Class Of Uncertain Chaotic Systems Research Articles

Fast convergence control of a class of uncertain chaotic systems with input nonlinearity by using a new sliding mode controller

This paper studies the fast stability of a class of 3-D chaotic systems in the presence of uncertainties, disturbances as well as input nonlinearity. Some original contributions are concluded: Firstly, this work introduces a special nonlinear input function and a fast convergence system which can be utilized to design controller and sliding mode, respectively. Secondly, a systematic design scheme is derived to ensure the fast stability of subsystem and several virtual controllers are obtained by means of backstepping method. Thirdly, considering the existence of compound disturbances, a new sliding mode is constructed to improve robustness of the controlled systems. Fourthly, by combining nonlinear input function with sliding mode control theory, a new controller is devised and some sufficient conditions of fast convergence control for the 3D chaotic system are derived. There are two features of the presented control criterion: (1) The convergence rate of state trajectories to the origin can be adjusted in advance by choosing the explicit parameters. (2) The time of state trajectories that move toward the sliding surface is finite and bounded by a constant. Numerical results are carried out by employing the Jerk chaotic system to testify the effectiveness of the proposed scheme.

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

This paper addresses the design of an observer-based adaptive neural network chaos synchronization scheme for a general class of uncertain chaotic systems. The controller consists of an adaptive neural network control law and an extended state observer. The parameterization of the designed extended observer and the sufficient stability conditions are derived in the light of the singular perturbation theory. The extended observer is incorporated into the controller to reconstruct the synchronization error vector as well as to estimate the error between an ideal control law and the actual control. These estimated error signals are utilized in the adaptation mechanism of the neural network weight vector. In the presented chaos synchronization method, the knowledge of the models of the master–slave systems is not required and the controller only needs the projective synchronization error for its implementation. Numerical simulations are performed along with a comparative study to demonstrate the efficiency and effectiveness of the suggested chaos synchronization approach.

Fixed time control and synchronization of a class of uncertain chaotic systems with disturbances via passive control method

This paper concerns with the fixed time control and synchronization of a class of uncertain chaotic systems by way of the passive control. Firstly, in the light of passivity theory and fixed time stability, some effective robust passive controllers are designed to force the system trajectories to the origin in a specified time. Secondly, a valid synchronization strategy is proposed to realize the global fixed time chaos synchronization by using the passive control. In our control strategy, the chaotic system can be regarded as a passive system under the given controllers, and the convergence time of the controlled system can be predefined in spite of initial values. Finally, the validity of control and synchronization schemes are confirmed by the numerical examples.

Predefined Time Synchronization Control for Uncertain Chaotic Systems.

In this study, the predefined time synchronization problem of a class of uncertain chaotic systems with unknown control gain function is considered. Based on the fuzzy logic system and varying-time terminal sliding mode control technology, the predefined time synchronization between the master system and the slave system can be realized by the proposed control method in this study. The simulation results confirm the theoretical analysis.

A novel fuzzy sliding mode control approach for chaotic systems

The purpose of this paper is to study the stabilization problem for a class of uncertain chaotic systems against unknown dynamics and disturbances, based on fuzzy sliding mode controller approaches. To fulfill this aim, the first- and the second-orders sliding mode controllers and an adaptive variable universe fuzzy sliding mode controller are combined to a set of linguistic rules, to design some novel approaches for improving the performance of the control action and eliminating the chattering issue. The stability analysis of the closed-loop system is proved via the Lyapunov stability theorem, and also the convergence of the tracking error to zero in finite-time is guaranteed. The new proposed control laws contribute the control actions to outperform the conventional one in terms of chattering reduction and elimination, along with lessening in the reaching time. Moreover, some numerical simulations are provided to depict that the proposed control laws are not only robust with respect to uncertainties and external disturbances, which lead the system to the desired state, but also can significantly eliminate the chattering effect.

(2008-6132) A novel fuzzy sliding mode control approach for chaotic systems

The purpose of this paper is to study the stabilization problem for a class of uncertain chaotic systems against unknown dynamics and disturbances, based on fuzzy sliding mode controller approaches. To fulfill this aim, the first- and the second-orders sliding mode controllers and an adaptive variable universe fuzzy sliding mode controller are combined to a set of linguistic rules, to design some novel approaches for improving the performance of the control action and eliminating the chattering issue. The stability analysis of the closed-loop system is proved via the Lyapunov stability theorem, and also the convergence of the tracking error to zero in finite-time is guaranteed. The new proposed control laws contribute the control actions to outperform the conventional one in terms of chattering reduction and elimination, along with lessening in the reaching time. Moreover, some numerical simulations are provided to depict that the proposed control laws are not only robust with respect to uncertainties and external disturbances, which lead the system to the desired state, but also can significantly eliminate the chattering effect.

An Integral Sliding Mode Control of Uncertain Chaotic Systems via Disturbance Observer

This paper proposes an integral sliding mode control (ISMC) method of a class of uncertain chaotic systems with saturation inputs. Firstly, fuzzy logic system (FLS) is used to estimate the unknown nonlinear function. Then, a disturbance observer is constructed to estimate a compound disturbance, which contains the external disturbance, the error of saturation input and control output, and the fuzzy estimation error. Subsequently, a proposed integral sliding mode controller can ensure that all signals of the closed-loop system are ultimately bounded, and based on the dynamic system of the integral sliding mode variable itself, the ultimate bound of the tracking error can be estimated. Simulation results show that the proposed ISMC method is more effective than the traditional ISMC method.

Robust Adaptive Synchronization of a Class of Uncertain Chaotic Systems with Unknown Time-Delay

In this paper, a robust adaptive control strategy is proposed to synchronize a class of uncertain chaotic systems with unknown time delays. Using Lyapunov theory and Lipschitz conditions in chaotic systems, the necessary adaptation rules for estimating uncertain parameters and unknown time delays are determined. Based on the proposed adaptation rules, an adaptive controller is recommended for the robust synchronization of the aforementioned uncertain systems that prove the robust stability of the proposed control mechanism utilizing the Lyapunov theorem. Finally, to evaluate the proposed robust and adaptive control mechanism, the synchronization of two Jerk chaotic systems with finite non-linear uncertainty and external disturbances as well as unknown fixed and variable time delays are simulated. The simulation results confirm the ability of the proposed control mechanism in robust synchronization of the uncertain chaotic systems as well as to estimate uncertain and unknown parameters.

Adaptive fuzzy control design for synchronization of chaotic time-delay system

This paper focuses on an adaptive synchronization for a class of uncertain chaotic systems (CSs) with time delay. The chaotic systems are represented by Takagi–Sugeno (T-S) fuzzy model. In order to estimate the unknown parameters of the uncertain chaotic systems, we use advanced adaptive laws with smooth projection operator to solve it. In addition, we take the adaptive law as a part of Lyapunov function to make the chaotic systems stable. Different from the previous study of adaptive synchronization of uncertain chaotic systems, this paper fully considers the effect of time delay on uncertain chaotic systems. Finally, by constructing a suitable Lyapunov function (LKF) and using linear matrix inequality (LMI) theory, we can obtain the stability condition of closed-loop system. Furthermore, the simulation cases in this paper illustrate the robust performance of the error system is guaranteed under the uncertain dynamic equation modeling.

Synchronization of a class of uncertain chaotic systems utilizing a new finite-time fractional adaptive sliding mode control

This paper mainly focuses on the issue of finite-time synchronization of a class of chaotic master and slave systems when they have uncertainties, disturbances, and unknown parameters. It is supposed that Uncertainties and disturbances bounds are unknown. First, using the concept of fractional calculus, a new fractional sliding surface is proposed and its finite-time convergence is also proved. Second, appropriate adaptive laws are introduced to overcome unknown system parameters and these laws correctly estimate the unknown values. With applying the controller, synchronization is achieved within a short time. Also after the synchronization, unstable fluctuations are removed and the controlled system has perfect robustness. The proposed approach is applicable to a wide range of identical or non-identical chaotic master and slave systems. Theoretical analysis and stability examination of the proposed method have been performed utilizing adaptive methods and Lyapunov stability theorem. Thereafter, two practical examples are presented to evaluate the effectiveness and usefulness of the suggested method. Furthermore, this method is compared with methods in recent articles, which shows the superiority of this method.

Adaptive Delayed Feedback Chaos Control of a Class of Uncertain Chaotic Systems Subject to External Disturbance

In this paper, an adaptive nonlinear delayed feedback control is proposed for stabilizing an unstable periodic orbit (UPO) of a class of uncertain chaotic systems using the sliding mode approach. The chaotic system is subjected to external disturbances with unknown bounds. Using the Lyapunov stability theorem and the concept of sliding mode control, an adaptive delayed feedback controller has been designed. The controller and adaptation law guarantee the asymptotic stability of the closed loop system on a periodic trajectory which can be sufficiently close to the UPO of the chaotic system. The capability of the proposed control method in stabilizing the UPO of chaotic systems is established analytically and the effectiveness of the proposed scheme is examined numerically by applying it to the chaotic Duffing and Gyro systems.

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

AbstractThis paper proposes a new state‐feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous‐bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady‐state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master–slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

Fuzzy Adaptive Prescribed Performance Control for a Class of Uncertain Nonlinear Systems with Unknown Dead-Zone Inputs

This paper proposes a fuzzy adaptive prescribed performance control scheme for a class of uncertain chaotic systems with unknown control gains and unknown dead-zone inputs. Firstly, an error transformation is introduced to transform the original constrained system into an equivalent unconstrained one. Then, based on the error transformation technique and the predefined performance technique, a fuzzy adaptive feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded. Finally, an illustrative example is given to demonstrate the effectiveness and usefulness of the proposed technique.

Optimisation of the synchronisation of a class of chaotic systems: combination of sliding mode and feedback control

This paper addresses the problem of optimisation of the synchronisation for a class of uncertain chaotic systems from a control theoretic point of view. A robust adaptive feedback which accomplishes the synchronisation of chaotic systems using an optimal tuning scheme based on Riccatti equations is successfully adapted. The underlying idea is to optimise the synchronisation of chaotic systems by accounting the control effort despite the uncertainties. The approach developed considers incomplete state measurements and no detailed model of the systems to guarantee robust stability. This approach includes a high-order sliding mode estimator and leads to a robust adaptive feedback control scheme. A finite horizon can be arbitrarily established by ensuring that the chaos synchronisation is achieved at established time. An advantage is that the studied scheme accounts the energy wasted by the controller and the closed-loop performance on synchronisation. Both mathematic proof and numerical simulations are presented o show the feasibility of the optimisation strategy for establishing the synchronisation of chaotic systems even if there are some modelling mismatches and parametric variations.

Anti-windup adaptive PID control design for a class of uncertain chaotic systems with input saturation

In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers.

Impulsive Control and Practical Generalized Synchronization of a Class of Uncertain Chaotic System with a Given Manifold

In this paper, we study practical generalized synchronization of uncertain chaotic system with a given manifold Y = H(X). We construct a class of the bi-directionally coupled chaotic systems with impulsive control, and demonstrate theoretically that the bi-coupled systems could realize practical generalized synchronization on the basis of stability theory of impulsive differential equations. Numerical simulations with super-chaotic system are provided to further demonstrate the effectiveness and generality of our approach.

Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities

An observer-based output feedback adaptive fuzzy controller is proposed to stabilize a class of uncertain chaotic systems with unknown time-varying time delays, unknown actuator nonlinearities and unknown external disturbances. The actuator nonlinearity can be backlash-like hysteresis or dead-zone. Based on universal approximation property of fuzzy systems the unknown nonlinear functions are approximated by fuzzy systems, where the consequent parts of fuzzy rules are tuned with adaptive schemes. The proposed method does not need the availability of the states and an observer based output feedback approach is proposed to estimate the states. To have more robustness and at the same time to alleviate chattering an adaptive discontinuous structure is suggested. Semi-global asymptotic stability of the overall system is ensured by proposing a suitable Lyapunov–Krasovskii functional candidate. The approach is applied to stabilize the time-delayed Lorenz chaotic system with uncertain dynamics amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of coping well with the modeling uncertainties, nonlinearities in actuators, unknown time-varying time-delays and unknown external disturbances while maintaining asymptotic convergence.

Synchronization and Antisynchronization of a Class of Chaotic Systems With Nonidentical Orders and Uncertain Parameters

In this paper, we study the synchronization of a class of uncertain chaotic systems. Based on the sliding mode control and stability theory in fractional calculus, a new controller is designed to achieve synchronization. Examples are presented to illustrate the effectiveness of the proposed controller, like the synchronization between an integer-order system and a fraction-order system, the synchronization between two fractional-order hyperchaotic systems (FOHS) with nonidentical fractional orders, the antisynchronization between an integer-order system and a fraction-order system, the synchronization between two new nonautonomous systems. The simulation results are in good agreement with the theory analysis and it is noted that the proposed control method is of vital importance for practical system parameters are uncertain and imprecise.

Fuzzy neural control of uncertain chaotic systems with backlash nonlinearity

In this paper, a class of uncertain chaotic systems preceded by unknown backlash nonlinearity is investigated. Combining backstepping technique with fuzzy neural network identifying, an adaptive backstepping fuzzy neural controller (ABFNC) for uncertain chaotic systems with unknown backlash is proposed. The proposed ABFNC system is comprised of a fuzzy neural network identifier (FNNI) and a robust controller. The FNNI is the principal controller utilized for online estimation of the unknown nonlinear function. The robust controller is used to attenuate the effects of the approximation error so that the stability and control performance of the closed-loop adaptive system is achieved always. Finally, simulation results show that the ABFNC can achieve favorable tracking performances.

Synchronization of a class of chaotic systems using small impulsive signal

In this paper the issue of impulsive synchronization of a class of uncertain chaotic systems with parameters perturbation is investigated. Applying the impulsive theory and linear matrix inequality technique, some less conservative and easily verified criteria for impulsive synchronization of chaotic systems are derived. The proposed impulsive synchronization scheme is applied to the chaotic Murali–Lakshmanan–Chua circuit and hyperchaotic Chen and the corresponding synchronization conditions are derived. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse interval. The effectiveness of the method is demonstrated by the computer simulation.