Adaptive Sliding Mode Control for Re-entry Attitude of Near Space Hypersonic Vehicle Based on Backstepping Design

Combining sliding mode control method with radial basis function neural network (RBFNN), this paper proposes a robust adaptive control scheme based on backstepping design for re-entry attitude tracking control of near space hypersonic vehicle (NSHV) in the presence of parameter variations and external disturbances. In the attitude angle loop, a robust adaptive virtual control law is designed by using the adaptive method to estimate the unknown upper bound of the compound uncertainties. In the angular velocity loop, an adaptive sliding mode control law is designed to suppress the effect of parameter variations and external disturbances. The main benefit of the sliding mode control is robustness to parameter variations and external disturbances. To further improve the control performance, RBFNNs are introduced to approximate the compound uncertainties in the attitude angle loop and angular velocity loop, respectively. Based on Lyapunov stability theory, the tracking errors are shown to be asymptotically stable. Simulation results show that the proposed control system attains a satisfied control performance and is robust against parameter variations and external disturbances.      

Robust adaptive fixed‐time tracking control of 6‐DOF spacecraft fly‐around mission for noncooperative target

The fixed‐time relative position tracking and attitude synchronization control problem of a spacecraft fly‐around mission for a noncooperative target in the presence of parameter uncertainties and external disturbances is investigated. Firstly, a novel and coupled relative position and attitude motion model for a noncooperative fly‐around mission is established. Subsequently, a novel nonsingular fast terminal sliding mode (NFTSM) surface is developed, and the explicit estimation of the convergence time independent of initial states is provided. Fair and systematic comparisons among several typical terminal sliding modes show that the designed NFTSM has faster convergence performance than the fast terminal sliding mode. Then, a robust integrated adaptive fixed‐time NFTSM control law with no precise knowledge of the mass and inertia matrix and disturbances by combining the nonsingular terminal sliding mode technique with an adaptive methodology is proposed, which can eliminate the chattering phenomenon and guarantee that the relative position and attitude tracking errors can converge into the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.     

航天器自适应快速非奇异终端滑模容错控制

针对存在外部干扰、转动惯量矩阵不确定以及执行器故障的航天器姿态跟踪控制问题,本文提出了基于自适应快速非奇异终端滑模的有限时间收敛故障容错控制方案.通过引入能够避免奇异点,且具有有限时间收敛特性的快速非奇异终端滑模面,设计了满足多约束条件有限时间收敛的姿态跟踪容错控制律,利用参数自适应方法使控制器不依赖转动惯量和外部干扰的上界信息.Lyapunov稳定性分析表明:在存在外部干扰、转动惯量矩阵不确定以及执行器故障等约束条件下,本文设计的控制律能够保证闭环系统的快速收敛性,而且对执行器故障具有良好的容错性能.数值仿真校验了该控制律在姿态跟踪控制中的优良性能.     

Adaptive sliding mode trajectory tracking control for wheeled mobile robots

This paper discusses the problem of adaptive sliding mode trajectory tracking control for wheeled mobile robots in the presence of external disturbances and inertia uncertainties. A new fast nonsingular terminal sliding mode surface without any constraint is proposed, which not only avoids singularity, but also retains the advantages of sliding mode control. In order to implement the trajectory tracking mission, the error dynamic system is divided into a second-order subsystem and a third-order one. First, an adaptive fast nonsingular terminal sliding mode control law of the angular velocity is constructed for stabilising the second-order subsystem in finite time. Then, another adaptive fast nonsingular terminal sliding mode control law of the linear velocity is designed to guarantee the stability of the third-order subsystem. Finally, a simulation example is provided to demonstrate the validity of the proposed control scheme.     

Adaptive attitude tracking control for rigid spacecraft with finite-time convergence

In this paper, the finite-time attitude tracking control problem for rigid spacecraft with external disturbances and inertia uncertainties is addressed. First, a novel fast nonsingular terminal sliding mode surface (FNTSMS) without any constraint is designed, which not only avoids the singularity problem, but also contains the advantages of the nonsingular terminal sliding mode (NTSM) and the conventional sliding-mode together. Second, the proposed FNTSM control laws (FNTSMCLs) by employing FNTSMS associated with adaptation provide finite-time convergence, robustness, faster, higher control precision. The proposed FNTSMCLs in light of novel adaptive control architecture are continuous. Thus, they are chattering-free. Finally, simulation results are presented to illustrate effectiveness of the control strategies. In addition, digital simulations of satellite Hubble Space Telescope (HST) are presented to verify the practical feasibility of the reorientation/ slew maneuvers mission.     

Finite‐time attitude stabilization for rigid spacecraft

This paper investigates the finite‐time attitude stabilization problem for rigid spacecraft in the presence of inertia uncertainties and external disturbances. Three nonsingular terminal sliding mode (NTSM) controllers are designed to make the spacecraft system converge to its equilibrium point or a region around its equilibrium point in finite time. In addition, these novel controllers are singularity‐free, and the presented adaptive NTSM control (ANTSMC) laws are chattering‐free. A rigorous proof of finite‐time convergence is developed. The proposed ANTSMC algorithms combine NTSM, adaptation and a constant plus power rate reaching law. Because the algorithms require no information about inertia uncertainties and external disturbances, they can be used in practical systems, where such knowledge is typically unavailable. Simulation results support the theoretical analysis.Copyright © 2013 John Wiley & Sons, Ltd.     

Second-order terminal sliding mode control for hypersonic vehicle in cruising flight with sliding mode disturbance observer

This paper focuses on the design of nonlinear robust controller and disturbance observer for the longitudinal dynamics of a hypersonic vehicle (HSV) in the presence of parameter uncertainties and external disturbances. First, by combining terminal sliding mode control (TSMC) and second-order sliding mode control (SOSMC) approach, the secondorder terminal sliding control (2TSMC) is proposed for the velocity and altitude tracking control of the HSV. The 2TSMC possesses the merits of both TSMC and SOSMC, which can provide fast convergence, continuous control law and hightracking precision. Then, in order to increase the robustness of the control system and improve the control performance, the sliding mode disturbance observer (SMDO) is presented. The closed-loop stability is analyzed using the Lyapunov technique. Finally, simulation results illustrate the effectiveness of the proposed method, as well as the improved overall performance over the conventional sliding mode control (SMC).     

基于快速终端滑模面的两旋翼飞行器有限时间姿态控制

针对带有模型不确定和外部干扰的两旋翼飞行器,提出一种基于快速终端滑模面的有限时间自适应姿态控制方法,保证两旋翼飞行器对期望姿态角度的有限时间跟踪。构造快速终端滑模面,并设计分段连续函数避免滑模变量求导产生的奇异值问题。在此基础上,设计有限时间姿态控制器,并设计系统不确定上界的自适应更新律,抵消模型不确定性和外部干扰的影响。经李雅普诺夫方法证明滑模变量、姿态角误差、角速度误差等闭环信号最终一致有界,且有限时间收敛至平衡点邻域,收敛时间与系统状态变量初始值有关。最后,采用了矩形波和 曲线作为设定信号,设计相应的跟踪实验,并在两旋翼飞行器平台上验证所提控制方法的有效性,且分析双曲正切函数对系统控制输入影响,经实验测试其可减少系统颤振现象。     

混沌系统的有限时间滑模同步控制

采用滑模控制的方法,研究了两个不同的带有不确定性和外部扰动的混沌系统之间的同步问题。基于Lyapunov稳定性理论和有限时间滑模控制方法,设计了终端滑模控制器来实现两个混沌系统的同步。在设计控制器过程中提出了一个新的非奇异的终端滑模面,并证明它能在有限时间内收敛于零平衡点。通过数值仿真验证了所设计的控制器的有效性。     

Finite-time attitude tracking control for a rigid spacecraft using time-varying terminal sliding mode techniques

This paper investigates the finite-time attitude tracking control for a rigid spacecraft in the presence of inertia uncertainties and external disturbances. Two novel time-varying terminal sliding mode control algorithms are derived for attitude tracking control system. The proposed two control algorithms not only eliminate the reaching phase of the conventional sliding mode control but also guarantee the tracking errors converge to zero in finite time. Moreover, the singularity problem can be avoided. Simulation results are provided to demonstrate the effectiveness of the proposed design methods.     

Adaptive terminal sliding mode control for rigid robotic manipulators

In order to apply the terminal sliding mode control to robot manipulators, prior knowledge of the exact upper bound of parameter uncertainties, and external disturbances is necessary. However, this bound will not be easily determined because of the complexity and unpredictability of the structure of uncertainties in the dynamics of the robot. To resolve this problem in robot control, we propose a new robust adaptive terminal sliding mode control for tracking problems in robotic manipulators. By applying this adaptive controller, prior knowledge is not required because the controller is able to estimate the upper bound of uncertainties and disturbances. Also, the proposed controller can eliminate the chattering effect without losing the robustness property. The stability of the control algorithm can be easily verified by using Lyapunov theory. The proposed controller is tested in simulation on a two-degree-of-freedom robot to prove its effectiveness.     

Adaptive finite‐time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints

The attitude stabilization problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator saturations, and actuator faults is addressed in this paper. First, a novel fast terminal sliding mode manifold is designed to avoid the singularity problem while providing high control ability. In addition, fast terminal sliding mode control laws are proposed to make the spacecraft system trajectory fast converge onto the fast terminal sliding mode surface and finally evolve into small region in finite time, which cannot be achieved by the previous literatures. Based on the real sliding mode context, a practical adaptive fast terminal sliding mode control law is presented to guarantee attitude stabilization in finite time. Also, simulation results are presented to illustrate the effectiveness of the control strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

基于自组织小波小脑模型关节控制器的不确定非线性系统鲁棒自适应终端滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以良好的跟踪性能及强鲁棒性为目标,提出基于自组织小脑模型(self-organizing wavelet cerebellar model articulation controller,SOWCMAC)的鲁棒自适应积分末端(terminal)滑模控制策略.首先,将小脑模型、自组织神经网络和小波函数各自优势相结合,给出一种SOWCMAC,以保证干扰估计方法具有快速学习能力和更好的泛化能力.其次,设计两种改进的terminal滑模面构造方法,并分别给出各自的收敛时间.然后,基于SOWCMAC和改进的积分terminal滑模面,给出不确定非线性系统鲁棒自适应非奇异terminal控制器的设计过程,其中通过构造自适应鲁棒项抑制干扰估计误差对系统跟踪性能的影响,并利用Lyapunov理论证明闭环系统的稳定性.最后,将该方法应用于近空间飞行器姿态的控制仿真实验,结果表明所提出方法有效性.     

Adaptive nonsingular fast terminal sliding mode control for underwater manipulator robotics with asymmetric saturation actuators

In this paper, an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) is proposed for underwater manipulator robotics with asymmetric actuator saturations and unknown time-varying (TV) external disturbances. Firstly, the nonsingular fast terminal sliding mode (NFTSM) control scheme is conducted for the underwater manipulator robotics, which guarantees the boundedness of all the signals in the control system. Secondly, the adaptive method and the smooth hyperbolic tangent (tanh) function are introduced to address the unknown TV external disturbances and the input saturation errors. Thus the prior knowledge about the upper bounds of the system uncertainties is not needed in this paper. To deal with the nonlinear asymmetric input saturation issue, a Gaussian error function is employed in the asymmetric saturation module so that the discontinuous input signals can be transformed into smooth forms. Thirdly, the rigorous mathematical verification is conducted to demonstrate the stability and finite-time convergence of the closed-loop control system via the Lyapunov theory. Finally, numerical simulations are performed on a two-link underwater manipulator robotic system to illustrate the effectiveness of the proposed controller.     

SECOND‐ORDER NONSINGULAR TERMINAL SLIDING MODE DECOMPOSED CONTROL OF UNCERTAIN MULTIVARIABLE SYSTEMS

This paper proposes a second‐order nonsingular terminal sliding mode decomposed control method for multivariable linear systems with internal parameter uncertainties and external disturbances. First, the systems are converted into the block controllable form, consisting of an input‐output subsystem and a stable internal dynamic subsystem. A special second‐order non‐singular terminal sliding mode is proposed for the input‐output subsystem. The control law is designed to drive the states of the input‐output subsystem to converge to the equilibrium point asymptotically. Then the states of the stable zero‐dynamics of the system converge to the equilibrium point asymptotically. The method proposed in the paper has advantages for higher‐dimensional multivariable systems, in the sense that it simplifies the design and makes it possible to realize a robust decomposed control. Meanwhile, because of the adoption of the second‐order sliding mode, the control signal is continuous. Simulation results are presented to validate the design.     

Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking

This paper studies finite-time attitude tracking control problem of a rigid spacecraft system with external disturbances and inertia uncertainties. Firstly, a new finite-time attitude tracking control law is designed using nonsingular terminal sliding mode concepts. In the absence and presence of external disturbances and inertia uncertainties, this controller can drive the attitude and angular velocity tracking errors to reach zero in finite time. Secondly, a finite-time disturbance observer is introduced to estimate the disturbance, and a composite controller is developed which consists of a feedback control based on nonsingular terminal sliding mode method and compensation term based on finite-time disturbance observer. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system is ensured by the Lyapunov approach. Numerical simulations on attitude control of spacecraft are also given to demonstrate the performance of the proposed controllers.     

一类3阶非线性系统的非奇异终端滑模控制

针对传统非奇异终端滑模控制方法不适用于3阶系统的问题,提出一类具有不确定和外干扰的3阶非线性系统的新型非奇异终端滑模控制方法.该方案首先结合backstepping控制中的动态面方法和传统2阶非奇异终端滑模控制构造非奇异3阶终端滑模面,首次提出采用高阶滑模微分器估计值代替控制器中的负指数项.采用非线性干扰观测器任意精度地估计不确定和干扰,设计控制器中的补偿项.采用终端吸引子函数做趋近律避免抖振的同时能保证有限时间趋近滑模面.基于有限时间稳定李雅普诺夫定理证明了被控状态将在有限时间内收敛到任意小的闭球内.所提出方案快于传统的递阶线性滑模控制和其他非奇异终端滑模控制.仿真中与其他滑模控制方案对比,总误差减小18%以上,超调及收敛时间也显著下降.     

Synchronization and Tracking of Multi‐Spacecraft Formation Attitude Control Using Adaptive Sliding Mode

This paper presents the finite‐time attitude synchronization and tracking control method of undirected multi‐spacecraft formation with external disturbances. First, a modified adaptive nonsingular fast terminal sliding mode surface (ANFTSMS) is designed by introducing a user‐defined function, both of which avoid the singularity problem and continuous sliding surface, and, therefore, can freely adjust relative weighting between angular velocity error and attitude error adaptively, such that the controller can provide sufficient maneuvers and precision. This provides designers with a new technique to adjust and improve formation control performance. Second, by applying the ANFTSMS associated with adaptation, two proposed decentralized ANFTSM‐controllers provide finite‐time convergence, robustness to disturbance, and chattering free for continuous design. Finally, simulation results validate the proposed algorithms.     

Velocity-free adaptive nonsingular fast terminal sliding mode finite-time attitude tracking control for spacecraft

Aiming at the attitude tracking control problem of rigid spacecraft under the condition of unmeasurable angular velocity information, a velocity-free adaptive nonsingular fast terminal sliding mode finite-time tracking control method is proposed. The finite-time extended-state observer is used to estimate the attitude tracking speed errors and the integrated disturbances. Combined with the above control method, a fast nonsingular terminal sliding mode controller with attitude measurement is designed and the adaptive technology is introduced to compensate for the influence of observation errors on the controller. The finite-time convergence of the observer and the control method was demonstrated based on Lyapunov theory, and the effectiveness of the proposed method is verified by numerical simulations.     

Non-linear adaptive sliding mode switching control with average dwell-time

In this article, an adaptive integral sliding mode control scheme is addressed for switched non-linear systems in the presence of model uncertainties and external disturbances. The control law includes two parts: a slide mode controller for the reduced model of the plant and a compensation controller to deal with the non-linear systems with parameter uncertainties. The adaptive updated laws have been derived from the switched multiple Lyapunov function method, also an admissible switching signal with average dwell-time technique is given. The simplicity of the proposed control scheme facilitates its implementation and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense such that the sliding surface of the control system is well reached. Simulation results are presented to demonstrate the effectiveness and the feasibility of the proposed approach.