Stabilization of nonlinear systems based on robust control Lyapunov function

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.

Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

Delay-dependent robust H_∞ control for uncertain discrete time-delay fuzzy systems

The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

基于公共Lyapunov函数的一类切换系统H_∞鲁棒控制

针对一类含有参数不确定性的离散时间切换系统,在任意切换的情况下研究了这类系统的H∞鲁棒控制问题,利用公共二次Lyapunov函数法,设计了切换系统的状态反馈控制器。切换系统的不确定性满足一定的匹配条件,所设计的控制器能保证闭环系统鲁棒稳定且具有H∞扰动衰减度。可以通过求解一组线性矩阵不等式获得状态反馈控制器,仿真结果验证了设计方案的有效性。

基于鲁棒控制Lyapunov函数的非线性自适应跟踪

研究了一类带有未知参数以及扰动的多输入非线性系统的自适应跟踪问题,利用控制Lyapunov方法设计出一种自适应控制器。该控制器对系统的参数和状态的不确定性具有鲁棒性,并且能保证系统闭环全局稳定。仿真结果表明,该控制方案具有良好的跟踪性能、鲁棒性及参数辨识能力。

控制Lyapunov函数在自适应控制中的应用

研究了一类带有未知参数的非线性系统的自适应稳定问题,利用控制Lyapunov函数方法设计出一种自适应控制器.该控制器对系统的参数和状态的不确定性具有鲁棒性,并且能保证系统自适应稳定.

基于控制Lyapunov函数的鲁棒自适应控制器设计

研究一类含有系统扰动,并且状态项与控制项中同时含有未知参数的非线性系统的反馈稳定问题。利用鲁棒控制Lyapunov函数方法及参数映射技术,讨论了当系统存在I型与II型自适应鲁棒控制Lyapunov函数(ARCLF)时,系统的自适应控制问题,并针对两种情况分别进行了控制器的设计。通过算例验证了所提方法的可行性。

基于鲁棒控制Lyapunov函数的CVT离合器起步非线性控制研究

新一代无级变速器(Continuously Variable Transmission, CVT)设计中,离合器传递的扭矩无法通过传感器直接获取。为满足其接合过程快速充油且避免扭矩冲击给金属带造成破坏等问题,提出一种离合器执行机构鲁棒性的模型预测控制算法。基于鲁棒控制Lyapunov函数(Rrobust Control Lyapunov Function, RCLF),构造离合器充油和滑摩阶段的鲁棒控制器,利用RCLF预测模型替代传统比例控制方法,并以此补偿传统控制所存在的充油时间不足问题。建立CVT起步控制系统,将离合器油缸压力接合速度与冲击度作为衡量整车的起步标准,完成传统控制和RCLF控制下,不同油门开度的起步性能仿真及实车验证。试验结果表明:与传统离合器起步控制相比,基于RCLF控制技术的离合器油缸压力能在目标时刻完成充油过程,且整车起步冲击度降低,RCLF控制效果优于传统控制。

基于参数相关Lyapunov函数的鲁棒H_2/H_∞控制

研究凸多面体不确定连续系统的鲁棒H_2/H_∞优化控制问题。为降低设计的保守性,提出一种具有参数相关Lyapunov函数的鲁棒H_2/H_∞性能准则。基于该性能准则,推导出鲁棒H2/H∞状态反馈控制器存在的充分条件,并以双线性矩阵不等式(BMI)的形式给出。给出了用于鲁棒H2/H∞控制器优化设计的迭代线性矩阵不等式(ILMI)算法。对某卫星姿态控制系统的仿真结果表明了该方法的有效性。

基于模糊Lyapunov-Krasovskii函数的模糊系统的鲁棒H_∞控制

针对公共Lyapunov-krasovskii函数(LKF)方法判断离散时滞模糊系统鲁棒稳定性的保守性,构造了模糊LKF,并给出了系统鲁棒稳定的充分条件。应用并行分布补偿算法(PDC),设计了全局鲁棒稳定的模糊控制器。多个附加矩阵变量的引入,使控制器可以通过求解一系列线性矩阵不等式(LMI)获得。最后,通过一个仿真例子验证了方法的有效性。

Robust stability for uncertain neutral systems with mixed time-varying delays

The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.

切换系统的鲁棒二次公共Lyapunov函数矩阵寻找算法

为了获得不确定线性切换系统稳定性判别的公共二次Lyapunov函数寻找方法,提出了鲁棒公共二次Lyapunov函数的概念,运用矩阵不等式分析,得到了在鲁棒稳定矩阵集对合和不对合的情况下,鲁棒公共二次Lyapunov函数存在的充分性条件以及LMI形式的递推搜寻算法。获得的结果便于计算机实现,对不确定切换系统鲁棒稳定性判别具有一定价值。应用仿真测试验证了其正确性。

Stable Adaptive Neural Control of a Robot Arm

In this paper, stable indirect adaptive control with recurrent neural networks (RNN) is presented for square multivariable non-linear plants with unknown dynamics. The control scheme is made of an adaptive instantaneous neural model, a neural controller based on fully connected “Real-Time Recurrent Learning” (RTRL) networks and an online parameters updating law. Closed-loop performances as well as sufficient conditions for asymptotic stability are derived from the Lyapunov approach according to the adaptive updating rate parameter. Robustness is also considered in terms of sensor noise and model uncertainties. This control scheme is applied to the manipulator robot process in order to illustrate the efficiency of the proposed method for real-world control problems.

On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

基于深度哈密顿神经网络的物料提升机的鲁棒控制

安装基座的随机振动给物料提升机系统带来不确定性,对此提出一种基于深度神经网络的非线性鲁棒控制策略。首先,采用一种嵌入哈密顿力学先验的深度神经网络(HNN),拟合了系统的动力学模型;然后,以此模型为基础,结合一种隐式Lyapunov(IL)函数,设计了系统的鲁棒镇定控制器。仿真显示,所提出的基于深度哈密顿神经网络结合IL函数控制器(HIL)的控制效果与基于精确模型的控制器IL几乎完全一致;相较传统的基于黑箱神经网络模型的IL控制(BIL)、基于误差模型(IL-E),其收敛时间分别减少了25.9%和32.5%。结果表明,所提出的控制策略能准确表征系统的非线性动力学特征,有效抑制基座振动不确定的影响,实现物料提升机的快速精确鲁棒镇定。

考虑执行器饱和的复杂动态网络鲁棒采样切换控制

随着计算机和网络技术的发展,复杂动态网络鲁棒采样切换控制受到广泛关注。探讨了在执行器饱和情况下不确定切换复杂动态网络的非周期采样控制问题。由于采样间隔上限受到停留时间的限制,采样数据控制器模式和系统模式之间的异步问题可能是由采样间隔内切换的子系统引起的。通过考虑无切换的采样间隔和有切换的采样间隔,分别构建了参数相关的李雅普诺夫闭环泛函。在平均停留时间的定义下,借助所构造的泛函,给出了不确定切换复杂动态网络误差系统的均方指数稳定性判据。此外,基于稳定性准则,针对执行器饱和情况下的不确定切换复杂动态网络,设计了全新的异步非周期采样控制器。根据提出的稳定性条件并采用非周期采样控制器设计方法,保证了不确定切换复杂动态网络与目标节点指数同步。最后,将利用蔡氏电路的算例与其他类似方法进行了对比,验证了所提方法的有效性,同时证明了利用所提方法得到的最大允许采样区间较大。

机械臂鲁棒自适应运动控制

针对具有不确定性的机械臂系统,文中阐述了一种基于势函数和Lyapunov稳定性理论的鲁棒自适应控制方法.它是通过合理选择与控制目标相关的势函数,并根据模型中不确定性的实时变化,在控制器中引入可在线可调参数,使得控制器机械臂能够跟踪给定的有界参考信号,跟踪误差收敛到包含零点的很小的邻域内.同时该闭环系统的所有状态半全局最终一致有界(SGUUB).仿真研究表明该方法的有效性.