the error system is further investigated.

Fractional-Order Modeling of Arterial Compliance in Vascular Aging: A Computational Biomechanical Approach for Investigating Cardiovascular Dynamics.

Goal: The goal of this study is to investigate the application of fractional-order calculus in modeling arterial compliance in human vascular aging. Methods: A novel fractional-order modified arterial Windkessel model that incorporates a fractional-order capacitor (FOC) element is proposed to capture the complex and frequency-dependent properties of arterial compliance. The model's performance is evaluated by verifying it using data collected from three different human subjects, with a specific focus on aortic pressure and flow rates. Results: The results show that the FOC model accurately captures the dynamics of arterial compliance, providing a flexible means to estimate central blood pressure distribution and arterial stiffness. Conclusions: This study demonstrates the potential of fractional-order calculus in advancing the modeling and characterization of arterial compliance in human vascular aging. The proposed FOC model can improve our understanding of the physiological changes in arterial compliance associated with aging and help to identify potential interventions for age-related cardiovascular diseases.

A new hybrid learning control system for robots based on spiking neural networks.

This paper presents a new hybrid learning and control method that can tune their parameters based on reinforcement learning. In the new proposed method, nonlinear controllers are considered multi-input multi-output functions and then the functions are replaced with SNNs with reinforcement learning algorithms. Dopamine-modulated spike-timing-dependent plasticity (STDP) is used for reinforcement learning and manipulating the synaptic weights between the input and output of neuronal groups (for parameter adjustment). Details of the method are presented and some case studies are done on nonlinear controllers such as Fractional Order PID (FOPID) and Feedback Linearization. The structure and the dynamic equations for learning are presented, and the proposed algorithm is tested on robots and results are compared with other works. Moreover, to demonstrate the effectiveness of SNNFOPID, we conducted rigorous testing on a variety of systems including a two-wheel mobile robot, a double inverted pendulum, and a four-link manipulator robot. The results revealed impressively low errors of 0.01 m, 0.03 rad, and 0.03 rad for each system, respectively. The method is tested on another controller named Feedback Linearization, which provides acceptable results. Results show that the new method has better performance in terms of Integral Absolute Error (IAE) and is highly useful in hardware implementation due to its low energy consumption, high speed, and accuracy. The duration necessary for achieving full and stable proficiency in the control of various robotic systems using SNNFOPD, and SNNFL on an Asus Core i5 system within Simulink's Simscape environment is as follows: - Two-link robot manipulator with SNNFOPID: 19.85656 hours - Two-link robot manipulator with SNNFL: 0.45828 hours - Double inverted pendulum with SNNFOPID: 3.455 hours - Mobile robot with SNNFOPID: 3.71948 hours - Four-link robot manipulator with SNNFOPID: 16.6789 hours. This method can be generalized to other controllers and systems like robots.

Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks.

This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.