Nonlinear Techniques Research Articles

On designing a configurable UAV autopilot for unmanned quadrotors.

Unmanned Aerial Vehicles (UAVs) and quadrotors are being used in an increasing number of applications. The detection and management of forest fires is continually improved by the incorporation of new economical technologies in order to prevent ecological degradation and disasters. Using an inner-outer loop design, this paper discusses an attitude and altitude controller for a quadrotor. As a highly nonlinear system, quadrotor dynamics can be simplified by assuming several assumptions. Quadrotor autopilot is developed using nonlinear feedback linearization technique, LQR, SMC, PD, and PID controllers. Often, these approaches are used to improve control and to reject disturbances. PD-PID controllers are also deployed in the tracking and surveillance of smoke or fire by intelligent algorithms. In this paper, the efficiency using a combined PD-PID controllers with adjustable parameters have been studied. The performance was assessed by simulation using matlab Simulink. The computational study conducted to assess the proposed approach showed that the PD-PID combination presented in this paper yields promising outcomes.

A neuro-fuzzy modular system for modeling nonlinear systems

The real world is nonlinear and in the control application field, this aspect needs to be resolved to build models so we need to refer to nonlinear system modeling techniques. Neuro-fuzzy systems and modular neural networks (NNs) are among the best modeling approaches for nonlinear systems. The combined features of both approaches provide better models. Thus, we propose in this paper a neuro-fuzzy modular architecture for modeling nonlinear systems. The modular architecture consists of dividing a nonlinear problem into several simpler subproblems. We assigned to each subproblem an NN. Each NN provides individual solutions that will be combined to provide a general solution to the original problem. In this respect, the decomposition of the original problem is based on a fuzzy decision mechanism. This mechanism consists of a set of fuzzy rules for processing nonlinear problems using two different strategies. The first involves training only the network weights, and the second adds the fuzzy set parameters to the training step. A comparative study of both strategies reveals the competence of the second strategy in providing better accuracy and simplicity. Using the neuro-fuzzy combination among the modular NNs reduces the complexity of the original problem and achieves much better performance. The proposed architecture is evaluated by two second-order nonlinear systems, a numerical system and a real system called “the chemical reactor,” which is used to carry out a chemical reaction not only in chemical and biochemical engineering, but also in the petrochemical industry. For both systems, the proposed approach provides better performance in terms of the learning time, learning error, and number of neurons.

Neural Preassigned Performance Control for State-Constrained Nonlinear Systems Subject to Disturbances.

This article addresses the finite-time neural predefined performance control (PPC) issue for state-constrained nonlinear systems (NSs) with exogenous disturbances. By integrating the predefined-time performance function (PTPF) and the conventional barrier Lyapunov function (BLF), a new set of time-varying BLFs is designed to constrain the error variables. This establishes conditions for satisfying full-state constraints while ensuring that the tracking error meets the predefined performance indicators (PPIs) within a predefined time. Additionally, the incorporation of the nonlinear disturbance observer technique (NDOT) in the control design significantly enhances the ability of the system to reject disturbances and improves overall robustness. Leveraging recursive design based on dynamic surface control (DSC), a finite-time neural adaptive PPC strategy is devised to ensure that the closed-loop system is semi-globally practically finite-time stable (SPFS) and achieves the desired PPIs. Finally, the simulation results of two practical examples validate the efficacy and viability of the proposed approach.

Lump and kink soliton phenomena of Vakhnenko equation

Understanding natural processes often involves intricate nonlinear dynamics. Nonlinear evolution equations are crucial for examining the behavior and possible solutions of specific nonlinear systems. The Vakhnenko equation is a typical example, considering that this equation demonstrates kink and lump soliton solutions. These solitons are possible waves with several intriguing features and have been characterized in other naturalistic nonlinear systems. The solution of nonlinear equations demands advanced analytical techniques. This work ultimately sought to find and study the kink and lump soliton solutions using the Riccati–Bernoulli sub-ode method for the Vakhnenko equation (VE). The results obtained in this work are lump and kink soliton solutions presented in hyperbolic trigonometric and rational functions. This work reveals the effectiveness and future of our method for solving complex solitary wave problems.

A Study on Restoration Plan after Blackout of a System with 100% Inverter Based Resources Considering Bus Inertia

This paper introduces a sequential black-start system restoration procedure in a system with 100% inverter based resources considering system inertia. First, the capability of virtual inertia supported by controlled grid-forming inverters at various locations in a 100% inverter based resources system is calculated through estimation of signal parameters via rotational invariance and nonlinear least square technique; second, a set of radiality constraints is designed for network topology to track inertia value at each bus to find the best restoration paths. Case studies on the modified 39 bus New England system demonstrate that the proposed approach outperforms the existing state-of-the-art approaches in tracking speed and accuracy.

Research progress of magnetic resonance wireless power transfer based on higher-order non-Hermitian physics

<sec>In recent years, wireless power transfer (WPT) leveraging parity-time (PT) symmetry has made significant progress , in terms of enhancing efficiency, transfer distance, and robustness. This paper overviews magnetic resonance WPT systems utilizing ideal, asymmetric, high-order, and anti-PT symmetry.</sec><sec>The first section discusses the second-order PT symmetry, evolving from inductive to resonant WPT. Active tuning and nonlinear saturation gain techniques optimize frequency and spontaneously achieve efficient WPT. These methods improve transmission efficiency, especially with the change of dynamic transfer distance. The second section focuses on the third-order PT and anti-PT symmetry. The third-order PT systems maintain a fixed eigenfrequency, making stable energy transfer possible. Generalized PT symmetry harnesses bandgaps for further efficiency. The BIC in asymmetric systems reveals a pure real mode for stable WPT. The anti-PT symmetry’s ‘level pinning’ maintains stability in dynamic changes. The final section summarizes high-order PT symmetry for long-range WPT. Heterojunction coupling and topologically non-trivial chains enhance efficiency and stability. Examples include long-range WPT via relay coils and directional WPT using asymmetric topological edge states.</sec><sec>In summary, this review emphasizes the pivotal role of various forms of PT symmetry in improving the performance and reliability of magnetic resonance WPT systems. By improving transmission efficiency, range, and stability, these symmetries pave the way for wider applications in fields such as smart homes, medical devices, and electric vehicles. The synthesis of current research results provides valuable insights and references for the future development of WPT technology.</sec>

True Order Determination of Sonochemical Degradation Kinetics of Organic Contaminants in Water Using the Half-lives Method

In the literature, the modeling of the sonolytic decomposition kinetics of organic contaminants in water has been carried out using the pseudo-first and pseudo-second order equations. The results obtained with this method are totally biased because it requires the assumption of the order of the degradation reaction, which is a real limitation, and the sonochemical oxidation mechanism is a very complex phenomenon that cannot be described by such simple models. In this paper, for the first time, the true order of the sonochemical degradation kinetics of organic pollutants in aqueous solutions at various initial substrate concentrations was determined using the half-lives method combined with the general rate law model, i.e., the pseudo-nth order equation. Linear and nonlinear regression techniques were used to determine the order of the sonolytic destruction reaction. The half-life technique for the general rate law model can adequately describe the experimental results of the sono-destruction of the investigated pollutants. For rhodamine B and naphthol blue black, the sono-destruction mechanism for both contaminants does not change as the initial contaminant concentration varies over the range examined, while for 4-isopropylphenol and furosemide, the sono-destruction mechanism changes as the initial substrate concentration varies. A fractional order of the sonolytic destruction reaction was determined for all the pollutants tested. These fractional orders of sono-destruction reactions indicate the complex nature and behavior of the reactions, often involving multiple steps or mechanisms. They also reveal a more complex interaction between pollutant concentration and sonolytic destruction rate. In a word, the method developed in this paper should be used to determine the real order of the sono-oxidation reaction of nonvolatile organic pollutants in aqueous phase.

Research on Piano Curriculum Education and Its Performance Ecosystem Based on Network Flow Optimization

Abstract This paper investigates music education, where an efficient and accurate performance evaluation system in the piano teaching and performance ecosystem is increasingly becoming an essential tool for improving teaching quality and performance level. The objective evaluation of students’ performance skills can be achieved by carefully analyzing piano performances using the network flow optimization technique. This technique optimizes the performance evaluation system’s audio recognition ability by analyzing the piano audio signal and solving the multi-constraint nonlinear optimization problem in a limited time domain. This paper establishes a network flow optimization model, applies the multi-constraint nonlinear optimization technique, and combines the non-negative matrix decomposition and dynamic time regularization algorithm to analyze the piano performance for experiments. After optimization processing, hundreds of piano audio samples were collected, and the audio recognition accuracy was improved by 20%. By optimizing and processing the audio signals from the network stream, the evaluation system could detect polyphony more accurately and track the musical score effectively, improving accuracy and efficiency. Using the non-negative matrix decomposition algorithm, the accuracy of detecting polyphony can reach 85%, while the dynamic temporal regularization algorithm can match the position of the musical score with 95% accuracy. The accuracy of piano performance evaluation is optimized by this network flow optimization method, providing new technical means for music education, and promoting the quality of teaching and performance.

Far-end delamination characterization of CFRP laminates using nonlinear ultrasonic spectra of scaling subtracted vibration response

The application of nonlinear ultrasonic techniques for the near-end damage characterization of carbon fiber reinforced polymers (CFRP) has proven to be successful and extensive. However, the nonlinear ultrasonic response is weak and may be overwhelmed by the linear component of signals if the damage is located at the far-end. In this paper, the scaling subtraction method (SSM) is adopted to filter out the nonlinear ultrasonic signature aimed at the better characterization of far-end delaminations in CFRP laminates. A three-dimensional finite element model is constructed first to validate the feasibility of separation effect of SSM. Then the experimental study is conducted for a delaminated CFRP plate using laser scanning Doppler vibrometer (LSDV) response measurements. Results show that the far-end delamination can be detected and localized clearly since the nonlinear features can be accurately separated from the surface vibration response by using SSM. Moreover, the far-end delamination size is qualitatively analyzed by using the maximum response amplitude (MRA) of the higher harmonics of SSM signals, and a positively correlated trend is shown as the delamination size increases. This work demonstrates the applicability and potential of SSM technique for the comparative assessment of far-end defect information in composites.

A Comprehensive Analysis of Turnout, Switching, and Nonlinear Control Technique to Enhance Safety, Efficiency, and Capacity in Hyperloop

A Comprehensive Analysis of Turnout, Switching, and Nonlinear Control Technique to Enhance Safety, Efficiency, and Capacity in Hyperloop

Application of the mixed integer nonlinear programming technique for the economic planning of transmission networks in new manner

Application of the mixed integer nonlinear programming technique for the economic planning of transmission networks in new manner

Using Linear and Non-Linear Techniques to Characterize Gait Coordination Patterns of Two Individuals with NGLY1 Deficiency

Using Linear and Non-Linear Techniques to Characterize Gait Coordination Patterns of Two Individuals with NGLY1 Deficiency

Sensorless nonlinear control based on integral backstepping technique for PMSG- based wind energy conversion system

This article addresses the control of the wind energy conversion system (WECS) based on a permanent magnet synchronous generator (PMSG) connected to the grid through a three-phase rectifier and an inverter followed by an L filter. Two observers have been developed to estimate the mechanical torque of the PMSG and the rotor flux. Integral backstepping control (IBC) has been employed to regulate the wind energy conversion system. Its objective is to achieve maximum power point tracking while maintaining the bus voltage at its reference and regulating the injected power into the grid to ensure a unity power factor. The developed control approach has been tested using Matlab/Simulink and compared with the linear PI controller. Simulation results demonstrate, on one hand, the robustness, efficiency, and superiority of the nonlinear technique employed, and on the other hand, the dynamic performance of the developed observers.

Female empowerment and crime patterns in Malaysia: A non-linear analysis

Using data from 1982 to 2020, this study evaluated the impact of female employment on violent crime in Malaysia using the non-linear ARDL technique. The study found that, in the long run, lower unemployment rates were linked to lower rates of violent crime, and increased female employment facilitated a short-term reduction in violent crime. Fewer women working resulted in a short-term rise in violent crime and, over the long term, higher rates of violent crime contributed to higher rates of jail population growth. Surprisingly, higher employment rates for women were eventually linked to higher rates of violent crime. Long-term trends showed a correlation between lower employment rates for women and greater rates of violent crime. For short-term analysis, negative economic growth was linked to a rise in violent crime, and positive economic growth could lower violent crime. These results demonstrated the complex interplay between a number of variables and violent crime rates. Thus, to successfully prevent violent crime and build safer societies, it is crucial to address socioeconomic inequalities, advance gender equality, and put into practice comprehensive methods that include community assistance, employment, education, and rehabilitation.

Bioclimatic similarity between species locations and their environment revealed by dimensionality reduction analysis

Species distribution modeling is an active research topic with applications in conservation management, pest risk assessment, and population ecology. Several machine-learning methods have been applied to estimate species distribution. Non-linear dimensionality reduction techniques aim to preserve the similarity among objects at a reduced dimension for visualization, clustering, and feature selection. We propose a framework that uses Uniform Manifold Approximation and Projection (UMAP) to analyze bioclimatic variables associated with environmental (background) and species samples. Our objective was to identify geographic areas similar to those inhabited by the species. We hypothesize that the similarity between species locations and their environment in the reduced dimension will reflect similarity in the multivariate bioclimatic space. We estimated the probability of background points near a species point utilizing the latent nearest neighbor distance distribution. We tested this procedure with ten insect pest species of global importance and found that UMAP was able to generate a gradient of similarity between geographic areas and species occurrence. We also found that background-species latent distance tends to have a convergent non-linear relationship with the mean value of bioclimatic variables, thus supporting our key assumption. The performance of UMAP as a binary classifier and comparison with MaxEnt supports its use in modeling of species distribution. Potential applications are discussed for multi-species and multi-scenario analysis, as well as projection to new regions.

Optimizing Nonlinear Control Strategies for Autonomous Vehicles

Maximizing the effectiveness of nonlinear control techniques (NCT) is crucial for the broad acceptance and smooth integration of autonomous vehicles. Navigating the intricacies of real-world settings, boosting vehicle stability, and enhancing overall performance are all greatly impacted by these tactics. For manufacturers to successfully deploy autonomous cars in environments that are both dynamic and unpredictable, it is crucial to strike a balance between rigid control and flexibility. Autonomous vehicles confront a number of obstacles when trying to optimize nonlinear control systems, including changing road conditions, unpredictable traffic, and the requirement to make decisions in real-time. Because of the complexity of these problems, traditional control methods are frequently not up to the task, thus one need to find new ways to make control strategies more resilient and flexible. A Nonlinear Control Optimization Framework (NCOF) is suggested in this research; it makes use of adaptive control mechanisms, high-level optimization methods, and machine learning approaches. NCOF is engineered to enhance the vehicle's performance in a variety of situations by continuously adapting and optimizing control parameters using environmental data and real-time feedback. Beyond conventional navigation, the NCOF finds use in situations including emergency response, complicated urban surroundings, and bad weather. Improved decision-making, navigating, and passenger safety in a variety of situations are all outcomes of NCOF's optimization of nonlinear control techniques for autonomous cars. Thorough simulation assessments are carried out across several virtual scenarios to verify the efficacy of the suggested NCOF. Displaying the flexibility, stability, and efficacy of NCOF in various contexts, the simulations evaluate the optimal nonlinear control schemes' effectiveness in contrast to conventional methods.

Optimizing Communication Systems with Applied Nonlinear Analysis Techniques

The introduction of applied nonlinear analytic techniques is a disruptive force in the field of modern communication systems, revolutionising the methodology for system optimisation. This investigation into nonlinear approaches provides a deep grasp of the complex dynamics in communication networks and opens a realm beyond the confines of conventional linear models. This paper has become a beacon, illuminating the potential of nonlinear optimisation to tackle issues inherent in linear frameworks by exploring the intricacies of nonlinear systems. Nonlinear analytic integration has impacted concrete implementations in various communication domains, surpassing theoretical limitations. The application of nonlinear optimisation has produced robust error correction schemes, optimised signal processing algorithms, and adaptive modulation techniques that can dynamically adapt to the unpredictable network landscape. These innovations span wireless and optical communication, error correction coding, and adaptive modulation techniques. But there are obstacles on this journey of transformation. Implementation challenges in real-time and computational complexity still exist. However, communication systems strengthened by nonlinear analysis have a bright future ahead of them. With new technologies like artificial intelligence (AI) and machine learning positioned to be powerful partners that may accelerate and simplify nonlinear optimisation, the field of communication systems seems set for a period of intelligent, responsive, and adaptive networks. In conclusion, a new age for communication systems is being heralded by the integration of applied nonlinear analytic techniques, which promises resilience, efficiency, and adaptability. With new technologies and methods emerging to overcome obstacles, it seems that communication systems will continue to evolve in the future, ushering in a new era of network architecture.

Unraveling the Complexity with Applications of Nonlinear Analysis in Signal Processing and Communication Engineering

Nonlinear analysis is an essential area of signal and communication engineering. Many different kinds of nonlinear analysis can be used in this study. Linear signal processing techniques had previously struggled to accurately capture complex data pattern and communication signals. However, the development of non-linear analysis is a game-changing advancement since it provides a solid framework for understanding and manipulating these complex and non-trivial dynamics. In order to understand the behaviour of a wide variety of signals, from financial market trends to biological and environmental data, non-linear techniques are essential in signal processing. Improved understanding of system behaviour and predictive models may result from the use of such techniques to extract complex data patterns that are not often used. Non-linear approaches also contribute to the development of image and video processing by easing the development of advanced compression, tracking, and object recognition algorithms. Non-linear analysis is crucial in communication engineering as it aids in comprehending and optimising the flow of information across various channels. A greater understanding of signal distortion is made possible by the nonlinear perspective, which makes it possible to build reliable communication systems that can withstand interference and noise. By facilitating the creation of sophisticated modulation systems, adaptive equalisation methods, and error control coding, it raises the communication networks' dependability and effectiveness. Designing complex systems that can handle the complexities of today's data and communication demands is made possible by the paradigm-shifting synergy of nonlinear analysis, signal processing, and communication engineering. This abstract highlights the role that nonlinear analysis plays in transforming various fields and highlights how it can be used to solve changing problems related to information comprehension, processing, and transmission in a technologically sophisticated world.

Exploring the dynamics of a multistable general model of discrete memristor-based map featuring an exponentially varying memristance

Chua’s groundbreaking discovery in 1971 introduced the memristor as the fourth essential electrical component, joining resistance, capacitance, and inductance. Over the past few years, numerous discrete memristor models have been developed following its formal proposal, expanding our understanding of this subject. However, there is limited discussion about multistable discrete memristor models. This research combines a comprehensive methodology for generating memristive maps using the modulo function and an exponential memristance, resulting in the development of a multistable discrete memristor model. Nonlinear techniques, such as bifurcation diagrams, Lyapunov spectrum diagrams, and phase portraits were utilized to analyze the dynamic characteristics of the system. The findings uncovered a range of captivating phenomena associated with chaos theory, including regular orbits, chaotic orbits, the mechanism of period doubling leading to chaos, crisis phenomena, and the presence of multistability.

Command filter‐based adaptive event‐triggered control for switched nonlinear systems with full state constraints

AbstractAn adaptive event‐triggered control issue based on command filter and dynamic surface control is studied for switched nonlinear systems with full state time‐varying constraints in this article. To handle state constraints, the nonlinear mapping conversion technique is used. Radial basis function neural networks (RBFNNs) are utilized to approximate unknown nonlinear continuous functions. Adaptive control algorithm is designed based on command filtered backstepping technology. Novel even triggered control is constructed for two different cases in the switching interval. Furthermore, all signals in the switched system are proved to be semi‐globally uniformly ultimate bounded (SGUUB) by the aid of dynamic surface control method under arbitrary switching. Meanwhile, all states do not violate the preset constraints and Zeno phenomenon is avoided. The validity of the presented approach is confirmed through a numerical simulation result.