Control Of Chaotic Systems Research Articles

Control and Function Projective Synchronization of 3D Chaotic System

In this paper, we study a linear feedback control to dampen the chaotic behavior of a 3D dynamic system. Based on the Routh-Hurwitz criterion, the conditions are determined to achieve control. Furthermore, function projective synchronization (FPS) between two identical 3D chaotic systems is demonstrated. The proof of asymptotic stability of solutions for the error dynamical system depends on the negative eigenvalues of the system. Additionally, numerical simulations are utilized to demonstrate the impact and effectiveness of the proposed methods.

Chaos suppression of a Seven-dimensional power system based on the predefined-time sliding mode control method

Abstract To suppress chaotic oscillation in the seven-dimensional power system model, the predefined-time sliding mode control of disturbed seven-dimensional chaotic power system is studied in this paper. Firstly, the dynamic characteristics of the seven-dimensional power system are analyzed, and the existence of chaotic attractors is demonstrated. Then, the seven-dimensional power system is divided into three subsystems according to control outputs, and the chaotic control of the seven-dimensional power system is decomposed into the control problem of three subsystems. For each subsystem, a predefined-time sliding mode controller is designed to regulate the system states converge to the desired values. Compared with other existing control methods, the proposed predefined-time sliding mode controller can control the chaotic power system to the expected states at any predefined time. The minimum upper bound of the convergence time is determined by the adjustable parameters of this controller, which make it meet the control requirements conveniently. Finally, the effective and excellent control performance of the predefined-time control scheme is proved by numerical simulation.

Adaptive arbitrary time synchronisation control for fractional order chaotic systems with external disturbances

In this paper, adaptive synchronisation of fractional order chaotic systems with external disturbances is studied. For this purpose, first, a new integer order system is introduced and its convergence to zero exponentially within an arbitrary time is proven. Using this system, a novel adaptive exponential arbitrary time sliding mode controller is established to synchronise the fractional order chaotic systems. Then, to estimate the disturbance terms of the fractional systems an exponential arbitrary time disturbance observer is developed. The use of the disturbance observer can lead to simple controller design, low chattering control input, and more accurate response. Finally, a disturbance observer based sliding mode control is presented, that by incorporating the disturbance estimation in controller design ensures synchronisation of chaotic systems. The exponential arbitrary time synchronisation and the stability of the closed loop control system are confirmed using the Lyapunov theory. Simulation results on synchronisation of different fractional order systems, validate the proposed control schemes. It is noteworthy that the introduced adaptive sliding mode controllers can be used for controlling a wide variety of fractional order systems.

Synchronization and control of fractional laser chaotic systems defined based on the regularized Prabhakar derivative with incommensurate parameters

Synchronization and control of fractional laser chaotic systems defined based on the regularized Prabhakar derivative with incommensurate parameters

Robust sliding mode control of discrete fractional difference chaotic system

Robust sliding mode control of discrete fractional difference chaotic system

Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems.

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper's method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

Chaos Control and Synchronization of a New Fractional Laser Chaotic System

In this article, we introduce a new fractional laser chaotic system derived from the Lorenz–Haken equations. We investigate the complex dynamics of the proposed system consisting chaos, stability, control and synchronization of chaos. Moreover, we numerically reveal the nonlinear dynamics of the fractional laser chaotic system through the phase portraits, time histories and bifurcation diagrams. Also, we indicate the chaotic behaviors of the system by means of Lyapunov exponents, bifurcation diagrams versus all parameters along the state variables, phase portraits and time histories with different trajectories and initial conditions. The necessary conditions to eliminate the chaotic vibration of the system are obtained via the feedback control procedure. Meanwhile, a synchronization mechanism based on the feedback control technique is achieved for coupled fractional laser chaotic systems. Furthermore, we show that the fractional derivative order is very effective on reducing the irregular and chaotic behaviors of the system.

Control and Stabilization of Chaotic System Based on Linear Feedback Control Method

In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.

Backstepping synchronization control for four-dimensional chaotic system based on DNA strand displacement

Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.

Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors

In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation.

Enhancing the trustworthiness of chaos and synchronization of chaotic satellite model: a practice of discrete fractional-order approaches

Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

A new predictive intelligent controller and path planning for mobile robots

This paper studies the synchronization and control of chaotic systems, and a new chaotic-based path is designed for Mobile robots (MRs). The chaotic systems are used to design an unpredictable path for a class of patrol MRs. To enhance security, multiple chaotic systems with a chaotic switching mechanism are introduced for path planning. The main challenge is that the dynamics of MRs are entirely unknown. The physical dynamics are not reliable in practice, because many parameters in MR dynamics are changed due to unknown environmental conditions such as noisy sensors, time delays, friction, and non-ideal actuators. Also, the chaotic switching of reference signals between chaotic signals imposes a high dynamic perturbation. So, a powerful fractional-order predictive controller on the basis of type-3 (T3) fuzzy-logic systems (FLSs) is developed. The estimation and prediction errors of T3-FLSs are compensated by a designed parallel compensator. T3-FLSs are online tuned such that stability is ensured, and the defined cost function for prediction controller is minimized. The suggested scheme is implemented on a real-world MR, and the results demonstrate the febrility and the accuracy. Also, in several simulations, the efficacy of the designed controller is examined. The simulation and experimental results show that the accuracy is improved more than 70% in comparison with conventional predictive controllers under noisy signals and uncertain dynamics.

Adaptive internal synchronization control of chaotic systems based on DNA strand displacement

AbstractIn the application of DNA‐based chaotic synchronization, the precise values of the system parameters are often complicated to attain due to the interference of external factors, thus weakening the performance of synchronization. In this paper, considering the case of unknown parameters in chaotic systems, a method of adaptive synchronization based on DNA strand displacement (DSD) is proposed. Firstly, the chain replacement reaction modules of emergence, activation and degradation are given through the design of DNA strand, which enable the realization of Yang chaotic system using the mass action dynamics law. Further, in order to achieve the estimation of the unknown parameters and the stability of the error system, the rules for identification of unknown parameters are derived and adaptive controllers are designed under the adaptive control principle. Finally, an internal synchronization approach is recommended to decompose the chaotic system into subsystems of different orders, which can freely choose subsystems to complete synchronization. Subsequently, numerical simulations show that DNA‐based adaptive controllers can fulfill the internal synchronization of Yang system with unknown parameters and are robust to parameter deviations. In addition, the strategy presented in this study can be extended to the synchronization control of other DSD‐based multivariable chaotic systems.

Modeling and optimal control of nonlinear fractional order chaotic system of factors affecting money laundering: genetic algorithms and particle swarm optimization

ABSTRACT The purpose of this article is to model and optimally control the non-linear chaotic system of the fractional order of factors affecting money laundering. The model of factors affecting money laundering was expressed as a system of fractional order differential equation. Due to the presence of chaos in this model, optimal control was provided for it. For optimal control of the chaos in the proposed model, particle swarm optimization algorithm and genetic algorithm were used. The implementation and simulation of this research was done by coding in MATLAB software. The results of the research show that the optimal control applied to the model can control the factors affecting money laundering. When the controller is applied from scratch, the results of the genetic algorithm method are excellent. All the results obtained for the particle swarm optimization method show that this method is also very successful and the results are very close to the genetic algorithm method. Due to the necessity of conducting this research, it can be mentioned that money laundering as an economic crime has a significant negative impact on the economic growth and development of countries.

Command Filtered Adaptive Backstepping Fuzzy Synchronization Control of Uncertain Fractional Order Chaotic Systems with External Disturbance

Command Filtered Adaptive Backstepping Fuzzy Synchronization Control of Uncertain Fractional Order Chaotic Systems with External Disturbance

Neural network control of fractional-order chaotic systems with unknown control direction

In this paper, neural network control of fractional order chaotic systems (FOCSs) with input saturation and unknown sign of the controller gain is addressed by employing the Nussbaum function, where neural networks are utilized to model system uncertainties. To get rid of the limitation that reaching phase should be active before sliding motion in the traditional sliding mode control, a stable sliding surface is constructed. Then, by using the integer order Nussbaum gain control method, a novel controller with neural network sliding mode variable structure is designed. Finally, the practicality of the designed method is confirmed by a simulation experiment.

Adaptive Predictive Control of Fractional Order Chaotic Systems

Adaptive Predictive Control of Fractional Order Chaotic Systems

Adaptive fuzzy finite-time PID backstepping control for chaotic systems with full states constraints and unmodeled dynamics

To solve the problem that the controlled object and system model cannot be fully mastered or the system parameters cannot be well obtained through conventional measurement methods, in this paper, a novel adaptive fuzzy finite-time PID backstepping control method is developed for a class of nonlinear chaotic systems with full state constraints and unmodeled dynamics. The unmodeled dynamics are handled by employing a dynamic signal. To avoid the violations of full state constraints (FSCs), a barrier Lyapunov function is used to implement a PID backstepping framework, whose merit consists in that three control gain constants KP, KI and KD with corresponding proportional relationships are designed to further improve control precision. Besides, the PID control method also embodies three dynamic gain components ΔKP, ΔKI and ΔKD, all of which are free functions that can be self-tuning online, and have a significant link with the adaptive law and modify accordingly. Finally, theoretical analysis confirms that all signals are ultimately uniformly bounded, the error signal converges to a nearby area near the origin in a finite-time, and the FSCs are not smashed. The practicality of the proposed method is confirmed by two simulation studies using the second-order Duffing chaotic system and third-order Chua's circuit.

Finite-time sliding-mode tracking control of uncertain chaotic systems in the presence of an external disturbance and an input saturation

ABSTRACT The study presents a Finite-time Sliding-mode Tracking Control (FSTC) technique to achieve the trajectory tracking of an uncertain chaotic system. The feature of the proposed control strategy possesses a high level of robustness even when the uncertain chaotic system is in the presence of external disturbances and input saturation. First, a nonlinear sliding surface with a fractional-order term is constructed using tracking errors so that the finite-time convergence of tracking errors can be attained. The design of the nonlinear sliding surface, i.e. the selection of control parameters, can shape the system response. Since chattering will result from such control design, a boundary layer is adopted in the controller design to mitigate the high-frequency switching of control signal inputs. The overall system stability and finite-time convergence of the tracking error are verified using Lyapunov stability criteria and the relevant lemma. Finally, the proposed FSTC is applied to the Genesio chaotic system in the presence of uncertainty, external disturbance, and input saturation. The simulation results reveal that the proposed control scheme is indeed feasible and effective for chaotic systems control.

Predefined-time sliding mode control of chaotic systems based on disturbance observer.

In this paper, in order to realize the predefined-time control of n-dimensional chaotic systems with disturbance and uncertainty, a disturbance observer and sliding mode control method were presented. A sliding manifold was designed for ensuring that when the error system runs on it, the tracking error was stable within a predefined time. A sliding mode controller was developed which enabled the dynamical system to reach the sliding surface within a predefined time. The total expected convergence time can be acquired through presetting two predefined-time parameters. The results demonstrated the feasibility of the proposed control method.