Chaotic Gyroscope Systems Research Articles

Nonsingular Terminal Sliding Mode Control of Uncertain Chaotic Gyroscope System Based on Disturbance Observer

Based on disturbance observer, this paper develops a nonsingular terminal sliding mode control method for uncertain chaotic gyroscope system. Firstly, fuzzy logic system (FLS) is used to estimate the unknown function; then disturbance observer (DOB) is constructed to estimate the mixed disturbance, which consists of the fuzzy estimation error, external disturbance, and dead-zone input error. Subsequently, by using a nonsingular terminal sliding mode function, the control method proposed in this paper can achieve the sliding mode variable approaching a small neighborhood of zero and reduce chattering phenomenon of the tracking error and controller. Finally, comparative simulation results confirm the effectiveness of the method proposed in this paper.

Control of a non-holonomic mobile robot system with parametric uncertainty

In this paper, the control of a mobile robot system via a feedback linearization controller and anti-control of chaos with parametric uncertainty is researched. Anti-control is also applied to convert non-chaotic systems to chaotic ones and to create chaos dynamic. The synchronization of system errors with a chaotic gyroscope system is researched for energy reduction and performance improvement. In the other words, control effort is based on synchronizing the error system with chaos for decreasing control cost. The combination of these techniques yields high efficiency and global convergence of trajectories, even in the presence of parametric uncertainty, which has been shown by simulation. Finally, the energy of control signals is calculated and compared for showing the energy reduction.

Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros

ABSTRACTThis paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainties and external disturbances. In order to design a robust finite-time controller, first, a novel terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then a terminal sliding mode controller is designed which can conquer the uncertainties and guarantees the finite-time stability of the sliding motion equations. In this regard, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization happenes in finite-time. Additionally, in order to show the applicability of the proposed controller, it is applied on two practical systems, the Duffing–Holmes system and chaotic gyroscope system. Computer simulations verify the theoretical results and also display the effective performance of the proposed controller.

Synchronization of Underactuated Unknown Heavy Symmetric Chaotic Gyroscopes via Optimal Gaussian Radial Basis Adaptive Variable Structure Control

This brief proposes modified projective synchronization (MPS) methods for underactuated unknown heavy symmetric chaotic gyroscope systems via optimal Gaussian radial basis adaptive variable structure control. Chaotic gyroscope systems are considered as underactuated systems where a control input is designed to synchronize the two degree of freedoms interactions. Until now, no investigation of this subject with one control input has been presented. The importance of obtaining synchronization objectives is specified when the dynamics of gyroscope system are unknown. In this brief, using the neural variable structure control technique, a control law is established that guarantees the MPS of underactuated unknown chaotic gyros. In the neural variable structure control, Gaussian radial basis functions are utilized to estimate online the system dynamic functions. Adaptation laws of the online estimator are derived in the sense of the Lyapunov function. Moreover, online and offline optimizers are applied to optimize the energy of the control signal. The proposed solution is generalized to chaos control of the mentioned gyroscopes. Numerical simulations are presented to verify the proposed synchronization methods.

Inverted Pendulum Fault Tolerant Control Based on Fuzzy Backstepping Design and Anti-Control of Chaos

This study presents fault tolerant control of inverted pendulum via on-line fuzzy backstepping and anti-control of chaos. The inverted pendulum, as a mechatronics system, is used frequently in robotic applications and can be found in different forms. Based on Lyapunov stability theory for backstepping design, the nonlinear controller and some generic sufficient conditions for asymptotic control are attained. Also in this study, anti-control of chaos is applied to increase the fault tolerant of inverted pendulum. To achieve this goal, the chaos dynamic must be created in the inverted pendulum system. So, the inverted pendulum system has been synchronized to chaotic gyroscope system. In this study, control and anti-control concepts are applied to achieve the high quality performance of inverted pendulum system. It is tried to design a controller which is capable to satisfy the control and anti- control aims. The performances of the proposed control are examined in terms of fault tolerant capability. Finally the efficacy of the proposed methods are illustrated by simulations.

Fault tolerant control of mechatronics system based on hybrid control

This study presents fault tolerant control of inverted pendulum via on-line fuzzy backstepping and anti-control of chaos. The inverted pendulum is used frequently in robotic applications and can be found in different forms. Based on Lyapunov stability theory for backstepping design, the nonlinear controller and some generic sufficient conditions for asymptotic control are attained. Also in this study, anti-control of chaos is applied to increase the fault tolerant of inverted pendulum. To achieve this goal, the chaos dynamic must be created in the inverted pendulum system. So, the inverted pendulum system has been synchronized to chaotic gyroscope system. In this study, control and anti-control concepts are applied to achieve the high quality performance of inverted pendulum system. The performances of the proposed control are examined in terms of fault tolerant capability. Finally, the efficacies of the proposed methods are illustrated by simulations. Key words: Backstepping design, anti-control, chaos, synchronization, chaotic gyroscope, on-line fuzzy design, inverted pendulum, fault tolerant control.

Modified projective synchronization of unknown chaotic dissipative gyroscope systems via Gaussian radial basis adaptive variable structure control

This paper proposes the modified projective synchronization method for unknown chaotic dissipative gyroscope systems via Gaussian radial basis adaptive variable structure control. Because of the nonlinear terms of the dissipative gyroscope system, the system exhibits chaotic motions. 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 the gyroscope system are unknown. In this paper, using the neural variable structure control technique, control laws are established, which guarantees the modified projective synchronization of an unknown chaotic dissipative gyroscope system. Switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. In the neural variable structure control, Gaussian radial basis functions are utilized online to estimate the system dynamic functions. Also, the adaptation laws of the online estimators are derived in the sense of Lyapunov function. Thus, the unknown chaotic gyroscope system can be guaranteed to be asymptotically stable. Also, the synchronization objectives have been achieved. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the eigenvalues of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for modified projective synchronization of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. The designed control system is robust versus model uncertainty. Numerical simulations are presented to verify the proposed synchronization method.

Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control

This paper proposes the chaos control and the generalized projective synchronization methods for heavy symmetric gyroscope systems via Gaussian radial basis adaptive variable structure 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 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. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyroscopes. In this paper, the switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. Using the neural variable structure control technique, control laws are established which guarantees the chaos control and the generalized projective synchronization of unknown gyroscope systems. In the neural variable structure control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimator are derived in the sense of Lyapunov function. Thus, the unknown gyro systems can be guaranteed to be asymptotically stable. Also, the proposed method can achieve the control objectives. Numerical simulations are presented to verify the proposed control and synchronization methods. Finally, the effectiveness of the proposed methods is discussed.

Fault tolerant synchronization of chaotic heavy symmetric gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control

In this paper, fault tolerant synchronization of chaotic gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control is investigated. Taking the general nature of faults in the slave system into account, a new synchronization scheme, namely, fault tolerant synchronization, is proposed, by which the synchronization can be achieved no matter whether the faults and disturbances occur or not. By making use of a slave observer and a Lyapunov rule-based fuzzy control, fault tolerant synchronization can be achieved. Two techniques are considered as control methods: classic Lyapunov-based control and Lyapunov rule-based fuzzy control. On the basis of Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are obtained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. Two proposed methods are compared. The Lyapunov rule-based fuzzy control can compensate for the actuator faults and disturbances occurring in the slave system. Numerical simulation results demonstrate the validity and feasibility of the proposed method for fault tolerant synchronization.

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.