Chaotic Control Research Articles

A modified function-link fuzzy cerebellar model articulation controller using a PI-type learning algorithm for nonlinear system synchronization and control

This paper aims to propose a novel modified fuzzy cerebellar model articulation controller (CMAC) combined with a function-link network for the synchronization of nonlinear chaotic systems and control of an inverted pendulum in the presence of uncertainties, external disturbance, and different initial conditions. The proposed method overlaps the previous state and the current state of Gaussian basis functions (GBFs) on each layer to make a combination between two states. This makes the inputs be able to simultaneously stir the current state and previous state to adjust the appropriate error values so that the modified function-link fuzzy CMAC (FLMFC) can easily learn parameters, improve the computational efficiency and predict the next state of the inputs. The proposed control system combines an FLMFC with the sliding mode control; therefore the input space element of FLMFC can be simplified. A function-link network is embedded in the FLMFC to give a more accurate approximation of the weights. A PI-type learning method is used to online tune the parameters for the connective weights of the proposed FLMFC. The control system consists of an FLMFC and a compensation controller. A Lyapunov stability theorem is applied to find the adaptation laws of the proposed controller and to guarantee the system's stability. Simulation studies for the synchronization of chaotic systems and control of inverted pendulum show that favorable tracking performance can be achieved by using the proposed control system.

Dynamical analysis of a new fractional-order Rabinovich system and its fractional matrix projective synchronization

This paper constructs a new physical system, i.e., the fractional-order Rabinovich system, and investigates its stability, chaotic behaviors, chaotic control and matrix projective synchronization. Firstly, two Lemmas of the new system's stability at three equilibrium points are given and proved. Next, the largest Lyapunov exponent, the corresponding bifurcation diagram and the chaotic behaviors are studied. Then, the linear and nonlinear feedback controllers are designed to realize the system's local asymptotical stability and the global asymptotical stability, respectively. It's particularly significant that, the fractional matrix projective synchronization between two Rabinovich systems is achieved and two kinds of proofs are provided for Theorem 4.1. Especially, under certain degenerative conditions, the fractional matrix projective synchronization can be reduced to the complete synchronization, anti-synchronization, projective synchronization and modified projective synchronization of the fractional-order Rabinovich systems. Finally, all the theoretical analysis is verified by numerical simulation.

Chaotic Behavior and Adaptive Control of the Arch MEMS Resonator With State Constraint and Sector Input

This paper mainly investigates adaptive control problem of the arch micro-electro-mechanical system (MEMS) resonator. To facilitate controller design, the power spectrum and bifurcation diagram are provided to judge whether the arch MEMS resonator is in chaotic oscillation or not under distributed electrostatic actuation. In the process of creating the controller, the Nussbaum function is employed to solve the issue of unknown control direction from the sector nonlinear input, and the barrier Lyapunov function is utilized to prevent constraint violation when the arch MEMS resonator faces physical limitations. Meanwhile a first-order filter is introduced to prevent repeated computation of the virtual control signal, and a Chebyshev neural network by merging an adaptive law is adopted to learn the behavior of unknown dynamics. Furthermore, an extended state observer which lifts the constraint against physical sensors is developed to estimate immeasurable states. Then, an adaptive control scheme fused with the Nussbaum function, filter and observer is created in the framework of backstepping without imposing any conditions on state variables and control direction of sector input. It is proved that all signals in the closed-loop system are bounded by selecting parameters appropriately. Finally, simulation verifications are presented to show the feasibility of the proposed method.

Chaotic characteristic analysis of spatial parallel mechanism with clearance in spherical joint

The spherical joint is one of the main motion pairs in spatial parallel mechanism, and the spherical clearance has a great effect on the nonlinear dynamic performance of parallel mechanism. Most previous studies mainly focused on planar mechanism with revolute joint, spatial parallel mechanism with spherical clearance researched rarely. In this paper, the chaotic characteristic analysis of spatial 4-UPS (universal joint-prismatic pair-spherical joint)-RPU (revolute joint-prismatic pair-universal joint) parallel mechanism with spherical clearance is investigated. The models of spherical joint with clearance are established, and then the nonlinear dynamics equation of the parallel mechanism with spherical clearance is derived by Lagrange method. The influence of clearance on displacement, velocity and acceleration of moving platform is both analyzed. And the influence of different clearance sizes on contact force and center trajectory of the spherical clearance is analyzed, and the chaotic characteristics of spherical joint and the mechanism are all studied by phase diagram, Poincare section mapping method and Lyapunov exponent. The results show that spherical clearance has great influence on the nonlinear dynamic performance of 4-UPS-RPU parallel mechanism, and chaos exists in the dynamic response of spherical clearance and the mechanism. As the clearance value increases, the stability of the mechanism is weakened. When the clearance value increases to 2.1 mm, chaotic motion appeared on the moving platform of the mechanism. This research is a useful attempt to study the nonlinear dynamics characteristic of parallel mechanisms with spherical clearance, which has guiding significance and practical value for further research on the design and chaotic control of parallel mechanism.

Nonlinear dynamic analysis and chaos control of multi-freedom semi-direct gear drive system in coal cutters

Abstract Under the nonlinear influence, the nonlinear oscillation of the semi-direct gear drive system (SDGDS) in coal cutters will happen, which will cause the system unstable. To solve this unstable problem, a multiple degrees of freedom (MDOF) nonlinear dynamic model of a gear pair is set up using mass centralized method, with both gear meshing features including time-varying mesh stiffness, mesh damping, backlash and dynamic transmission errors and nonlinear coupling effect such as radial clearance of ball bearing being taken into account. After the application of dimensionless treatment, the system is calculated using Runge-Kutta method. Meanwhile, the main parameters which may cause chaos and bifurcation are studied, for example, exciting frequency, radial clearance of ball bearing and mesh stiffness ratio. Then, the kinematic phase diagram, the Poincare map, the largest Lyapunov exponent chart as well as the bifurcation diagram are presented with different parameters. Furthermore, a chaos control method by means of proportion integral (PI) is proposed within a selected reasonable range. The results demonstrate that different parameters can lead to the occurrence of different chaotic behavior. It is also found that the chaotic control method suggested in this paper may not only reduce the area of chaos sufficiently but also suppress the chaotic phenomenon effectively. Besides, as there exists many nonlinear parameters, the study of parameters will lay a profound theoretical basis and practical significance for the improvement of the system stability and the optimization of the system parameters.

Bifurcation and chaos analysis of a gear pair system with multi-clearance

In order to investigate the characteristics of bifurcation and chaos for a spur gear pair system, a three-degree-of-freedom nonlinear dynamic model with multi-clearance is established, in which time-varying meshing stiffness, static transmission error, gear backlash and bearing clearance are comprehensively taken into account. Through introducing a relative generalized coordinate, the dimensionless dynamic equations of motion of system are derived and then solved by using Runge-Kutta numerical integration method. And the bifurcation and chaos features of gear pair are systematically analyzed and discussed from bifurcation diagrams with meshing frequency, gear backlash, bearing clearance and damping ratio as control parameters under different loaded conditions. Meantime, with the help of Poincaré map and phase diagram, the motion forms of system are accurately identified. The analysis results reveal that as meshing frequency increases, the system shows various types of motion states which contain periodic motion, quasi-periodic motion and chaotic motion. Similarly, with the increasing of gear backlash, the system undergoes complex motion forms under lightly loaded condition, whereas it is only in period-one motion state under heavily loaded condition. Furthermore, the system motion state is gradually switched from chaos to periodic or quasi-periodic motion under lightly loaded condition when bearing clearance changes. However, under heavily loaded condition, the bearing clearance has a weak effect on dynamic behavior of the gear system. Apparently, the system tends to be more stable under heavily loaded condition than that under lightly loaded condition. In addition, the growing damping ratio can effectively suppress the chaotic behavior and control nonlinear vibration of gear system. The research results provide useful guidance for dynamic design and vibration control for gear set.

Chaotic Self-Tuning PID Controller Based on Fuzzy Wavelet Neural Network Model

PID controller has been quite successful when its parameters are tuned properly. However, it fails in varying situations. This is even more critical where the system is not known. In this paper, after illustrating the capability of fuzzy wavelet neural network (FWNN) in modeling of nonlinear systems, a self-tuning PID controller based on this model has been designed. The auto-tuner effectively handles the limitation of PID controller in unpredictable conditions such as environmental changes. Chaotic optimization method which is a robust algorithm of escaping from local minimum is applied for tuning of the controller parameters. This supports finding optimal values of controller parameters in a short time which enables online implementation. Unlike most of the researches in this area, the tuning rules could be begun without any trial and error. Since it contains no extra parameters, it has the feature of simplicity in the tuning. The proposed method with few parameters has the ability to increase the speed of tracking with very little steady-state error. The capability of FWNN in the modeling of nonlinear systems with a few rules and susceptibility of the proposed controller will be shown by simulation.

A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

A 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is q≥0.8477. The fractional-order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractional order q is given. Furthermore, there are the coexisting “positive attractor” and “negative attractor” in this fractional-order chaotic system, and the necessary condition for “positive attractor” and “negative attractor” is obtained. Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller. Numerical results show that the control scheme is valid.

Adaptive critic-based quaternion neuro-fuzzy controller design with application to chaos control

Neuro-fuzzy control structures despite all of the advantages from both neural networks features and fuzzy inference engines always get in trouble due to a large number of fuzzy rules which is because of the high order of the system or the large number of divisions considered for each input. In this paper, a new adaptive neuro-fuzzy controller is proposed based on the quaternion numbers, and thus the mentioned problem of large rule numbers is solved by using the quaternion back propagation concept. Furthermore, utilizing reinforcement learning which assesses output value produced by a critic is another strength of the proposed method. Finally, in order to show the superiority and effectiveness of the proposed controller in comparison with conventional neuro-fuzzy ones, a complex and challenging chaos control problem which is a chaotic spinning disk control is provided.

Switching event-triggered network-synchronization for chaotic systems with different dimensions

Abstract In this paper, a novel switching event-triggered synchronization scheme is established for chaotic networked control systems with different dimensions. First, a reduced-dimension observer is constructed to help the response system estimate all the states of the drive system. Next, a switching event-triggered networked control method which depends both on relative error and absolute error of the sampled-data is designed to reduce the burden of network bandwidth effectively while ensuring the desirable synchronization performance. On the basis of the above, some sufficient synchronization criterions are derived in the form of linear matrix inequalities. Finally, the numerical simulation is carried out to demonstrate the effectiveness and superiority of the synchronization method.

Movement Stabilizing Using Afferent Control of Spinal Locomotor CPG Using Chaotic Takagi-Sugeno Fuzzy Logic Systems: A Simulation Study

Background: External control of the function of the central pattern generators (CPGs), exist in the spinal cord, is possible by electrical or chemical stimulation of some of the spinal Afferents. After restarting the activity of spinal cord CPG, the dynamics of movements such as gait can be changed through the time by controlling the rhythm of the CPG. Methods: The purpose of this study was provision of closed loop control algorithm based on the Takagi-Sugeno fuzzy controller in order to adjust the weight of the spinal cord afferents in a neuro-mechanical model with the aim of controlling the rhythm of the CPGs. Rhythm control of CPGs has been done with the aim of implementing the process of resetting the phase during gait in order to stabilize the movement against external disturbances. In this paper, the efficiency of a continuous Takagi-Sugeno fuzzy controller with the efficiency of 2 fuzzy Takagi-Sugeno chaotic controllers has been compared. Results: It was shown by the results obtained from the simulation that the process of resetting the motion phase of the skeletal angle in face of applying disturbance in method of chaotic Takagi-Sugeno fuzzy controller is done with good features in the presence of delayed feedback in decreasing overshoot and undershoot to the amount of 1.982 and 0.17 radians, respectively so that the best amount of afferent to reset the phase and return to the desired angle is provided at the shortest possible time. Conclusion: In this paper, the efficiency of a continuous Takagi-Sugeno fuzzy controller with the efficiency of 2 fuzzy Takagi-Sugeno chaotic controllers has been compared for movement stabilization using spinal cord afferent control. According to the results, the best performance was observed when the chaotic fuzzy Takagi-Sugenocontroller in the presence of delayed feedback was used.

Multi-switching combination synchronization of different fractional-order non-linear dynamical systems

In this paper, multi-switching combination synchronization (MSCS) scheme has been investigated between a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen System are taken as drive systems. The combination of multi drive systems is then synchronized with the fractional-order Rössler chaotic system. In MSCS, the state variables of two drive systems synchronize with different state variables of response system, simultaneously. Based on the stability of fractional-order chaotic systems, the multi-switching combination synchronization of three fractional-order non-identical systems has been investigated. For the synchronization of three non-identical fractional-order chaotic systems suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

Bifurcation Analysis and Chaos Control in a Second-Order Rational Difference Equation

AbstractThis work is related to dynamics of a second-order rational difference equation. We investigate the parametric conditions for local asymptotic stability of equilibria. Center manifold theorem and bifurcation theory are implemented to discuss the parametric conditions for existence and direction of period-doubling bifurcation and pitchfork bifurcation at trivial equilibrium point. Moreover, the parametric conditions for existence and direction of Neimark–Sacker bifurcation at positive steady state are investigated with the help of bifurcation theory. The chaos control in the system is discussed through implementation of OGY feedback control method. In particular, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control. Finally, numerical simulations are provided to illustrate theoretical results. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the system.

An application of the Caputo-Fabrizio operator to replicator-mutator dynamics: Bifurcation, chaotic limit cycles and control

The physical behaviors of replicator-mutator processes found in theoretical biophysics, physical chemistry, biochemistry and population biology remain complex with unlimited expressibility. People languages, for instance, have impressively and unpredictably changed over the time in human history. This is mainly due to the collection of small changes and collaboration with other languages. In this paper, the Caputo-Fabrizio operator is applied to a replicator-mutator dynamic taking place in midsts with movement. The model is fully analyzed and solved numerically via the Crank-Nicolson scheme. Stability and convergence results are provided. A concrete application to replicator-mutator dynamics for a population with three strategies is performed with numerical simulations provided for some fixed values of the physical position of the population symbolized by r and the grid points. Physically, it happens that limit cycles appear, not only in function of the mutation parameter μ but also in function of the values given to r . The amplitudes of limit cycles also appear to be proportional to r but the stability of the system remains unaffected. However, those limit cycles instead of disappearing as expected, are immediately followed by chaotic and unpredictable behaviors certainly due to the non-singular kernel used in the model and suitable to non-linear dynamics. Hence, the appearance and disappearance of limit cycles might be controlled by the position variable r which can also apprehend chaos.

Chaotic Adaptive Synchronization Control and Application in Chaotic Secure Communication for Industrial Internet of Things

In this paper, a Lyapunov stability theorem is used to design a model system with adaptive control synchronization. The system uses the pseudo-randomness of chaotic signals to hide the signals that need to be transmitted in seemingly messy chaotic signals. The small input signals are superimposed on the chaotic signals, and the receiving end demodulates the useful information with a synchronized chaotic signal. The system can dynamically adjust the value of the controller according to the initial value of the neuron model so that the two coupling Hindmarsh–Rose neural system can be in a better synchronous state, with good stability and self-adaptability. In this paper, the controller is applied to chaotic secure communication. The simulation results verify the feasibility and effectiveness of the designed controller, and the capability of realizing the transmission of confidential information.

Chaotic behavior analysis and control of a toxin producing phytoplankton and zooplankton system based on linear feedback

In this paper, we study the dynamic behavior and control of the fractional-order nutrientphytoplankton-zooplankton system. First, we analyze the stability of the fractional-order nutrient-plankton system and get the critical stable value of fractional orders. Then, by applying the linear feedback control and Routh-Hurwitz criterion, we yield the sufficient conditions to stabilize the system to its equilibrium points. Finally, Under a modified fractional-order Adams-Bashforth-Monlton algorithm, we simulate the results respectively.

Controlling uncertain Genesio–Tesi chaotic system using adaptive dynamic surface and nonlinear feedback

An adaptive dynamic surface control method using nonlinear feedback is proposed for controlling the uncertain Genesio-Tesi chaotic system. The feature of the nonlinear feedback technique lies in that the feedback gains self-adjust under different amplitudes of system states. Based on the dynamic surface control technique, the complexity explosion problem existing in the backstepping-based chaotic controllers is circumvented. Moreover, the closed-loop stability is guaranteed with rigorous mathematical proof using Lyapunov stability theorem. Comparative results are given to verify the effectiveness and advantage of the proposed method with comparison to the existing linear feedback control.

Chaotic Behavior and Feedback Control of Magnetorheological Suspension System With Fractional-Order Derivative

The fractional differential equations of the single-degree-of-freedom (DOF) quarter vehicle with a magnetorheological (MR) suspension system under the excitation of sine are established, and the numerical solution is acquired based on the predictor–corrector method. The analysis of phase trajectory, time domain response, and Poincaré section shows that the nonlinear dynamic characteristics between fractional and integer-order suspension systems are quite different, which proves the superiority of using fractional order to describe the physical properties. By discussing the influence of each parameter on the vibration, the range of parameters to avoid the chaotic vibration is obtained. The variable feedback control is used to control the chaotic vibration effectively.

An assessment of implementation and evaluation phases of strategic plans in Iranian hospitals.

Objectives:To assess the implementation and evaluation phases of strategic plans in selected hospitals.Methods:We conducted a cross-sectional study of implementation and evaluation of strategic plan in 24 hospitals in 2015, using a questionnaire which consisted of two separate sections for strategic implementation and strategic evaluation. Data were analyzed with SPSS version 18.Results:Nearly one-third of hospitals claimed that they allocate their budget based on priorities and strategic goals. However, it turned out that although goals had been set, no formal announcements had been made. Most of the hospitals stated that they used measures when evaluating the plan. For hospital staff, clarifying the hospital’s priorities was the most important advantage of a strategic plan.Conclusion:There is no clear definition for strategic management in Iranian hospitals, which results in chaotic implementation and control of strategic planning.

Biologically inspired rate control of chaos.

The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.