欠驱动船舶的运动规划和全局指数跟踪控制

针对目前欠驱动船舶航迹跟踪控制难以实现跟踪任意可行航迹问题,提出一种运动规划方法。利用多项式拟合,并结合船舶动力学模型,通过离散期望点规划出操作性可实现的全部期望姿态。同时,为实现欠驱动船舶的航迹快速跟踪控制,提出一种全局指数航迹跟踪控制律。引入微分同胚变换,建立两个级联的子系统构成的航迹跟踪误差动态方程;基于反步法的设计原理,运用Lyapunov直接方法对变换后的误差系统设计了全局指数航迹跟踪控制律。仿真结果验证了所提出的全局指数航迹跟踪控制律能够有效实现跟踪任意可行航迹。     

非完整移动机器人的连续时变鲁棒K指数镇定

针对带有参数不确定性动态非完整移动机器人的镇定问题,提出一个全局连续的时变鲁棒控制律.首先,使用全局可逆变换将系统的动力学模型转换成一个不确定性线性子系统和一个不确定性非线性子系统;然后,引入一个与初值有关的指数衰减项,将非线性子系统转换成带扰动项的线性系统;最后,设计鲁棒控制律将整个系统镇定到原点.与已有的控制器相比,所提出的控制器能同时获得连续性、渐近性和指数收敛速度,仿真结果也验证了这一点.     

Robot robust path tracking

A new discontinuous robust control law for a rigid manipulator with bounded parameter uncertainties to track a desired trajectory, is presented. Global exponential stability is proved by the use of a natural Lyapunov function based on a transformation of the manipulator's differential equation due to Slotine and Li [2]. Convergence is to a sliding mode along which the tracking error is reduced at an arbitrary exponential rate. It is also shown how adaptation of bounds on uncertainties, and parameter adaptation, can be incorporated. For a continuous approximation of the discontinuous control law,practical stability (essentially, global uniform ultimate boundedness) of the tracking error is proved. Simulation results for the continuous control law exhibit excellent robust tracking.     

一种新的模糊滑模控制器设计方法

针对具有较大且不可观测外界干扰的一类不确定系统,提出一种新的模糊滑模控制器设计方法.首先基于模糊滑模控制原理,引入全局快速终端滑模控制,使系统在有限时间内达到稳态;然后构造以李雅普诺夫函数导数的绝对值为补偿的自适应干扰估计项,对外界干扰进行准确估计,进而提出一种双层递阶指数趋近全局快速终端模糊滑模控制器,通过指数趋近率来调节滑模面的动态品质,该控制器能快速收敛到稳定状态,且有效消除控制器的抖振情况;最后通过仿真算例验证所提方法的有效性.     

Discontinuous exponential stabilization of chained form systems

In this paper a novel approach to exponential stabilization of chained form system is proposed. Provided that the control law fulfills mild assumptions, it is shown that a Brunovsky-like change of coordinates depending on the control transforms any chained form system into a system having a linearly bounded nonlinear part. Using linear tools, it is possible to exponentially stabilize a chained form system for any initial condition outside a submanifold containing the origin. This result is then generalized to global exponential stabilization. The so obtained static discontinuous feedback is bounded for bounded states and exponentially converges to zero along the closed-loop trajectories of the system.     

一类带有加速度约束的非线性系统最优滑模控制

针对加速度受约束的非线性时变系统,设计了一种全局最优滑模控制算法.首先引入全程滑态因子,保证滑模面一开始就在零值附近,然后选取位置跟踪误差绝对值的积分为指标函数,通过求解该指标函数的最小值来确定滑模面方程的相关参数,最后设计了基于指数趋近律的滑模控制算法.仿真结果表明了该方法的有效性和强鲁棒性.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Comments on `On the robust control of robot manipulators by M.W.Spong

In the above-title paper (ibid., vol.37, no.11, pp.1782-1786, Nov. 1992) a simple robust control is given for guaranteeing uniform ultimate boundedness of tracking errors for n-link robot manipulators. It is pointed out here that an equally simple control law, which is also continuous in nature, can guarantee global exponential stability of tracking errors under the same set of conditions     

Global time-varying stabilization of underactuated surface vessel

This note considers the stabilization problem of an underactuated surface vessel. Three global smooth time-varying control laws are proposed with the aid of different techniques. The first proposed control law makes the state of the closed-loop system asymptotically converge to zero, while the second and the third control laws make the state of the closed-loop system globally exponentially converge to zero. Moreover, the exponential convergence rate of the state of the closed-loop system can be arbitrarily assigned with the third control law. Simulation results show that the proposed control laws are effective.     

Robust discontinuous exponential regulation of dynamic nonholonomic wheeled mobile robots with parameter uncertainties

For regulating a dynamic nonholonomic WMR (wheeled mobile robot) with parameter uncertainties, we derive a simple robust discontinuous control law, yielding a global exponential convergence of position and orientation to the desired set point despite parameter uncertainties. The controller design relies on separating the error dynamics into two subsystems, followed by robust feedback control laws to stabilize the subsystems. The effectiveness of the proposed control laws is verified by simulation. Copyright © 2007 John Wiley & Sons, Ltd.     

Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling.      

Global exponential tracking control of a mobile robot system via aPE condition

This paper presents the design of a differentiable, kinematic control law that achieves global asymptotic tracking. In addition, we also illustrate how the proposed kinematic controller provides global exponential tracking provided the reference trajectory satisfies a mild persistency of excitation (PE) condition. We also illustrate how the proposed kinematic controller can be slightly modified to provide for global asymptotic regulation of both the position and orientation of the mobile robot. Finally, we embed the differentiable kinematic controller inside of an adaptive controller that fosters global asymptotic tracking despite parametric uncertainty associated with the dynamic model. Experimental results are also provided to illustrate the performance of the proposed adaptive tracking controller.     

Lyapunov function-based control laws for revolute robot arms:tracking control, robustness, and adaptive control

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to an energy-like Lyapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates     

Logarithmic control,trajectory tracking,and formation for nonholonomic vehicles on Lie group SE(2)

This paper studies the problem of set-point stabilisation, trajectory tracking, and formation tracking for unicycle-type vehicles by taking advantage of the exponential coordinates and the other mathematical tools provided by the Lie group setting of the special Euclidean group SE(2). Motivated by recent developments in geometric control approaches for holonomic systems, we first study the stabilisation problem for nonholonomic constrained kinematic systems by improving the logarithmic stabilising control laws in such a way that they can satisfy nonholonomic constraints too. We then extend the control design to the problem of trajectory tracking by proposing auxiliary systems and investigating the conditions for which the adjoint map in the Lie algebra preserves the velocity constraint. This leads to a global control law which is valid for general time-varying as well as non-smooth trajectories. The tracking control law is also applied to the problem of leader-follower formation tracking by constructing nonholonomic virtual leaders in the desired formation. Finally, the kinematic control law is translated to a differential drive robot using the backstepping technique. To demonstrate the effectiveness of the controllers, the numerical results are presented and the performances are compared with the other three controllers in the literature.     

变时滞分布参数系统的全局指数稳定性

基于比较原理,利用推广的向量Hanalay微分不等式,Dini导数,结合Green公式及不等式分析技术,研究几类变时滞分布参数控制系统所导出的滑动模运动方程的全局指数稳定性问题,在仅要求系数矩阵是个M-矩阵的条件下,获得了几类滑动模运动方程全局指数稳定性的充分条件,建立了滑动模运动方程全局指数稳定性定理.推广和改进了前人的结论.并为研究时滞分布参数系统的变结构控制问题奠定了基础.     

Global exponential stabilization for a class of uncertain nonlinearsystems with control constraint

In this paper, the global exponential stabilization for a class of uncertain nonlinear systems with control constraint is investigated. A bounded and continuous feedback control is constructed, under which the global exponential convergence for such systems can be guaranteed. A numerical example is also provided to illustrate the use of our main result     

基于三阶干扰观测器的三轴MEMS陀螺稳定控制

微机电系统(Micro-Electro-Mechanic System,MEMS)陀螺仪是一种新兴的惯性传感器,然而在加工制造和现场应用过程中,MEMS陀螺不可避免地会受到外界干扰的影响,降低角速率检测精度。针对无法等效到输入通道且频率成分复杂的不匹配干扰,提出一种基于三阶干扰观测器的全局滑模控制方法。利用三阶干扰观测器估计频率成分复杂的不匹配干扰,在此基础上提出一种新的非线性滑模面实现滑动模态的全局鲁棒性,滑模面的可达性由指数趋近律保证。仿真结果表明了该基于干扰观测器的全局滑模控制器能够有效抑制不匹配成分,干扰估计误差由0.58降至0.18,且陀螺三轴位置响应呈现更小的超调。     

基于观测器的轮式移动机器人路径跟踪控制

研究基于状态观测器的轮式移动机器人的路径跟踪控制问题.首先简要回顾了基于状态反馈的移动机器人的路径跟踪控制问题;进而通过适当的状态变换将移动机器人模型转换为合适的形式,并在移动机器人的位置可以测量的情况下设计了一种可保证状态观测误差指数收敛的状态观测器;最后结合状态反馈路径跟踪控制器和所设计的观测器得到了一种基于观测器的路径跟踪控制器,该控制器可以保证移动机器人的运动轨迹指数收敛到期望路径上.仿真结果证实了所提出的基于观测器的路径跟踪控制器的有效性.     

Multivariable extension of global finite‐time HOSM based differentiator for output‐feedback unit vector and smooth binary control

In this paper, we propose a unit vector control law by output feedback to solve the problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to face the nonuniform arbitrary relative degree obstacle, we extend our earlier estimation scheme based on global finite‐time differentiators using dynamic gains to a multivariable architecture. A diagonally stable condition over the system high‐frequency gain (HFG) matrix has to be assumed. Preserving the simplicity of its mono variable framework, variable gain super‐twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. Moreover, state‐norm observers for the unmeasured state variables are constructed to upper bound the disturbances as well as to update the differentiator gains, being both state dependent. Uniform global exponential stability and ultimate exact tracking are proved. As an alternative to chattering alleviation, we appeal to the Emelyanov's concept of binary control in order to obtain a continuous control signal replacing the unit vector function in the controller by a high‐gain gradient adaptive law with parameter projection. As shown in the existing literature for mono variable systems, the proposed multiparameter binary‐adaptive formulation tends to the unit vector control as the adaptation gain increases to infinity, also smoothing the transition from adaptive to sliding mode control. A numerical example is portrayed to illustrate the potentialities of the developed multivariable techniques.