Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.     

Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach

In this paper, an adaptive sliding mode control method is introduced to ensure robust synchronization of two different fractional-order chaotic systems with fully unknown parameters and external disturbances. For this purpose, a fractional integral sliding surface is defined and an adaptive sliding mode controller is designed. In this method, no knowledge of the bounds of parameters and perturbation is required in advance and the parameters are updated through an adaptive control process. The proposed scheme is global and theoretically rigorous. Two examples are given to illustrate effectiveness of the scheme, in which the synchronizations between fractional-order chaotic Chen system and fractional-order chaotic Rössler system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.

     

Intelligent quadratic optimal synchronization of?uncertain chaotic systems via LMI approach

This paper proposes an intelligent quadratic optimal control scheme via linear matrix inequality (LMI) approach for the synchronization of uncertain chaotic systems with both external disturbances and parametric perturbations. First, a four-layered neural fuzzy network (NFN) identifier is constructed to estimate system nonlinear dynamics. Based on the NFN identifier, an intelligent quadratic optimal controller is developed with robust hybrid control scheme, in which H _?? optimal control and variable structure control (VSC) are embedded to attenuate the effects of external disturbances and parametric perturbations. The adaptive tuning laws of network parameters are derived in the sense of the Lyapunov synthesis approach to ensure network convergence, and the sufficient criterion for existence of the controller is formulated in the linear matrix inequality (LMI) form to guarantee the quadratic optimal synchronization performance. Finally, a numerical simulation example is illustrated by the chaotic Chua??s circuit system to demonstrate the effectiveness of our scheme.     

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.     

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.     

Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control

Due to resource constraints in wireless sensor networks and the presence of unwanted conditions in communication systems and transmission channels, the suggestion of a robust method which provides battery lifetime increment and relative security is of vital importance. This paper considers the secure communication in wireless sensor networks based on new robust adaptive finite time chaos synchronization approach in the presence of noise and uncertainty. For this purpose, the modified Chua oscillators are added to the base station and sensor nodes to generate the chaotic signals. Chaotic signals are impregnated with the noise and uncertainty. At first, we apply the modified independent component analysis to separate the noise from the chaotic signals. Then, using the adaptive finite-time sliding mode controller, a control law and an adaptive parameter-tuning method is proposed to achieve the finite-time chaos synchronization under the noisy conditions and parametric uncertainties. Synchronization between the base station and each of the sensor nodes is realized by multiplying a selection matrix by the specified chaotic signal which is broadcasted by the base station to the sensor nodes. Simulation results are presented to show the effectiveness and applicability of the proposed technique.     

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 chaos synchronization of fractional-order chaotic systems with unknown parameters and uncertain perturbations

Chaotic systems in practice are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems. Based on Lyapunov stability theory and a fractional-order differential inequality, a modified adaptive control scheme and adaptive laws of parameters are developed to robustly synchronize coupled fractional-order chaotic systems with unknown parameters and uncertain perturbations. This synchronization approach is simple, global and theoretically rigorous. Simulation results for two fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

Robust adaptive synchronization for a class of chaotic systems with actuator failures and nonlinear uncertainty

This paper is concerned with the robust adaptive synchronization problem for a class of chaotic systems with actuator failures and unknown nonlinear uncertainty. Combining adaptive method and linear matrix inequality (LMI) technique, a novel type of robust adaptive reliable synchronization controller is proposed, which can eliminate the effect of actuator fault and nonlinear uncertainty on systems. After solving a set of LMIs, synchronization error between the master chaotic and slave chaotic systems can converge asymptotically to zero. Finally, illustrate examples about chaotic Chua’s circuit system and Lorenz systems are provided to demonstrate the effectiveness and applicability of the proposed design method.     

Fractional order fixed-time nonsingular terminal sliding mode synchronization and control of fractional order chaotic systems

This paper presents fractional order fixed-time nonsingular terminal sliding mode control for stabilization and synchronization of fractional order chaotic systems with uncertainties and disturbances. First, a novel fractional order terminal sliding mode surface is proposed to guarantee the fixed-time convergence of system states along the sliding surface. Second, a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and remain on it forever. Furthermore, the fractional Lyapunov stability theory is used to prove the fixed-time stability and the robustness of the proposed control scheme and estimate the upper bound of convergence time. Next, the proposed control scheme is applied to the synchronization of two nonidentical fractional order Liu chaotic systems and chaos suppression of fractional order power system. Simulation results verify the effectiveness of the proposed control scheme. Finally, some application issues about the proposed scheme are discussed.

     

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 finite-time tracking for a square fully actuated class of nonlinear systems

In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

     

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 synchronization of fractional-order chaotic systems via a single driving variable

This letter investigates the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on sliding mode variable structure control theory and adaptive control technique, a single-state adaptive-feedback controller containing a novel fractional integral sliding surface is developed to synchronize a class of fractional-order chaotic systems. The present controller, which only contains a single driving variable, is simple both in design and implementation. Simulation results for three fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization

This paper introduces two novel fractional-order chaotic systems with cubic nonlinear resistor and investigates its adaptive sliding mode synchronization. Firstly the novel two equilibrium chaotic system with cubic nonlinear resistor (NCCNR) is derived and its dynamic properties are investigated. The fractional-order cubic nonlinear resistor system (FONCCNR) is then derived from the integer-order model and its stability and fractional-order bifurcation are discussed. Next a novel no-equilibrium chaotic cubic nonlinear resistor system (NECNR) is derived from NCCNR system. Dynamic properties of NECNR system are investigated. The fractional-order no equilibrium cubic nonlinear resistor system (FONECNR) is derived from NECNR. Stability and fractional-order bifurcation are investigated for the FONECNR system. The non-identical adaptive sliding mode synchronization of FONCCNR and FONECNR systems are achieved. Finally the proposed systems, adaptive control laws, sliding surfaces and adaptive controllers are implemented in FPGA.     

Adaptive synchronization for uncertain complex dynamical network using fuzzy disturbance observer

This paper proposes a robust adaptive controller design method for synchronization of a complex dynamical network with uncertainty and disturbance. A fuzzy disturbance observer is used to estimate the overall disturbances without any prior knowledge about them. The proposed control method globally asymptotically synchronizes the network using adaptation laws obtained by using Lyapunov stability theory. The proposed method is applied to two chaotic systems and the results show the effectiveness of the approach.     

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.     

A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems

This paper presents a polynomial chaos-based framework for designing optimal linear feedback control laws for nonlinear systems with stochastic parametric uncertainty. The spectral decomposition of the original stochastic dynamical model in an orthogonal polynomial basis, prescribed by the Wiener–Askey scheme, provides a deterministic model from which the optimal linear control law is designed. Optimality of the proposed control law is proved by solving the Hamilton–Jacobi–Bellman equation, and asymptotic stability of the controlled nonlinear systems is guaranteed in the Lyapunov sense. We are especially interested in synchronization of chaotic systems. For this reason, the control strategy is applied in the trajectory tracking of periodic orbits for the Duffing oscillator and the Rössler system with uncertain stochastic parameters and initial conditions. The results are verified with Monte Carlo simulations.     

Mean square function synchronization of chaotic systems with stochastic effects

In this paper, we give the definition of mean square function synchronization. Secondly, we investigate mean square function synchronization of chaotic systems with stochastic perturbation and unknown parameters. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, the controller, and adaptive laws are designed to ensure achieving stochastic synchronization of chaotic systems. A sufficient synchronization condition is given to ensure the chaotic systems to be mean-square stable. Furthermore, a numerical simulation is also given to demonstrate the effectiveness of the proposed scheme.     

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Backstepping design is proposed for adaptive synchronization of a class of chaotic systems with unknown bounded uncertainties. An adaptive backstepping control law is derived to make the error signals between the master and slave systems asymptotically synchronized without knowing the upper-bounds of the uncertainties in advance. The stability analysis is proved by using a well-known Lyapunov stability. Two illustrative examples are presented to show the effectiveness of the proposed adaptive chaos synchronization.