Control Of Uncertain Chaotic Systems Research Articles

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.

Disturbance observer-based adaptive sliding mode synchronization control for uncertain chaotic systems

<abstract><p>The synchronization control problem of a class of chaotic systems with unknown uncertainties and outside perturbation is addressed in this article by employing an innovative adaptive sliding mode controller (SM, SMC) constructed using a disturbance observer (DO). For the synchronous error system, the external disturbances estimated by the disturbance observer cannot be measured directly. If the appropriate gain matrix is chosen, the DO can approximate the unknown external disturbances well. Then a continuous adaptive SM controller based on the DO's output is designed by using adaptive techniques and the system dimensional expansion method. The Duffing-Holmes chaotic system is finally selected to numerically test the efficiency of the suggested strategy.</p></abstract>

Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders

The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works.

Intuitionistic Fuzzy Sliding Controller for Uncertain Hyperchaotic Synchronization

In this study, the design of an intuitionistic fuzzy controller for synchronization of two non-identical hyperchaotic systems is proposed. Since hyperchaotic systems has high sensitivity to the initial condition, disturbance and parameter variability. Synchronization of hyperchaotic systems is used to test the controller performance. On the other hand, using of fuzzy logic-based controller has an increasing tendency. As known, fuzzy logic control (FLC), only membership functions are used to obtain a realistic model of the systems. But the intuitionistic fuzzy logic control (IFLC) allows us to obtain a more realistic model than FLC because it also takes into account the degree of non-membership and the degree of uncertainty beside of degree of membership to model examined system. Fuzzy logic-based controllers are hybridized with robust control methods such as sliding mode controller to improve the performance of controller. To take advantages of SMC with fuzzy logic-based IFLC, the IFSMC controller obtained by hybridizing these two methods was designed for hyperchaotic systems. To demonstrate the performance of IFSMC, the results obtained from the synchronization of hyperchaotic systems with FSMC (fuzzy sliding mode controller) and IFSMC were compared. The stability of IFSMC is proved by Lyapunov stability condition. The numerical results and analysis show the efficiency of the IFSMC with regards to synchronization control of uncertain chaotic systems having challenging external disturbances in terms of robustness, minimum tracking error.

Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead‐zone nonlinearities

In this article, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two identical or different chaotic (or hyperchaotic) systems in the presence of unknown dynamic disturbances and input nonlinearities (dead‐zone and sector nonlinearities). This proposed synchronization scheme can be considered as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization, and so forth) in the sense that the master and slave outputs are assumed to be some general function vectors. To practically deal with the input nonlinearities, the adaptive fuzzy control system is designed in a variable‐structure framework. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is used to prove the boundedness of all signals of the closed‐loop control system as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two identical systems (chaotic satellite systems) and two different systems (chaotic Chen and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–249, 2016

Neural adaptive control of uncertain chaotic systems with input and output saturation

This paper is concerned with the neural adaptive control design problem of a class of chaotic systems with uncertain dynamics, input and output saturation. To attenuate the effect caused by input and output saturation, a constructed auxiliary system is used to prevent the stability of closed loop system from being destroyed. Radial basis function neural networks are used in online approximation of the uncertain dynamics. Both state feedback and output feedback control laws are designed. In the output feedback situation, a high-order sliding-mode observer is used to estimate the system states. The stability of closed loop system is proved rigorously based on Lyapunov theorem. The effectiveness of the proposed methods is demonstrated by controlling Duffing system and Genesio system.

Passivity-Sliding Mode Control of Uncertain Chaotic Systems with Stochastic Disturbances

This paper is concerned with the stabilization problem of uncertain chaotic systems with stochastic disturbances. A novel sliding function is designed, and then a sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time. Using a virtual state feedback control technique, sufficient condition for the mean square asymptotic stability and passivity of sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

This paper is concerned with the stabilization problem of uncertain chaotic systems with input nonlinearity. The slope parameters of this nonlinearity are unmeasured. A new sliding function is designed, then an adaptive sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time and finite-time reachability is theoretically proved. Using a virtual state feedback control technique, sufficient condition for the asymptotic stability of sliding mode dynamics is derived via linear matrix inequality (LMI). Then the results can be extended to uncertain chaotic systems with disturbances and adaptive sliding mode H∞ controllers are designed. Finally, a simulation example is presented to show the validity and advantage of the proposed method.

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.

Adaptive fuzzy nonlinear inversion-based control for uncertain chaotic systems

This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the unknown nonlinear function by using a fuzzy system, whose inputs are not the state variables but feedback error signals. The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique. The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems. Theoretical results are illustrated through two simulation examples.

Disturbance-observer-based robust synchronization control of uncertain chaotic systems

In this paper, a robust synchronization control scheme is proposed for chaotic systems in the presence of system uncertainties and unknown external disturbances. For the synchronization error system, the compound disturbance which is estimated using the disturbance observer cannot be directly measured. If the gain matrix is properly chosen, the disturbance observer can approximate the unknown compound disturbance well. And then, the constrained robust synchronization control scheme is presented for uncertain chaotic systems based on the output of disturbance observer. In the design of a robust synchronization control scheme, the effect of unknown control input constraint has been explicitly considered to guarantee the synchronization performance. Numerical simulation results are presented to illustrate the effectiveness of the proposed constrained synchronization control scheme for uncertain chaotic systems.

Development of PI training algorithms for neuro-wavelet control on the synchronization of uncertain chaotic systems

This paper investigates a neuro-wavelet control (NWC) system to address the problem of synchronization control of uncertain chaotic systems. In this NWC system, a wavelet neural network (WNN) controller is the principal tracking controller designed to mimic the perfect control law and an auxiliary compensation controller is used to recover the residual approximation error so that the favorable synchronization can be achieved. Moreover, the proportional-integral (PI) training algorithms of the control system are derived from the Lyapunov stability theorem, which are utilized to update the adjustable parameters of WNN controller on-line for further assuring system stability and obtaining a fast convergence. In addition, to relax the requirement of unknown uncertainty bound, a bound estimation law is derived to estimate the uncertainty bound. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed control strategy. The simulation results demonstrate that the proposed NWC with PI training algorithms can synchronize the chaotic systems more accurately than the other control strategies.

Sliding mode control for uncertain chaotic systems with input nonlinearity

For the sliding mode controller of uncertain chaotic systems subject to input nonlinearity, the upper bound of the norm of uncertainties is commonly used to determine the controller parameter. However, this will cause serious chattering. In order to overcome this drawback, two new sliding mode controllers are proposed to ensure robust synchronization for a classes of chaotic systems with input nonlinearities and external uncertainty. Compared with the existing results, the proposed controllers can effectively reduce the chattering nearby sliding mode and improve the dynamic performance of the systems. Simulation results are provided to verify the proposed methods.

Non‐Fragile Sliding Mode Control of Uncertain Chaotic Systems

This paper is concerned with non‐fragile sliding mode control of uncertain chaotic systems with external disturbance. Firstly, a new sliding surface is proposed, and sufficient conditions are derived to guarantee that sliding mode dynamics is asymptotically stable with a generalized H2 disturbance rejection level. Secondly, non‐fragile sliding mode controller is established to make the state of system reach the sliding surface in a finite time. Finally, an example is given to illustrate the effectiveness of the proposed method.

Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems

A simple and systematic approach is developed for modeling and neural adaptive backstepping control of an uncertain chaotic system, using only input–output data obtained from the underlying dynamical systems. Gaussian fuzzy membership functions are used in conjunction with the least-squares principle for modeling and control. Based on the dynamic fuzzy neural network (DFNN) modeling, an adaptive backstepping controller is devised, which works through structure and parameter-learning phases for adaptation. The DFNN implements Takagi–Sugeno–Kang fuzzy systems based on extended radial basis function (RBF) neural networks. The design procedure is illustrated by using the multiscroll chaotic attractors as an example, on which simulation results demonstrate the effectiveness of the proposed methodology.

Adaptive robust fuzzy control for a class of uncertain chaotic systems

In this paper, the output feedback control of uncertain chaotic systems is addressed via an adaptive robust fuzzy approach. Fuzzy logic systems are employed to approximate uncertain nonlinear functions in the chaotic systems. Because only partial information of the system’s states is needed to be known, an observer is given to estimate the unmeasured states. Compared with the existing results in the observer design, the prior knowledge on dynamic uncertainties is relaxed and a class of more general chaotic systems is considered as well as robustness to the approximation error is improved. It can be proven that the closed-loop system is stable in the sense that all the variables are bounded. Simulation example for the unified chaotic systems is given to verify the effectiveness of the proposed method.

Adaptive control of uncertain chaotic systems with time delays using dynamic structure neural network

A kind of control methods is surveyed to deal with a class of nonlinear systems with uncertain time delay. By combining the Lyapunov-Krasovskii function and Lyapunov function, the time-delay compensator with adjustable parameters is presented to make the control input independent of the multiple time delays. At the same time, the dynamic structure adaptive neural network is introduced to eliminate the uncertainties in the chaotic system, which approximates the function with better relationship between the calculation rate and structure complexity by increasing hidden units when the tracking error is beyond the allowable bound. The demonstration with a given Duffing chaotic system shows the presented control method is effective.

Chaos control via a simple fractional-order controller

In this Letter, we propose a fractional-order controller to stabilize the unstable fixed points of an unstable open-loop system. Also, we show that this controller has strong ability to eliminate chaotic oscillations or reduce them to regular oscillations in the chaotic systems. This controller has simple structure and is designed very easily. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of uncertain chaotic systems.

Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity

Abstract This paper addresses a practical tracking problem for a class of uncertain chaotic systems with dead-zone nonlinearity in the input function. Based on the Lyapunov stability theorem and Barbalat lemma, an adaptive variable structure controller (AVSC) is proposed to ensure the occurrence of the sliding mode even though the control input contains a dead-zone. Also it is worthy of note that the proposed AVSC involves no information of the upper bound of uncertainty. Thus, the limitation of knowing the bound of uncertainty in advance is certainly released. Furthermore, in the sliding mode, the investigated uncertain chaotic system remains insensitive to the uncertainty, and behaves like a linear system. Finally, a well-known Duffing–Holmes chaotic system is used to demonstrate the feasibility of the proposed AVSC.

Fuzzy modeling, prediction, and control of uncertain chaotic systems based on time series

A fuzzy logic-based approach is taken in this paper for modeling, prediction, and predictive control of unknown or uncertain chaotic systems. Only output data of the underlying system are required. A fuzzy predictive framework using a general structure of a linear combination of Gaussian basis functions is developed, where the basis functions are expressed as probability density functions and are empirically determined from the time-series data. A real-time one-pass learning algorithm is developed for identification of the chaotic system. Based on this framework, a fuzzy predictive controller is designed, which is especially suitable for sparse data in a real-time environment. Several simulation examples are then given for demonstration.