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     

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     

Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input

In this paper, the problem of synchronizing two chaotic gyros in the presence of uncertainties, external disturbances and dead-zone nonlinearity in the control input is studied while the structure of the gyros, parameters of the dead-zone and the bounds of uncertainties and external disturbances are unknown. The dead-zone nonlinearity in the control input might cause the perturbed chaotic system to show unpredictable behavior. This is due to the high sensitivity of these systems to small changes in their parameters. Thereby, the effect of these issues should not be ignored in the control design for these systems. In order to eliminate the effects from the dead-zone nonlinearity, in this paper, a robust adaptive fuzzy sliding mode control scheme is proposed to overcome the synchronization problem for a class of unknown nonlinear chaotic gyros. The main contribution of our paper in comparison with other works that attempt to solve the problem of dead-zone in the synchronization of chaotic gyros is that we assume that the structure of the system, uncertainties, external disturbances, and dead-zone are fully unknown. Simulation results are provided to illustrate the effectiveness of the proposed method.     

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.     

Robust output feedback sliding mode control for uncertain discrete time systems

This paper proposes a robust output feedback controller for a class of uncertain discrete-time, multi-input multi-output, linear, systems. This method, which is based on the combination of discrete-time sliding mode control (DTSMC) and Kalman estimator, ensures the stability, robustness and an output tracking against the modeling uncertainties at large sampling periods. For this purpose, an appropriate structure is considered for sliding surface and the Lyapunov theory for the mismatched uncertain system is then used to design its parameter. This problem leads to solve a set of linear matrix inequalities. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show the effectiveness of the proposed method in the presence of parameter uncertainties and external disturbances at large sampling periods.     

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.     

Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems

In this paper, a novel direct adaptive interval type-2 fuzzy-neural tracking control equipped with sliding mode and Lyapunov synthesis approach is proposed to handle the training data corrupted by noise or rule uncertainties for nonlinear SISO nonlinear systems involving external disturbances. By employing adaptive fuzzy-neural control theory, the update laws will be derived for approximating the uncertain nonlinear dynamical system. In the meantime, the sliding mode control method and the Lyapunov stability criterion are incorporated into the adaptive fuzzy-neural control scheme such that the derived controller is robust with respect to unmodeled dynamics, external disturbance and approximation errors. In comparison with conventional methods, the advocated approach not only guarantees closed-loop stability but also the output tracking error of the overall system will converge to zero asymptotically without prior knowledge on the upper bound of the lumped uncertainty. Furthermore, chattering effect of the control input will be substantially reduced by the proposed technique. To illustrate the performance of the proposed method, finally simulation example will be given.     

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.     

Finite-time disturbance observer-based trajectory tracking control for quadrotor unmanned aerial vehicle with obstacle avoidance

This paper investigates the problem of trajectory tracking control for quadrotor unmanned aerial vehicle (UAV) in the presence of dynamic obstacles and external disturbance forces/torques. More specifically, two new sliding mode disturbance observers are firstly designed to estimate the external disturbances, in which the observation errors can converge to zero in finite time. Furthermore, utilizing the observation information, a new sliding mode surface-like variable-based position tracking control scheme and a novel nonsingular terminal sliding mode-based attitude synchronization control scheme are developed to drive the UAV tracking the reference trajectory with obstacle avoiding. Moreover, the tracking errors of the close-loop control system can converge to zero within finite time by the analyses of Lyapunov methodology. Finally, the numerical simulation results are presented to illustrate the effectiveness of the proposed control schemes.     

Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros

Under the existence of system uncertainties, external disturbances, and input nonlinearity, complete synchronization and anti-synchronization between two chaotic gyros are achieved by introducing a novel adaptive terminal sliding mode (ATSM) controller. In the literature, by taking account of input nonlinearity, the magnitudes of bounded nonlinear dynamics of synchronous error system were required in the designed sliding mode controller. In this study, the proposed ATSM controller associated with time-varying feedback gains can tackle nonlinear dynamics according to the novel adaptive rules. These feedback gains are not necessary to be determined in advance but updated by the adaptive rules without known the magnitudes of bounded nonlinear dynamics, system uncertainties, and external disturbances. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem, and the numerical simulations are performed to verify the effectiveness of presented schemes.     

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.     

Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities

In this paper, the problem of chaos synchronization between two different uncertain chaotic systems with input nonlinearities is investigated. Both master and slave systems are perturbed by model uncertainties, external disturbances and unknown parameters. The bounds of the model uncertainties and external disturbances are assumed to be unknown in advance. First, a simple linear sliding surface is selected. Then, appropriate adaptive laws are derived to tackle the model uncertainties, external disturbances and unknown parameters. Subsequently, based on the adaptive laws and Lyapunov stability theory, a robust adaptive sliding mode control law is designed to guarantee the existence of the sliding motion. Two illustrative examples are presented to verify the usefulness and applicability of the proposed technique.     

Fast terminal sliding mode controller design for nonlinear second‐order systems with time‐varying uncertainties

This article investigates a novel fast terminal sliding mode control approach combined with global sliding surface structure for the robust tracking control of nonlinear second‐order systems with time‐varying uncertainties. The suggested control technique is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Using the new form of switching surface, the reaching phase elimination and the robustness improvement of the whole system are satisfied. Simulation results demonstrate the efficiency of the proposed technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 239–244, 2015     

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.     

航天器编队飞行多目标姿态快速跟踪鲁棒控制

研究了航天器编队飞行多目标姿态跟踪鲁棒控制问题．主航天器装有一个快速机动天线和一个星载相机．考虑相机对地面目标跟踪,同时考虑天线与从航天器通信的空间任务．通过引入角速度约束和姿态角约束,分别推导了相机和天线的参考姿态角、角速度和角加速度．提出期望逆系统的概念,将三维空间姿态跟踪问题转化为调节问题,简化了控制器的设计．考虑存在参数摄动和外部干扰力矩的情况,基于期望逆系统和滑模控制,设计了鲁棒姿态跟踪控制器,并利用Liapunov稳定性理论证明了控制系统的渐近稳定性．以两航天器编队飞行多目标跟踪为例进行数值仿真,结果表明所设计的控制器具有良好的鲁棒性和优越的跟踪性能．     

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.     

An adaptive sliding mode backstepping control for the mobile manipulator with nonholonomic constraints

To solve disturbances, nonlinearity, nonholonomic constraints and dynamic coupling between the platform and its mounted robot manipulator, an adaptive sliding mode controller based on the backstepping method applied to the robust trajectory tracking of the wheeled mobile manipulator is described in this article. The control algorithm rests on adopting the backstepping method to improve the global ultimate asymptotic stability and applying the sliding mode control to obtain high response and invariability to uncertainties. According to the Lyapunov stability criterion, the wheeled mobile manipulator is divided into several stabilizing subsystems, and an adaptive law is designed to estimate the general nondeterminacy, which make the controller be capable to drive the trajectory tracking error of the mobile manipulator to converge to zero even in the presence of perturbations and mathematical model errors. We compare our controller with the robust neural network based algorithm in nonholonomic constraints and uncertainties, and simulation results prove the effectivity and feasibility of the proposed method in the trajectory tracking of the wheeled mobile manipulator.     

Robust decentralized adaptive control for a class of uncertain neural networks with time-varying delays

This paper considers the robust control problem for a class of uncertain time-varying delayed neural networks, in which the activation function may be a discontinuous function. A robust decentralized adaptive sliding mode controller is proposed to guarantee the asymptotically stability of the system. The proposed controller, which does not dependent on the time delay, ensures the occurrence of the sliding manifold even when the system is undergoing parameter uncertainties and nonlinear input. Two numerical examples are given to show the effectiveness of the proposed controller.     

Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller

In this paper, a robust adaptive sliding mode controller (RASMC) is proposed to realize chaos synchronization between two different chaotic systems with uncertainties, external disturbances and fully unknown parameters. It is assumed that both master and slave chaotic systems are perturbed by uncertainties, external disturbances and unknown parameters. The bounds of the uncertainties and external disturbances are assumed to be unknown in advance. Suitable update laws are designed to tackle the uncertainties, external disturbances and unknown parameters. For constructing the RASMC a simple sliding surface is first designed. Then, the RASMC is derived to guarantee the occurrence of the sliding motion. The robustness and stability of the proposed RASMC is proved using Lyapunov stability theory. Finally, the introduced RASMC is applied to achieve chaos synchronization between three different pairs of the chaotic systems (Lorenz–Chen, Chen–Lorenz, and Liu–Lorenz) in the presence of the uncertainties, external disturbances and unknown parameters. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed RASMC.     

A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations

In industrial applications, the performance of robot manipulators is always affected due to the presence of uncertainties and disturbances. This paper proposes a novel adaptive control scheme for robust control of robotic manipulators perturbed by unknown uncertainties and disturbances. First, an active sliding mode controller is designed and a sufficient condition is obtained guarantying reachability of the states to hit the sliding surface in finite time. Then, based on a Lyapunov function candidate an adaptive switching gain is derived which make the controller capable to bring the tracking error to zero without any disturbance exerted upon the stability. By virtue of this controller it can be shown that the controller can track the desired trajectories even in the presence of unknown perturbations. For the problem of determining the control parameters Particle Swarm Optimization (PSO) algorithm has been employed. Our theoretic achievements are verified by numerical simulations.