A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances

In this paper, a robust adaptive sliding mode controller (RASMC) is introduced to synchronize two different chaotic systems in the presence of unknown bounded uncertainties and external disturbances. The structure of the master and slave chaotic systems has no restrictive assumption. Appropriate adaptation laws are derived to tackle the uncertainties and external disturbances. Based on the adaptation laws and Lyapunov stability theory, an adaptive sliding control law is designed to ensure the occurrence of the sliding motion even when both master and slave systems are perturbed with unknown uncertainties and external disturbances. Since the conventional sliding mode controllers contain the sign function, the undesirable chattering is occurred. We propose a new simple adaptive scheme to eliminate the chattering. Finally, numerical simulations are presented to verify the usefulness and applicability of the proposed control strategy.     

Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity

In this paper, an adaptive controller is designed to ensure robust synchronization of two different chaotic systems with input nonlinearities. For this purpose, a stable sliding surface is defined and an adaptive sliding mode controller is designed to achieve robust synchronization of the systems when the control input is influenced through nonlinearities produced by actuator or external uncertainty recourses. The adaptation law guarantees the synchronization assuming of unknown model uncertainty. Furthermore by adding an integrator and incorporating a saturation function in the control law, the chattering phenomenon caused by the sign function is avoided. The simulation results for synchronization of Chua’s circuit and Genesio systems show the efficiency of the proposed technique.     

Suppression of chaotic behavior in horizontal platform systems based on an adaptive sliding mode control scheme

This work presents an adaptive sliding mode control scheme to elucidate the robust chaos suppression control of non-autonomous chaotic systems. The proposed control scheme utilizes extended systems to ensure that continuous control input is obtained in order to avoid chattering phenomenon as frequently in conventional sliding mode control systems. A switching surface is adopted to ensure the relative ease in stabilizing the extended error dynamics in the sliding mode. An adaptive sliding mode controller (ASMC) is then derived to guarantee the occurrence of the sliding motion, even when the chaotic horizontal platform system (HPS) is undergoing parametric uncertainties. Based on Lyapunov stability theorem, control laws are derived. In addition to guaranteeing that uncertain horizontal platform chaotic systems can be stabilized to a steady state, the proposed control scheme ensures asymptotically tracking of any desired trajectory. Furthermore, the numerical simulations verify the accuracy of the proposed control scheme, which is applicable to another chaotic system based on the same design scheme.     

Sliding mode control for chaotic systems based on LMI

This paper investigates the chaos control problem for a general class of chaotic systems. A feedback controller is established to guarantee asymptotical stability of the chaotic systems based on the sliding mode control theory. A new reaching law is introduced to solve the chattering problem that is produced by traditional sliding mode control. A dynamic compensator is designed to improve the performance of the closed-loop system in sliding mode, and its parameter is obtained from a linear matrix inequality (LMI). Simulation results for the well known Chua’s circuit and Lorenz chaotic system are provided to illustrate the effectiveness of the proposed scheme.     

Exponential synchronization of chaotic systems subject to uncertainties in the control input

A sliding mode control technique is introduced for exponential synchronization of chaotic systems. These systems are described by a general form including matched and unmatched nonlinear functions. A new hitting-free switching surface of proportional-integral type is proposed. This type of switching surface is without the hitting process if the attraction of sliding manifold is ensured. This property makes it easy to exponentially synchronize the master-slave chaotic systems. Based on this switching surface, a robust sliding mode controller (SMC) is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties. An example is included to illustrate the results developed in this paper.     

Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity

This paper addresses chaos anti-synchronization of uncertain unified chaotic systems with dead-zone input nonlinearity. Using the sliding mode control technique and Lyapunov stability theory, a proportional–integral (PI) switching surface is proposed to ensure the stability of the closed-loop error system in sliding mode. Then a sliding mode controller (SMC) is proposed to guarantee the hitting of the switching surface even with uncertainties and the control input containing dead-zone nonlinearity. Some simulation results are included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.     

Synchronization of the unified chaotic systems using a sliding mode controller

The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lü chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zero of the errors between the states of the master and the slave systems is shown. Simulations results are presented to illustrate the proposed controller; they indicate that the designed controller is able to synchronize the unified chaotic systems. Also, simulation results show that the proposed control scheme is robust to random bounded disturbances acting on the master system. Moreover, the proposed scheme is applied to the secure communications field, where simulation results indicate that the proposed scheme is effective.     

Chaos suppression of a class of unknown uncertain chaotic systems via single input

This paper deals with the design of a robust adaptive control scheme for chaos suppression of a class of chaotic systems. We assume that model uncertainties and external disturbances disturb the system’s dynamics. The bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. Moreover, it is assumed that the nonlinear terms of the chaotic system dynamics are unknown bounded. Based on the global boundedness feature of the chaotic systems’ trajectories, a simple one input adaptive sliding mode control approach is proposed to suppress the chaos of the uncertain chaotic system. Furthermore, using a dynamical sliding manifold the discontinuous sign function in the control input is diverted to the first derivative of the control input to eliminate the chattering. Finally, the robustness of the proposed approach is mathematically proved and numerically illustrated.     

Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems

A second order sliding mode (SOSM) controller using nonlinear sliding surface is proposed in this paper. The aim of the proposed controller is to guarantee stability as well as enhance the transient performance of uncertain linear systems with parametric uncertainty. The nonlinear sliding surface consists of a linear term and a nonlinear term. The linear term comprises a gain matrix which has a very low value of damping ratio and thereby facilitates fast response. The nonlinear term is introduced to accommodate a variable damping ratio to reduce overshoot and settling time of the closed loop system as the output reaches nearer the desired reference position. A major gain of the proposed SOSM controller is the elimination of chattering in the control input. The proposed nonlinear sliding surface based SOSM controller achieves fast rise, low overshoot and low settling time. Simulation results demonstrate the effectiveness of the proposed SOSM controller.     

An adaptive-dynamic sliding mode controller for non-minimum phase systems

This paper presents a new algorithm for designing dynamic sliding-mode controllers. The proposed controller is based on dynamic sliding manifolds to circumvent the difficulties associated with the conventional sliding mode controllers in the face of non-minimum phase systems. Unlike previous works, a proper and easy to implement algorithm is presented for designing the dynamic sliding manifold which facilitates the design of the controller. The output tracking problem in nonlinear non-minimum phase systems with matched and unmatched disturbances and matched nonlinearities is addressed. Then, the performance of the dynamic sliding mode controller is significantly improved by combining the given dynamic sliding manifold with online parameter adaptation. Simulations results are presented to demonstrate the effectiveness of the proposed sliding mode controller in terms of performance, robustness and stability.     

An adaptive sliding mode control scheme for a class of chaotic systems with mismatched perturbations and input nonlinearities

This paper is concerned with the stabilization problem for a class of chaotic systems with mismatched perturbations and input nonlinearities. A novel sliding surface is specially designed so that when the system enters the sliding mode, the mismatched perturbations can be effectively overcome and achieve asymptotic stability. Then, an adaptive sliding mode controller (ASMC) is proposed to drive the controlled state trajectories into the designated sliding surface in finite time even subjected to input nonlinearities. Finally, the corresponding numerical simulations are demonstrated to verify the effectiveness of proposed method.     

Simple adaptive variable structure control for unknown chaotic systems

This paper proposes two novel adaptive variable structure tracking controllers for a large class of chaotic systems with unknown dynamics in presence of both external disturbances and input nonlinearities. The pros and cons of each proposed methodology is also represented. In order to eliminate the chattering effect in the former controlled system, two corresponding fuzzy adaptive controllers are presented. Besides, synchronization of two non-identical uncertain chaotic systems is investigated using our proposed methods in both full and reduced-order forms. It can be seen that not only our proposed control schemes can be applied to a wide class of uncertain chaotic systems but also it is simple to implement in practical application. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.     

RBF‐based discrete sliding mode control for robust tracking of uncertain time‐delay systems with input nonlinearity

In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time‐delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016     

Robust control of a spatial robot using fuzzy sliding modes

In order to improve the performance of the sliding mode controller, fuzzy logic sliding mode controller is proposed in this study. The control gain of the conventional sliding mode controller is tuned by a fuzzy logic rule base and, also dynamic sliding surfaces are obtained by changing their slopes using the error states of the system in another fuzzy logic algorithm. These controllers are then combined in order to enhance the performance. Afterwards, proposed controllers were used in trajectory control of a three degrees of freedom spatial robot, which is subjected to noise and parameter variations. Finally, the controllers introduced are compared with a PID controller which is commonly used for control of robotic manipulators in industry. The results indicate the superior performance of the proposed controller.     

Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, chattering phenomena in the control efforts can be reduced. The sliding mode design procedure not only guarantees the stability and robustness of the proposed AFSMC, but also the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.     

Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach

In this paper, an adaptive sliding mode controller for a novel class of fractional-order chaotic systems with uncertainty and external disturbance is proposed to realize chaos control. The bounds of the uncertainty and external disturbance are assumed to be unknown. Appropriate adaptive laws are designed to tackle the uncertainty and external disturbance. In the adaptive sliding mode control (ASMC) strategy, fractional-order derivative is introduced to obtain a novel sliding surface. The adaptive sliding mode controller is shown to guarantee asymptotical stability of the considered fractional-order chaotic systems in the presence of uncertainty and external disturbance. Some numerical simulations demonstrate the effectiveness of the proposed ASMC scheme.     

Control of non‐integer‐order dynamical systems using sliding mode scheme

This article deals with the problem of control of canonical non‐integer‐order dynamical systems. We design a simple dynamical fractional‐order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering‐free fractional‐order sliding mode controller. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–233, 2016     

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed‐loop uncertain time‐delay chaotic system with input dead‐zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead‐zone nonlinearity, time‐delays, nonlinear real‐valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 13–20, 2016     

Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems

This study is concerned with the design of a disturbance-observer-based fuzzy terminal sliding mode controller (FTSMC) for multi-input multi-output (MIMO) uncertain nonlinear systems by considering unknown non-symmetric input saturation and control singularity. The disturbance observer is proposed for the unmeasured external disturbance and guarantees the convergence of the disturbance estimation error to zero in a finite time. The terminal sliding mode controller (TSMC) is designed for MIMO uncertain nonlinear systems by utilizing the output of the proposed disturbance observer. This control scheme combines the disturbance-observer-based TSMC with a fuzzy logic system in the presence of unknown non-symmetric input saturation and control singularity in order to reduce chattering phenomena. Finite time asymptotic stability, convergence of the disturbance observer, and convergence of the closed-loop system are proved via Lyapunov stability theorem. In addition, a five-rotor unmanned aerial vehicle (UAV) is employed in the numerical simulations to demonstrate the effectiveness and performance of the proposed control scheme. Disturbance observer estimates the payload and flight endurance of the five-rotor UAV. Genetic algorithm (GA) optimization is used to specify the parameters of the disturbance-observer-based TSMC (GATSMC) to decrease chattering. Finally, the superior performance of FTSMC is investigated over TSMC and GATSMC.     

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.