Complex Nonlinear Systems Research Articles

Evaluation on Collaborative Control Algorithm for Automotive Braking Based on Artificial Intelligence Simulation

Nowadays, cars have become the mainstream means of transportation, and traffic accidents caused by cars often occur on the road. Therefore, its safety is very important and has also attracted the attention of the general public. The braking system of a car is a very important part of its composition and structure, which determines the smoothness and safety of the car. The automobile braking system is a complex nonlinear system, which has multiple inputs, multiple outputs, uncertainties and multiple interference sources. Due to the complex relationship between input, interference, and output, the uncertainty of internal and external parameters in automobiles makes it very difficult to maintain appropriate braking. In order to improve the stability and safety of automobiles, this article conducts research on artificial intelligence technology, collaborative control algorithms, and automobile braking systems. The aim is to strengthen automobile braking systems through artificial intelligence technology and design an intelligent braking system to ensure smooth and safe driving of automobiles. Experiments have shown that the intelligent braking system can maintain a constant speed and maintain relative stability during emergency braking. The intelligent braking system can automatically detect accident prone road sections for reminders and speed reduction, and also automatically detect the situation around the car to give a warning. The experimental results show that when the car's speed reaches 25m/s or above (90km/h), the warning distance of the system is nearly 150 meters, which can fully ensure the safety of the driver; when driving at low speeds, the warning distance would not be too long to avoid affecting the driver's driving experience.

Playability of self-sustained musical instrument models: statistical approaches

Self-sustained musical instruments, such as wind or bowed string instruments, are complex nonlinear systems. They admit a wide variety of regimes, which sometimes coexist for certain values of the control parameters. This phenomenon is known as multistability. With fixed parameters, the selection of a regime and the shape of the transient depend not only on the values of the control parameters, but also on the initial conditions. In this article, we focus on the statistical influence of initial conditions on regime selection and transient duration. An existing sample-based method called basin stability is presented to calculate the probability of occurrence of each regime. A second sample-based method is proposed for the calculation of the probability density function of transient durations. Additionally, a study taking into account specific control scenarios is presented to highlight the influence of the distribution of initial conditions considered for the statistical methods. These methods are presented on a Van der Pol oscillator seen as a prototypical musical instrument model. They are then applied to a physical model of trumpet, to demonstrate their potential for a high dimensional self-oscillating musical instrument. Finally, their interest regarding questions of playability is discussed.

Online Adaptive Dynamic Programming for Optimal Self-Learning Control of VTOL Aircraft Systems With Disturbances

In this paper, a novel online adaptive dynamic programming control algorithm is developed to solve optimal control problems for Vertical Take Off and Landing (VTOL) aircraft systems. Considering the input disturbances of the VTOL systems and adding perturbation interference term to the value function, a robust policy iteration-based ADP method will be introduced to obtain the optimal controller with an approximate optimal control approach. The convergence property is developed to ensure the value function converges to a finite neighborhood of the optimal one. The uniform ultimate boundedness (UUB) of the iterative errors will be strictly proved by Lyapunov stability theory. Finally, we will give mathematical simulation results with the developed method. Compared with sliding mode control (SMC) and linear quadratic regulator (LQR) methods, the simulation results illustrate better overall performance of the novel method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As an effective tool to solve the optimal control problem of complex nonlinear systems, adaptive dynamic programming (ADP) can effectively overcome the computational problems caused by “curse of dimensionality”. VTOL aircraft system is a typical strongly coupled, underactuate, non-minimum phase system, and the sudden random disturbances will make the control task more challenging. Aiming at the particularity of VTOL system, a new online policy iteration-based ADP algorithm is developed to obtain optimal control with an approximate optimal control strategy in this paper. Decoupling and disturbances can be effectively avoided. convergence will be analyzed to make sure the value function converge to a finite neighborhood of the optimal value function. The UUB property of the system will be proved by the Lyapunov approach.

A Promising Solution to Nucleon–Nucleon Inverse Scattering Problem

This study deals with the inverse elastic two-body quantum scattering problem using Volterra approximations and neural networks, offering a novel approach for solving complex nonlinear systems.

Port-Hamiltonian Modelling of Complex Non-Linear Systems, Application to a Liquid Propelled Rocket Engine

Port-Hamiltonian (PH) systems theory is a well-established framework for modelling the dynamics of non-linear systems. It has been used extensively for complex mechanical systems. Recent developments have extended this representation to multiphysical systems. In this paper, a PH formulation of a Liquid Propelled Rocket Engine model is proposed. Starting from a classical state-space representation, a new model is derived which allows to demonstrate the global passivity feature of the system using the property of passivity inheritance by composition of several PH subsystems. The resulting representation allows to consider passivity-based control perspective for this class of complex thermodynamics system.

Numerical solution of nonlinear complex integral equations using quasi- wavelets

&lt;p&gt;In this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. Finally, several numerical examples were provided to demonstrate the efficiency and precision of our proposed approach, which also confirmed its superiority over polynomial collocation methods.&lt;/p&gt;

Study of Soliton Interaction in Optical Fibers with Third Order Dispersion and Higher Order Nonlinear Effects

In this paper, we present a numerical approach to solve the GNLSE and analyze soliton interaction phenomena using COMSOL environment. By leveraging the capabilities of COMSOL's PDE module, we can accurately capture the dynamics of solitons and investigate their interactions. We analyze the impact of different parameters such as soliton power, initial separation distance, and dispersion characteristics on the soliton dynamics. Furthermore, we examine the role of higher-order dispersion terms in shaping the soliton interactions. Our findings demonstrate the effectiveness of the proposed numerical approach in accurately simulating and analyzing soliton interaction phenomena. The COMSOL-based methodology provides a flexible and efficient framework for studying complex nonlinear optical systems, enabling researchers to gain insights into the behavior of solitons in different media and design optimized communication systems. This paper contributes to the understanding of soliton dynamics and provides a practical tool for investigating the behavior of solitons in nonlinear dispersive media. The presented numerical approach using COMSOL opens avenues for further research in nonlinear optics and fiber optic communication systems.

SD-ARX modeling and robust MPC with variable feedback gain for nonlinear systems

As a generalized input-output model, the state-dependent exogenous variable autoregressive (SD-ARX) model has been intensively utilized to model complex nonlinear systems. Considering that more freedom can be provided by the state feedback control with variable feedback gain for constructing robust controllers, we propose a robust model predictive control (RMPC) algorithm with variable feedback gain on the basis of the SD-ARX model. First, the polytopic state space models (SSMs) of the system are constructed and the prediction accuracy of the SSMs is further improved by using the parameter variation rate information of the SD-ARX model. Then, an RMPC algorithm with variable feedback gain is synthesized for increasing the design freedom and enhancing the control performance. Two simulation examples, that is, the modeling and control of a continuous stirred tank reactor (CSTR) and a water tank system, are provided to demonstrate the feasibility and effectiveness of the proposed RMPC algorithm.

Neural Network-Based Hammerstein Model Identification of a Lab-Scale Batch Reactor.

This paper focuses on two types of neural network-based Hammerstein model identification methods for the acrylamide polymerization reaction of a batch reactor process. The first neural-based identification type formulates the weights of the multilayer network directly as parameters of the nonlinear static and linear dynamic blocks of the Hammerstein model and trains the weights using a gradient-based backpropagation algorithm. In the second identification type, the nonlinear static block of the Hammerstein model is framed as a single hidden-layer feedforward network and both nonlinear and linear block parameters are trained using an extreme learning machine, where the training procedure is exempted from gradient calculation. The primary focus of the paper is neural-based model identification of a complex nonlinear system, which facilitates ease of linear/nonlinear controller design with good learning speed and less computations. A future work toward the machine learning-based nonlinear model predictive controller implementation using the Jetson Orin Nano board is also described.

Improving Model-Free Control Algorithms Based on Data-Driven and Model-Driven Approaches: A Research Study

Given the challenges associated with accurately modeling complex nonlinear systems with time delays in industrial processes, this paper introduces an advanced model-free control algorithm that combines data-driven and model-driven approaches. Initially, an enhanced algorithm for multi-innovation model-free control, incorporating error feedback, is presented based on the error feedback principle. Subsequently, a novel control strategy is introduced by delving into PID neural network (NN) recognition and control theory, merging PID NN control with multi-innovation feedback control. Through meticulous mathematical derivation, the proposed strategy is proven to ensure system stability. Compared with traditional NN PID controllers, the convergence rate of the proposed scheme is 50 s faster and the steady-state errors are limited to ±1.

The Efficiency of Using Machine Learning Techniques in Fiber-Reinforced-Polymer Applications in Structural Engineering

Sustainable solutions in the building construction industry have emerged as a new method for retrofitting applications in the last two decades. Fiber-reinforced polymers (FRPs) have garnered much attention among researchers for improving reinforced concrete (RC) structures. The existing design guidelines for FRP-strengthened RC members were developed using empirical methods that are based on specific databases, limiting the accuracy of the predicted results. Therefore, the use of innovative and efficient prediction tools to predict the behavior of FRP-strengthened RC members has become essential. During the last few years, efforts have been progressively focused on the use of machine learning (ML) as a feasible and effective technique for solving various structural engineering problems. Its capability to predict the behavior of complex nonlinear structural systems while considering a wide range of parameters offers a distinctive opportunity to make the behavior of RC members more predictable and accurate. This paper aims to evaluate the current state of using various ML algorithms in RC members strengthened with FRP to enable researchers to determine the capabilities of current solutions as well as to find research gaps to carry out more research to bridge revealed knowledge and practice gaps. Scopus databases were searched using predefined standards. The search revealed ninety-six articles published between 2016 and 2023. Consequently, these articles were analyzed for ML applications in the field of FRP retrofitting, including flexural and shear strengthening of RC beams, flexural strengthening of slabs, confinement and compressive strength of columns, and FRP bond strength. The results reveal that 32% of the reviewed studies focused on the application of ML techniques to the flexural and shear strengthening of RC beams, 32% on the confinement and compressive strength of columns, 6.5% on the flexural strengthening of slabs, 22% on FRP bond strength, 6.5% on materials, and 1% on beam–column joints. This research also revealed that the application of various ML algorithms has shown a significant improvement in resistance prediction accuracy as compared with the existing empirical solutions. Supervised learning techniques were the most favorable learning method due to their good generalization, interpretability, adaptability, and predictive efficiency. In addition, the selection of suitable ML algorithms and optimization techniques is found to be mainly dictated by the nature of the problem and the characteristics of the dataset. Nonetheless, selecting the most appropriate ML model and optimization algorithm for each specific application remains a challenge, given that each algorithm is developed with different principles and methodologies.

Self-similarity and vanishing diffusion in fluvial landscapes.

Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems.

Deep reinforcement learning-based active control for drag reduction of three equilateral-triangular circular cylinders

Deep reinforcement learning (DRL) is gaining attention as a machine learning tool for effective active control strategy development. This study focuses on employing DRL to develop an efficient active control strategy for flow around three circular cylinders arranged in an equilateral-triangular configuration in a two-dimensional channel. The analysis of control outcomes reveals that DRL induces vortices of varying sizes between the cylinders, resulting in large elliptical vortices at the rear. This enhancement in flow stability leads to a significant 40.40% reduction in cylinder drag force and an approximate 8.23% decrease in overall drag oscillations. Our research represents a pioneering application of DRL for stabilizing complex flow around multiple cylinders, yielding remarkable control effectiveness. The noteworthy outcomes in controlling the stability of complex flows highlight the capability of DRL to grasp intricate nonlinear flow dynamics, showcasing its potential for investigating active control strategies within complex nonlinear systems.

The Covid-19 pandemic as a complex dynamical nonlinear system. Overcoming the Argentinean experience

The Covid-19 pandemic as a complex dynamical nonlinear system. Overcoming the Argentinean experience

Collision dynamics of high-order localized waves in a novel [formula omitted]-dimensional integrable Boussinesq model

The pursuit of finding precise solutions for complex nonlinear systems in high dimensions has long been a significant goal in the fields of mathematics and physics. This paper focuses on investigating a novel equation, referred to as the (3+1)-dimensional Boussinesq equation, which accurately describes the behavior of gravity waves on the surface of water. Using the Hirota bilinear method, the study successfully derives multiple-soliton and multi-breather solutions for the Boussinesq equation. Moreover, it presents mixed solutions that combine solitons and breathers under specific parameter conditions. By considering the long wave limit for these solitons, rational and semi-rational solutions for the equation are obtained. These rational solutions encompass line rogue waves and lump waves, while the semi-rational solutions emerge from the interaction between line rogue waves and solitons. Additionally, employing symbolic computation, the paper introduces a class of multiple lumps for the (3+1)-d Boussinesq equation, showcasing intriguing triangular formations and circular patterns. Overall, the findings of this research enhance our understanding of unique nonlinear phenomena and offer valuable theoretical support for future experimental investigations.

Stock Price Prediction Based on ARIMA and Neural Network

The stock price is affected by many factors and is a very complex nonlinear and non-stationary system. Predicting stock prices is a classic problem. People hope to predict stock prices more accurately, so as to make profits through stocks. This article selects five stocks in the Nasdaq stock market from 2020 to 2023, and tries to use 3 AI models (ARIMA, CNN, LTSM) to predict and analyze their next days closing prices and use the RMSE as the index to analyze the prediction performance. This paper finds that the three models can predict the stock price next day well, among which the ARIMA model and LSTM model have better prediction results, average RMSE for them are about 3.3 and 4.5 while the CNN model has poorer prediction performance with RMSE 7.2. At the same time, paper is found that when the model has a turning point for the stock, all the models predict poorly. In the future, we can consider combining the eigenvalues of more stocks to reduce the impact of turning points on price prediction.

Design of Fuzzy Controller for Lithium Battery Formation LLC Converter Based on Sparrow Search Algorithm Optimization

This paper provides a novel fuzzy PI controller design for LLC resonant converters that make use of the sparrow search algorithm optimization. The LLC resonant converter is a complex nonlinear and time-varying system. As the trend in lithium battery energy conversion systems shifts toward high-power applications, they frequently encounter wide load variations. When employing traditional linear PI controllers of LLC resonant converters, the transient response is slow and fails to adapt effectively to the requirements of wide load changes. In this proposed approach, fuzzy control and PI control are combined to enhance the controller’s flexibility and transient response characteristics. The PI controller parameters are continuously adjusted online, incorporating fuzzy control outputs to improve the controller’s performance. Furthermore, the sparrow search algorithm is applied to optimize the proportional and quantization factors, minimizing the impact of improper parameter selection on the performance of the fuzzy PI controller. This method successfully addresses the challenges posed by the LLC resonant converter, improving adaptability and transient response characteristics in varying load conditions by combining fuzzy control and PI control, online parameter modification, and utilizing the sparrow search algorithm to optimize proportional and quantization factors.

Agents of social change in the institutional field of medicine

The pragmatic goal of this article is to study agent activity aimed at changes in the medical institutional field, under conditions of high social instability. The implementation of the empirical part of аrticle required an adequate methodological and conceptual approach, on the basis of which it could be designed and implemented. As a general methodological platform, the author chose the paradigm of complexity, which builds its methodological proposals on the assumption that large complex nonlinear systems change according to laws that are fundamentally different from those by which simple linear system formations function. Society refers precisely to such complex system objects, and therefore the appeal to such a methodological basis is adequate and fruitful. The work offers the author’s view on the processes of social changes, which are conceptualized as the process of changing the social order. The latter, in turn, is considered as a set of all the practices of social interactions that are currently present in society. The key point in this concept is the statement about the presence of two fundamentally different mechanisms of social change — organizational and self-organizational. It is emphasized that high social instability increases the weight of the self-organizing component of changes, which can fade into the background in relatively stable periods. Applying this theoretical framework to the processes in the institutional field of medicine, we get a model of relevant changes, where both organizational (formal rules of the game, laws, government regulations) and self-organization (informal, spontaneously formed rules of everyday interactions in this institutional field) are equally important. Both of these mechanisms have their conductors-agents, through whom they are implemented. The issue of consistency and balance between these different rules of the game is key for institutional management. At the empirical level, the work examines in detail the agentic actions of U. Suprun in the process of her attempts to reform domestic medicine during 2016-2019 (organizational mechanisms), as well as the agentic activity of volunteers from the "Svoi" Foundation, which is headed by Lesia Lytvynova (self-organizational mechanisms). All the features of these two processes of change, their fundamental difference and the complexities that arise in the process of their coordination are shown. The need to build managerial strategies that take these circumstances into account is emphasized.

Innovations in Computational Approaches for Nonlinear Problems and Complex System Simulations

Nonlinear problem solving and complex system simulation have become critical issues in many fields of science. The development of novel computational methods is crucial to understanding these complex systems. In this abstract, we explore the dynamic landscape of computational techniques, focusing on their uses in simulating complex systems and tackling nonlinear challenges. Creating complex algorithms that can deal with nonlinearity, chaos, and emergent behaviours is where it's at. Tools for modelling and comprehending such complex systems are few, but machine learning, artificial intelligence, and evolutionary computation are at the forefront. The way problems are solved has been completely rethought because of their nonlinearity-tolerance and ability to operate in high-dimensional domains. In addition, novel opportunities have arisen due to the combination of classical mathematical models with computer methods. The behaviour and emergent features of complex systems are best understood by hybrid approaches that combine differential equations, agent-based modelling, and cellular automata. These techniques provide a fine-grained comprehension of component interactions, illuminating emergent events. Moreover, the advent of high-performance computing has substantially expanded the breadth and resolution of simulations. Scientists are now able to probe increasingly complex systems, shedding light on their dynamics and behaviours. Computational capacities have been vastly improved by parallel computing, distributed systems, and cloud computing infrastructures, allowing for the study of systems that were once thought to be intractable. Nonlinear issues and complex system simulations can benefit greatly from the combination of cutting-edge computational approaches with domain-specific expertise. This abstract is a testament to the expanding significance and potential of these computational approaches in understanding complex systems and opening up new frontiers for research and solving problems.

Frequency response of a mass grounded by linear and nonlinear springs in series: An exact analysis

An exact analytical solution for the frequency response of a system consisting of a mass grounded by linear and nonlinear springs in series was derived. The system is applicable in the study of beams carrying intermediate rigid mass. The exact solution was derived by naturally transforming the integral of the governing nonlinear ODE into a form that can be expressed in terms of elliptic integrals. Hence, the exact frequency–amplitude solution was derived in terms of the complete elliptic integral of the first and third kinds. Periodic solutions were found to exist for all real values of [Formula: see text] and for [Formula: see text]. On the other hand, linear or weakly nonlinear frequency–amplitude responses were found to occur during small-amplitude vibrations ([Formula: see text]), very large-amplitude vibrations with strong hardening nonlinearity ([Formula: see text] and [Formula: see text]), and for all amplitudes when [Formula: see text]. Simulations showed that the system’s periodic response is significantly influenced by the nonlinearity parameter ([Formula: see text]), linearity parameter ([Formula: see text]), and amplitude of vibration ([Formula: see text]). Besides, the existence of bifurcation points at [Formula: see text] and different values of [Formula: see text] was confirmed. Lastly, an approximate frequency solution obtained using the He’s frequency–amplitude formulation was found to produce errors less than 1.0% for a wide range of input parameters. In conclusion, the present study provides a benchmark solution for verification of other approximate solutions, and the He’s frequency–amplitude formulation can be used to obtain fast and accurate solutions for complex nonlinear systems.