Chaotic Control Research Articles

Chaotic control of a simply supported beam in a multidimensional system

In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton’s principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam’s multidimensional system.

Chaotic vibration control of an axially moving string of multidimensional nonlinear dynamic system with an improved FSMC

A new control approach based on fuzzy sliding mode control (FSMC) is proposed to regulate the chaotic vibration of an axial string. Hamilton’s principle is used to formulate the nonlinear equation of motion of the axial translation string, and the von Kármán equations are used to analyse the geometric nonlinearity. The governing equations are nondimensionalized as partial differential equations and transformed into a nonlinear 3-dimensional system via the third-order Galerkin approach. An active control technique based on the FSMC approach is suggested for the derived dynamic system. By using a recurrent neural network model, we can accurately predict and effectively apply a control strategy to suppress chaotic movements. The necessity of the suggested active control method in the regulation of the nonlinear axial translation string system is proven using different chaotic vibrations. The results show that the study of the chaotic vibrations of axially translating strings requires nonlinear multidimensional dynamic systems of axially moving strings; the validity of the proposed control strategy in controlling the chaotic vibration of axially moving strings in a multidimensional form is demonstrated.

Based on improved crayfish optimization algorithm cooperative optimal scheduling of multi-microgrid system

In order to solve the influence of the complex interaction relationships among subjects on the system solution accuracy and speed of the Multi-Microgrid system under the high penetration rate of new energy. Firstly, the paper establishes the bi-level optimal scheduling Stackelberg game model based on shared energy storage, considering the inter-subject interaction in MMG. Subsequently, based on the four improvement methods of Chaotic Map, Quantum Behavior, Gaussian Distribution, and Nonlinear Control Strategy, the Chaotic Gaussian Quantum Crayfish Optimization Algorithm is proposed to solve the optimization scheduling model. The improved algorithm exhibits superior initial solutions and enhanced search capability. In comparison to the original algorithm, the relative errors of the CGQCOA optimization outcomes are 98%, 20.96%, 98.74% and 16.55%, respectively, enhancing the model-solving accuracy and the speed of convergence to the optimal solution. Finally, the simulation demonstrates that the revenue of Microgrid 1, Microgrid 2, and Microgrid 3 have increased by 0.73%, 1.17%, and 1.04%, respectively. Concurrently, the penalty cost of pollutant emission has decreased by 5.9%, 11.5%, and 12.68%, respectively. Furthermore, the revenue of the shared storage have increased by 1.91%. These findings validate the efficacy of the methodology proposed in enhancing the revenue of the various subjects and reducing pollutant gas emission.

Halvorsen chaotic system based microwave absorber modelling for fighter jet stealth technologies

This study focuses on the development and detailed analysis of a broadband microwave absorber utilizing Halvorsen chaotic dynamics, that focuses at enhancing stealth capabilities for fighter jets. The investigation begins by exploring the mathematical formulation of the Halvorsen chaotic system and conducting a parametric sweep of its control parameters to generate distinct two-dimensional and three-dimensional chaotic attractor plots. These plots are then post-processed using Julia set theory to develop intricate fractal patterns, which serve as the foundation for the absorber design. Image processing techniques, including filtering and thresholding, are employed to refine the patterns by removing artifacts and noise, ensuring they are suitable for practical implementation. The refined fractal patterns are then imported into a computational electromagnetic simulation environment where they are patterned onto a 0.035 mm thick copper sheet. Moreover, the Magtrex 555 substrate with a thickness of 1.52 mm, is selected for its high permittivity and low-loss characteristics. A comprehensive series of parametric studies are conducted to evaluate the influence of various design parameters such as side length, unit cell geometry, and substrate thickness on the absorber’s electromagnetic performance. Important parameters include the effects of chaotic control parameter optimization and the electromagnetic boundary conditions applied during the simulations. Extensive simulations are performed across the 2–20 GHz frequency range to evaluate absorption efficiency, focusing on key metrics like absorptivity, surface current distribution, and electric field distribution. The final design achieves over 90 % absorption efficiency within the target frequency band when the chaotic control parameters are optimized. Finally, comparative analysis using different commercially available substrates, including FR-4 and Rogers RO3003, reveals that Magtrex 555 offers superior absorption performance. The study concludes with a detailed presentation of the final absorber design, alongside an indepth discussion of the frequency range, parametric variations, and the impact of chaotic system dynamics on the absorption properties. This research provides crucial insights into the design and optimization of chaotic-system-based microwave absorbers, that advances the development of stealth technology in military applications.

Multi-frequency weak signal detection based on Liu-like chaotic synchronization system and its hardware circuit implementation

Considering the shortcomings of traditional chaotic systems in weak signal detection methods, such as the high threshold sensitivity requirement and the narrow detection frequency domain. This study proposes a novel three-dimensional chaotic synchronization system, and the dynamical of the system are exhaustively characterized using equilibrium points, phase diagrams, Lyapunov exponential spectra, and bifurcation diagrams. This method involves weak signal detection by means of chaotic synchronization control. Synchronization of a chaotic system using a backstepping synchronization method is used to detect weak signals by analyzing the synchronization error after the introduction of weak signals in a strong noise background. The chaotic system is implemented by hardware circuits, and the simulation of chaotic synchronization control and detection of weak signals from the perspective of circuits is carried out by circuit simulation software. Additionally, the frequency range within which the system is capable of weak signal detection is tested through extensive simulation experiments. Finally, multi-frequency signals detection experiments are performed. The experimental results demonstrate that the system can accurately detect the frequency of weak signals address the limitations of narrow-band detection and multi-frequency signal detection is possible. Meanwhile, the circuit structure proposed in this paper is simple and has some value for engineering applications.

A memristor-based magnetized Hopfield neural network for hidden scroll chaotic attractors and control analysis with reduced input

A memristor-based magnetized Hopfield neural network for hidden scroll chaotic attractors and control analysis with reduced input

Chaotic libration and control of a space tether-sail system in Earth polar orbits with J2 perturbation

The recently proposed space tether-sail system could enable various interesting and important potential space missions thanks to its thin and long connecting tether and solar radiation pressure (SRP) force without consuming propellants. This paper focuses on nonlinear libration and its control of a tether-sail system in Earth polar orbits. Firstly, nonlinear coupled in-plane and out-of-plane dynamics of the system with a rigid mass-distributed tether and two point masses (a chief satellite and sail respectively) is established using the Lagrangian equation method. Secondly, the predicted occurrence of chaotic in- and out-of-plane librational motions is verified utilizing numerical tools such as presenting the time history of libration, the phase plane, the Poincaré section and power spectral density(PSD). Specifically, the paper investigates the sensitivity of nonlinear dynamical responses to initial values, focuses on the chaotic motion caused by the coupling between the in- and out-of-plane librations, the J2 perturbation of the Earth gravitational field and the small eccentricity of the orbits, also studies the nonlinear librational characteristics influenced by the initial mechanical energy (the Hamiltonian). Thirdly, chaotic librational motions will be controlled merely using modulatable SRP force by the sail propellantlessly. A sliding mode controller based on exponential approaching law is developed. To mitigate the effects of control torque saturation, an input compensator based on Radial Basis Function (RBF) neural network is designed. In addition, to address the cumbersome and inefficient manual tuning of control parameters for the sliding mode controller, a parameter tuning algorithm based on Learning Automata is designed. This algorithm is capable of tuning a high-quality set of controller parameters within 100 iterations. The effectiveness of the propellantless actuators for chaotic libration motion control and developed control algorithm is supported by numerical simulations.

Investigation of a high-performance control algorithm for a unified chaotic system synchronization control based on parameter adaptive method

With the rapid development of computer technology, parameter adaptive control methods are becoming more and more widely used in nonlinear systems. However, there are still many problems with synchronous controllers with multiple inputs and a single output, uncertainty, and dynamic characteristics. This paper analyzed a synchronization control strategy of uncoupled nonlinear systems based on parameter dynamic factors to adjust the performance of the synchronization controller, and briefly introduced the manifestations of chaotic motion. The characteristics and differences of continuous feedback control methods and transmission and transfer control methods were pointed out. Simple, effective, stable, and feasible synchronous control was analyzed using parameter-adaptive control theory. By analyzing the non-linear relationships between various models at different orders, the fuzzy distribution of the second-order mean and their independent and uncorrelated matrices were obtained, and their corresponding law formulas were established to solve the functional expression between the corresponding state variables and the dynamic characteristics of the system. The error risk test, computational complexity test, synchronization performance score test, and chaos system control effect score test were carried out on the control algorithms of traditional chaos system synchronization methods and chaos system synchronization methods based on parameter adaptive methods. Parameter adaptive methods were found to effectively reduce the error risk of high-performance control algorithms for synchronization of the unified chaos system. The complexity of the calculation process was simplified and the complexity score of the calculation process was reduced by 0.6. The application of parameter adaptive methods could effectively improve the synchronization performance of control algorithms, and the control effectiveness rating of control algorithms was improved. The experimental test results proved the effectiveness of control algorithms, which greatly enriched the field of modern control applications and also drove the vigorous development of nonlinear dynamics research, thus making significant progress in chaos application research.

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

Aiming at the control problem of chaotic motion of a kind of collision vibration system with gap, a chaotic motion control of collision vibration system based on RBF neural network is proposed. Firstly, the system mechanical model and chaotic motion are introduced, and then a chaotic controller based on RBFNN is designed to control and simulate the chaotic attractor. The model information of the system is not used in the control method. In this paper, the model of the system is used only to generate the input / output data of the system, and it is not used for the design of the controller. The parameters of AHGSA algorithm are set as follows: the population size is 30, the maximum number of iterations is 100,G0, a = 18, and the proportional coefficient P = 0.96. Small disturbances are applied to the controllable parameter ωof the system to suppress the chaotic motion of the system and make the system tend to stable periodic motion. In order to more clearly show the control effect of chaotic motion, the chaotic motion is controlled when the system iterates 400 times. The results show that the chaotic motion can be quickly controlled to periodic 1-1 motion, the phase diagram is a closed curve, and there is a peak in the spectrum diagram. Chaotic motion can be quickly controlled as periodic 2-2 motion, the phase diagram is two closed curves, and two obvious peaks appear in the spectrum diagram. The proposed method can effectively control the chaotic motion of the system, and the expected target can be not only the fixed point of period 1, but also other periodic orbits.

Method for the Trajectory Tracking Control of Unmanned Ground Vehicles Based on Chaotic Particle Swarm Optimization and Model Predictive Control

Method for the Trajectory Tracking Control of Unmanned Ground Vehicles Based on Chaotic Particle Swarm Optimization and Model Predictive Control

Dynamical analysis of a novel memristor-type chaotic map

As a unique nonlinear component, the discrete memristor, with its simple structure, is associated with the ability to lead to excellent chaotic performance in the construction of chaotic systems. This characteristic has elevated the discrete memristor to a hot topic in the field of chaos. This paper introduces a cosine hyperchaotic map. Numerical simulations reveal its rich dynamical behaviors. The chaotic map exhibits diverse chaotic control models, including partial amplitude control, total amplitude control, initial boosting, and parameter-offset boosting, with dynamical distribution diagrams plotted for amplitude control to quantify the range of amplitude modulation. Additionally, a localized boosting free region is identified, which exhibits extreme sensitivity to initial values. Dual offset parameters are introduced to control this localized boosting free region, enhancing the flexibility of the system. Finally, the map is implemented on STM32 to validate the numerical simulation results.

Robust Adaptive Controller Design for Uncertain Second-Order Jerk Chaotic Systems

In this paper, the stabilization problem for a class of uncertain second-order jerk chaotic control systems is investigated. Combining differential and integral inequalities with nonlinear theory, we intend to construct a robust adaptive controller to promote a class of uncertain second-order jerk chaotic control systems to achieve the goal of adaptive stability. Finally, an example will be provided to illustrate the design process of the adaptive controller, and some numerical simulation results will be offered to demonstrate the correctness and effectiveness of the main result

An Adaptive Robust Control Method for Chaotic State of Permanent Magnet Synchronous Motor

In this paper, a chaotic control method based on adaptive robust controller is proposed to solve the chaos phenomenon of the permanent magnet synchronous motor system by mathematically analyzing the dynamic model of the permanent magnet synchronous motor system to eliminate or suppress chaos in the permanent magnet synchronous motors. This method also takes into account the parameter uncertainties (structural uncertainties) of the system and the external load torque interference (unstructured uncertainty).The former is compensated by adaptive control, and the latter by robust term. Feedforward elimination technology can integrate them together, and effectively reduce the influence of chaos on system performance and realize the high precision position tracking of the permanent magnet synchronous motor system. The Lyapunov method is used to prove the stability of the controller. The simulation results show that the method is better in robustness and control precision.

Enhanced Whale Optimization Algorithm for Fuzzy Proportional–Integral–Derivative Control Optimization in Unmanned Aerial Vehicles

The traditional PID controller in quadrotor UAVs has poor performance, a large overshoot, and a long adjustment time, which limit its stability and accuracy in practical applications. In order to solve this problem, an improved whale optimization fuzzy PID control strategy based on CRICLE chaos map initialization is proposed, and a detailed simulation analysis was carried out using MATLAB software (MATLAB R2022B). Firstly, to more realistically reflect quadrotor UAVs’ flight behavior, a dynamic simulation model was established, and the dynamics and kinematic characteristics of the aircraft were considered. Then, CRICLE chaotic mapping initialization was introduced to improve the global search ability of the whale optimization algorithm and to effectively initialize the parameters of the fuzzy PID controller. This improved initialization method helped to speed up the convergence process and improve the stability of the control system. In the simulation experiments, we compared the performance indicators of the improved CRICLE chaotic mapping initialization whale optimization fuzzy PID controller to the traditional PID and fuzzy PID controllers, including overshoot, adjustment time, etc. The results show that the proposed control strategy has better performance than the traditional PID and fuzzy PID controllers, significantly reduces overshoot, and achieves a significant improvement in adjustment time. Therefore, the improved CRICLE chaotic mapping initialization whale optimization fuzzy PID control strategy proposed in this study provides an effective solution for improving the performance of the quadrotor control system and has practical application potential.

Effect of nonlinear stiffness on single link flexible joint robotic manipulator and its control

This study aims to investigate the significant dynamics of a Single Link Flexible Joint (SLFJ) Robotic Manipulator and implement chaotic control using the Adaptive Sliding Mode Control (ASMC) algorithm. The mathematical model of the system incorporates stiffness nonlinearity by introducing the function (x-x3) Various dynamical tools such as stability analysis of equilibrium points, sensitivity to initial conditions, orbit diagrams for parameter variations, Lyapunov spectrum, and frequency spectrum analysis are employed. The ASMC algorithm is utilized to suppress the chaotic behavior of the system. The equilibrium points are determined for critical parameter values, with the Jacobian matrix and corresponding eigenvalues exhibiting conjugate complex with negative real parts, indicating stability resembling a spiral saddle. Phase portraits illustrate the location and range of the chaotic attractor. Investigation of parameter ′a′ using orbit diagrams and Lyapunov spectrum reveals the transition from periodic to chaotic oscillations. The frequency spectrum confirms the chaotic nature of the system. Parameter estimation, state trajectories, and sliding surface analysis demonstrate that the ASMC scheme can effectively control the system in less than 0.3 s. Nonlinear stiffness has not been previously considered in SLFJ Robotic Manipulators, highlighting a novel aspect of this study. The results unveil new chaotic ranges for parameter variation previously undocumented. Frequency spectrum analysis is employed to distinguish between noise and chaotic oscillations, addressing a significant challenge in real-time systems. The ASMC algorithm is specifically designed to control chaotic oscillations, demonstrating its effectiveness in this context.

Integrated Two-Level New Energy Monitoring and Big Data Centers: A Comprehensive Approach for Urban Sustainability

With the help of the quick development of big data, the Internet of Things, and other related technologies, the construction of new energy monitoring and big data centres aims to enhance the control capability of urban new energy stations. Inefficient operation and maintenance of new energy stations, as well as chaotic production control, are the reasons behind this action. Given the limitations of the current stage of new energy big data platform construction, the construction of group-level new energy monitoring and big data centres to achieve a high degree of integration and sharing of resources and experience has become an inevitable development of the new energy industry. This project aims to achieve multi-level integration in decision-making from the bottom up by using the background of the construction of the Wenzhou New Energy Two-Level Centre as a guide, organising the business processes for new energy production and equipment control, designing the technical architecture of the platform for cloud-side collaboration, providing guidance for the heterogeneous data processing and analysis of new energy assets in the cloud, and acting as a model for the development of the group-level intelligent platform for the new energy industry.

Chaos-Based NMPC as a Novel MPPT Approach for Organıc Photovoltaıcs

Environmental degradation, alongside the dire consequences of climate change such as the melting of glaciers and rising sea levels, highlight the severe challenges associated with reliance on fossil fuels. As such, the shift towards sustainable and clean renewable energy sources, like photovoltaic systems, is becoming increasingly critical. This paper introduces a novel approach leveraging a chaotic-based nonlinear model predictive control to maximize the power output from organic photovoltaic cells. This method is distinguished by its rapid tracking capabilities and its effectiveness in enhancing the distribution network's performance under fault conditions. Utilizing a feedback-driven recursive control strategy, this approach efficiently predicts and adjusts to the optimal operating state, thereby minimizing its cost function. It comprises two primary phases: estimating the reference point and subsequently adjusting the operating point in alignment with this reference. In this process, the Lagrange function plays a pivotal role in optimizing the estimator's performance, while a chaotic neural network model predictive controller manages the boost converter's operation. Implementing this chaos-based nonlinear model predictive controller has successfully reduced overvoltage incidents by more than 1.3%. Notably, in the absence of such control methods, the penetration of OPV panels leads to voltage fluctuations beyond acceptable limits. The findings demonstrate that, alongside a decrease in network losses, there is an increase in the capacity of distribution feeders and a notable enhancement in the system's overall efficiency.

Chaotic model and control of an atmospheric convective system coupled with large-scale circulation

Large-scale weather systems affect or determine the generation, development and movement of small- and medium-scale convective weather systems, and the understanding of their influence mechanism is of great significance for the prediction and forecasting of small- and medium-scale convective systems. From the perspective of dynamics, based on the Lorenz–Stenflo model describing convective systems and the Lorenz84 model describing low-order atmospheric circulation, we constructed a chaotic model of an atmospheric convective system considering large-scale circulation, analyzed the influence of the system parameters on the convective system, and designed a state feedback controller to adjust the convective motion. For the constructed convective weather system model, the existence and boundedness of its solution were analyzed, the Hamiltonian quantity was solved, the dynamic characteristics of the Lyapunov exponent, bifurcation diagram, attractor phase diagram and other methods were used to analyze its dynamic characteristics, the physical significance of its dynamic behavior was discussed, and the influence mechanism of the system parameters on convective weather was given. Additionally, the temperature difference between the upper and lower air currents is changed by the state feedback method, which provides a feasible scheme for adjusting the intensity of convective motion. The simulation experiments show that the chaotic model can explain and reveal the complex dynamic behavior of large-scale weather circulation in small- and medium-scale convective systems, which is of great significance for improving the prediction accuracy of convective systems in local areas, and feedback control can obtain the desired convective motion state.

Chaotic control problem of BEC system based on Hartree–Fock mean field theory

Abstract Due to the difficulty of studying nonlinear quantum systems and the unique composition of Bose–Einstein condensate (BEC) systems, BECs face significant difficulties in solving dynamic analysis and chaotic control problems. Therefore, Hartree–Fock mean field theory is introduced to study the chaotic characteristics, control, and synchronization issues of BEC systems loaded on optical lattices. First, the stability and chaos of BECs in optical lattices were analyzed. Subsequently, constant shift method and activation control were introduced based on the Gross–Pitaevskii equation to achieve control and synchronization of the BEC system. Second, based on the Lyapunov exponent theory, offset parameters are added to BEC chaotic control to achieve control of particle density. Finally, based on the stability theory of linear systems, a control term is introduced to achieve variable analysis of the system’s drive–response system, ensuring that chaotic systems with different initial conditions can still achieve good synchronization and anti-synchronization control. The chaotic problem of BEC system was analyzed using numerical and theoretical methods in the experiment. The effect of adjusting the parameters of the BEC system under the constant shift method is significant. The system exhibits a chaotic state under the Lyapunov exponent, which is mainly concentrated between [3.4, 4.5], demonstrating good system stability. When the offset constant range is [4.21, 5.67], the maximum Lyapunov exponent value is below 0. In the problem of chaotic synchronization, adding activation control causes the system’s time series to exhibit anti-synchronization with spatiotemporal variable variation, while adding control terms leads the system to tend towards synchronization and anti-synchronization with time evolution. The analysis of chaotic control problems in BEC systems can provide reference value and theoretical basis for the dynamic research of quantum physics and related nonlinear systems.

Robust Stabilization of Uncertain Jerk Chaotic Control Systems with Mixed Uncertainties

In this paper, the problem of robust stabilizability of jerk chaotic control systems with mixed uncertainties is investigated. Combining robust control theory and differential-integral inequalities, a nonlinear controller will be derived and guaranteed to achieve the goal of practical stabilization. Besides, both the convergence radius and the exponential convergence rate can be specified in advance. Finally, some numerical simulation results are supplemented to demonstrate the correctness and effectiveness of the main result