Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs

Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos.In this paper,the problem of robust stabi...     

A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs

In this paper, the problem of finite-time chaos synchronization between two different uncertain chaotic systems with unknown parameters and input nonlinearities is investigated. It is assumed that both master and slave systems are perturbed by unknown model uncertainties, external disturbances, and fully unknown parameters. Proper update laws are proposed to estimate the systems?? unknown parameters. Based on the update laws and finite-time control technique, a robust adaptive controller is introduced to guarantee the convergence of the slave system trajectories to the trajectories of the master system in a given finite time. Two illustrative examples are presented to illustrate the effectiveness and applicability of the proposed finite-time controller and to validate the theoretical results of the paper.     

Adaptive finite-time stabilization of uncertain non-autonomous chaotic electromechanical gyrostat systems with unknown parameters

This paper deals with the problem of robust finite-time stabilization of non-autonomous chaotic gyrostat systems. It is assumed that the parameters of the gyrostat system are completely unknown in advance and the system is perturbed by unknown uncertainties and disturbances. Some update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and the update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in a finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to demonstrate the applicability and robustness of the proposed finite-time controller and to verify the theoretical results.     

Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

This paper solves the problem of robust synchronization of nonlinear chaotic gyrostat systems in a given finite time. The parameters of both master and slave chaotic gyrostat systems are assumed to be unknown in advance. In addition, the gyrostat systems are disturbed by unknown model uncertainties and external disturbances. Suitable update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in finite time. The precise value of the convergence time is given. A numerical simulation demonstrates the applicability and efficiency of the proposed finite-time synchronization strategy.     

Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs

Centrifugal flywheel governors are known as chaotic non-autonomous mechanical devices used for automatic control of the speed of engines. The main characteristic of them is avoiding the damage caused by sudden change of the load torques. In this paper, the problem of robust finite-time synchronization of centrifugal flywheel governor systems is studied. The effects of unknown parameters, model uncertainties, external noises, and input nonlinearities are fully taken into account. We propose some adaptive laws to overcome the side effects of the unknown parameters of the system on the synchronization performance. Then, a robust adaptive switching controller is introduced to synchronize centrifugal flywheel governors with nonlinear control inputs in a given finite time. The finite-time fast convergence property of the proposed scheme is analytically proved and numerically illustrated.     

Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.     

Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control

The problem of real combination synchronization between three complex-variable chaotic systems with unknown parameters is investigated by nonsingular terminal sliding mode control in a finite time. Based on the adaptive laws and finite-time stability theory, a nonsingular terminal sliding mode control is designed to ensure the real combination synchronization of three complex-variable chaotic systems in a given finite time. It is theoretically gained that the introduced sliding mode technique has finite-time convergence and stability in both arriving and sliding mode phases. Numerical simulation results are given to show the effectiveness and reliability of the finite-time real combination synchronization.     

Adaptive control for electromechanical systems considering dead-zone phenomenon

The electromechanical gyrostat is a fourth-order nonautonomous system that exhibits very rich behavior such as chaos. In recent years, synchronization of nonautonomous chaotic systems has found many useful applications in nonlinear science and engineering fields. On the other hand, it is well known that the finite-time control techniques demonstrate good robustness and disturbance rejection properties. This paper studies the potential application of the finite-time control techniques for synchronization of nonautonomous chaotic electromechanical gyrostat systems in finite time. It is assumed that all the parameters of both drive and response systems are unknown parameters in advance. Moreover, the effects of dead-zone nonlinearities in the control inputs are also taken into account. Some adaptive controllers are introduced to synchronize two gyrostat systems in different scenarios within a given finite-time. Two illustrative examples are presented to demonstrate the efficiency and robustness of the proposed finite-time synchronization strategy.     

A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems

In this paper, a projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive controller is investigated for a projective synchronization of uncertain multivariable chaotic systems. The adaptive fuzzy-logic systems are used to approximate the unknown functions. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the synchronization errors to an adjustable region. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.     

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.     

A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems

This paper introduces a finite-time control technique for control of a class of non-autonomous fractional-order nonlinear systems in the presence of system uncertainties and external noises. It is known that finite-time control methods demonstrate better robustness and disturbance rejection properties. Moreover, finite time control methods have optimal settling time. In order to design a robust finite-time controller, a new nonsingular terminal sliding manifold is proposed. The proposed sliding mode dynamics has the property of fast convergence to zero. Afterwards, a novel fractional sliding mode control law is introduced to guarantee the occurrence of the sliding motion in finite time. The convergence times of both reaching and sliding phases are estimated. The main characteristics of the proposed fractional sliding mode technique are (1) finite-time convergence to the origin; (2) the use of only one control input; (3) robustness against system uncertainties and external noises; and (4) the ability of control of non-autonomous fractional-order systems. At the end of this paper, some computer simulations are included to highlight the applicability and efficacy of the proposed fractional control method.     

Complete synchronization of delay hyperchaotic Lü system via a single linear input

This work is devoted to investigating the complete synchronization of two identical delay hyperchaotic Lü systems with different initial conditions, and a simple complete synchronization scheme only with a single linear input is proposed. Based on the Lyapunov stability theory, sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches. The problem of adaptive synchronization between two nearly identical delay hyperchaotic Lü systems with unknown parameters is also studied. A?single input adaptive synchronization controller is proposed, and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.     

Adaptive terminal sliding mode control for nonlinear differential inclusion systems with disturbance

This paper deals with the adaptive terminal sliding mode control for nonlinear differential inclusion systems subjected to disturbance. The upper bound of the disturbance is unknown. First, the fast terminal sliding mode surface is established and sufficient condition for fast convergence is given. Then the adaptive sliding mode controller is designed to make the state of system arrive at the sliding mode in finite time. A numerical example is provided to show the effectiveness of the proposed method.     

A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems

This paper concerns the problem of robust stabilization of autonomous and non-autonomous fractional-order chaotic systems with uncertain parameters and external noises. We propose a simple efficient fractional integral-type sliding surface with some desired stability properties. We use the fractional version of the Lyapunov theory to derive a robust sliding mode control law. The obtained control law is single input and guarantees the occurrence of the sliding motion in a given finite time. Furthermore, the proposed nonlinear control strategy is able to deal with a large class of uncertain autonomous and non-autonomous fractional-order complex systems. Also, Rigorous mathematical and analytical analyses are provided to prove the correctness and robustness of the introduced approach. At last, two illustrative examples are given to show the applicability and usefulness of the proposed fractional-order variable structure controller.     

Chaos control and modified projective synchronization of unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control

This paper proposes the chaos control and the modified projective synchronization methods for unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a regular or periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise-like, synchronized chaotic systems can be used as cipher generators for secure communication. Obviously, the importance of obtaining these objectives is specified when the dynamics of gyroscope system are unknown. In this paper, using the neural backstepping control technique, control laws are established which guarantees the chaos control and the modified projective synchronization of unknown chaotic gyroscope system. In the neural backstepping control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimators are derived in the sense of Lyapunov function. Thus, the unknown chaotic gyroscope system can be guaranteed to be asymptotically stable. Also, the control objectives have been achieved.     

Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters

This letter investigates the adaptive finite-time synchronization of different coupled chaotic (or hyperchaotic) systems with unknown parameters. The sufficient conditions for achieving the generalized finite-time synchronization of two chaotic systems are derived based on the theory of finite-time stability of dynamical systems. By the adaptive control technique, the control laws and the corresponding parameters update laws are proposed such that the generalized finite-time synchronization of nonidentical chaotic (or hyperchaotic) systems is to be obtained. These results obtained are in good agreement with the existing one in open literature and it is shown that the technique introduced here can be further applied to various finite-time synchronizations between dynamical systems. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed scheme.     

Robust adaptive nonlinear control for uncertain control-affine systems and its applications

This paper addresses the robust tracking control problem for a class of uncertain nonlinear systems with time-varying parameters, perturbed by external disturbances. The unknown time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Depending on the characteristics of disturbance signals, two adaptive-based control algorithms are developed. First, an adaptive H _∞ control is designed that achieves: (i) an H _∞ tracking performance when the external disturbances are L ₂ signals, and (ii) the convergence of tracking error to zero if the disturbances are bounded and L ₂ signals. Then a novel adaptive control algorithm is proposed, only with the assumption of boundedness of disturbances, to drive the tracking error to zero. The designed tracking controllers are then used for controlling a cart-pendulum system, as an underactuated mechanical system, and chaos synchronization of uncertain Genesio–Tesi chaotic system. Numerical simulations are also given to demonstrate the effectiveness of the proposed control schemes.     

Robust adaptive intelligent sliding model control for a class of uncertain chaotic systems with unknown time-delay

In this paper, a robust adaptive intelligent sliding model control (RAISMC) scheme for a class of uncertain chaotic systems with unknown time-delay is proposed. A sliding surface dynamic is appropriately constructed to guarantee the reachability of the specified sliding surface. Within this scheme, neuro-fuzzy network (NFN) is utilized to approximate the unknown continuous function. The robust controller is an adaptive controller used to dispel the unknown uncertainty and approximation errors. The adaptive parameters of the control system are tuned on-line by the derived adaptive laws based on a Lyapunov stability analysis. Using appropriate Lyapunov–Krasovskii (L–K) functional in the Lyapunov function candidate, the uncertainty caused by unknown time delay is compensated and the global asymptotic stability of the error dynamics system in the specified switching surface is accomplished. Finally, the proposed RAISMC system is applied to control a Hopfield neural network, Cellular neural networks, Rössler system, and to achieve synchronization between the Chen system with two time delays with Rössler system without time delay. The results are representative of outperformance of the proposed method in all cases.     

Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances

This paper studies the robust adaptive full state hybrid projective synchronization (FSHPS) scheme for a class of chaotic complex systems with uncertain parameters and external disturbances. By introducing a compensator and using nonlinear control and adaptive control, the robust adaptive FSHPS scheme is derived, which can eliminate the influence of uncertainties effectively and achieve adaptive FSHPS of the chaotic (hyperchaotic) complex systems asymptotically with a small error bound. The adaptive laws of the unknown parameters are given, and the sufficient conditions of realizing FSHPS are derived as well. Moreover, we also discuss the case that parameters of chaotic complex system are complex. Finally, the complex Chen system and Lü system, and the hyperchaotic complex Lorenz system are taken as two examples and the numerical simulations are provided to verify the effectiveness and robustness of the proposed control scheme.     

Direct adaptive neural control of chaos in the permanent magnet synchronous motor

In this paper, a direct adaptive neural speed tracking control is addressed for the chaotic permanent magnet synchronous motor (PMSM) drive systems via backstepping. Neural networks are directly used to approximate unknown and desired control signals and a novel direct adaptive tracking controller is constructed via backstepping. The proposed adaptive neural controllers guarantee that the tracking error converges to a small neighborhood of the origin. Compared with the conventional backstepping method, the designed neural controller??s structure is very simple. Simulation results show that the proposed control scheme can suppress the chaos of PMSM and guarantees the perfect tracking performance even with the existence of unknown parameters.