力矩受限的机器人吸引域估计方法

针对力矩受限的机器人组合非线性反馈控制的局部稳定区域描述问题,研究了吸引域的估计方法.利用不变集属性和椭球性质,定义两种不同意义的最大椭球不变集来逼近吸引域,分别采用设置初始状态法和参考形状集法求解.通过带有约束的优化问题描述,所有条件均能转化为线性矩阵不等式条件,易于求解.由于采用优化技术,能够减小吸引域估计的保守性.数值算例验证了所提方法的有效性.

     

一种估计奇异摄动饱和系统稳定域的方法

针对奇异摄动饱和系统, 提出了一种估计其稳定域的降阶方法. 结合饱和函数的特殊性质, 证明了此类系统的稳定域可分解为伴随系统的不变集与一个足够大球体的笛卡尔积. 将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题, 利用线性矩阵不等式(Linear matrix inequality, LMI)优化方法估计伴随系统的稳定域以减少保守性. 本方法不仅可以克服奇异摄动饱和系统的奇异性, 还可以一定程度克服系统的``维数灾'等问题.     

一类饱和非有理系统状态反馈设计

本文研究了一类饱和非有理系统状态反馈镇定问题.通过线性分式表示技术,这类非有理系统可以转化为带有两个非线性回路的线性时不变(linear time-invariant,LTI)系统.假设非有理函数项分别满足局部扇形区间不等式以及局部Lipschitz条件,提出了两种基于LMI条件的镇定方法.最后,举例证明了所提出方法的有效性.     

一类受限柔性机器人的鲁棒性力／位置控制方法*

本文研究受限柔性连杆机器人的力／位置控制问题，首先导出受限柔性机器人的动力学模型，然后借助于微分几何理论将动力学模型转化为仿射非线性形式，再使用非线性反使系统线性化，最后对线性子系统设计变结构补偿器，使控制方法具有较高的精度和强鲁棒性。     

饱和约束控制系统的吸引域估计

饱和约束控制系统的吸引域估计是非线性系统领域的一个基本问题,主要涉及到饱和约束的处理和Lyapunov函数的选取.围绕这两个关键问题,梳理了解决饱和约束控制系统吸引域估计问题的一系列方法,总结了文献及最近的一些研究结果.     

一类时延反馈神经网络的稳定性及吸引域的估计

反馈型神经网络由于具有极为丰富的动力学行为和整体计算能力（如优化、联想、振荡和混饨）而倍受关注，近几年的研究表明，当网络的时延足够小时，具有延时的对称Hopfield型神经网络和无时延情况一样也是全局稳定的．本文通过构造适当Lyapunov泛函的方法，对一类具有时延的反馈型神经网络平衡点的渐近稳定性进行了分析，得到了平衡点渐近稳定的充分条件：要检验一个有时间延迟的反馈型神经网络的稳定性，只要测试一个特定矩阵的定性性质或一个特定不等式即可．最后我们也提供了一种估计网络渐近稳定平衡点吸引域的方法．     

应用于力矩受限自由漂浮空间机器人的神经网络自适应控制

在控制力矩受限情况下,为实现具有模型不确定性自由漂浮空间机器人的轨迹跟踪控制,文章设计了一种新的神经网络自适应控制策略;首先,用双曲函数对控制力矩输入进行限制;其次,设计一种神经网络自适应控制律,对输入力矩受限条件下的非线性系统模型进行在线逼近,同时,利用鲁棒项对神经网络逼近误差和外界干扰进行消除;最后,根据李雅普诺夫理论,证明了所设计控制策略能够使自由漂浮空间机器人系统渐进稳定;仿真实验表明,该控制策略在无需建立复杂系统模型的情况下,便能够对控制力矩进行有效限制,从而使自由漂浮空间机器人在控制力矩受限情况下得到较好的控制.     

连续TS模糊控制系统稳定吸引域估计方法的进一步研究

研究了连续TS模糊控制系统稳定性判别条件与平衡点稳定吸引域估计方法的进一点改进。首先基于模糊李亚普诺夫函数,给出了连续TS模糊控制系统的稳定性充分条件;该条件更一步减小了判别的保守性。其次基于模糊李亚普诺夫函数,进一步改进了连续TS模糊控制系统渐近稳定平衡点稳定吸引域的估计方法;该方法简单实用,最大限度地估计稳定吸引域大小。实例验证了该方法的有效性和实用性。     

一种基于LMI的非线性模型预测控制终端域优化方法

对于具有约束的非线性系统, 提出了一种模型预测控制 (Model predictive control, MPC) 的终端域优化方法. 基于线性矩阵不等式(Linear matrix inequality, LMI) 优化和非线性系统的范数有界线性微分包含 (Linear differential inclusion, LDI), 给出了求解非线性 MPC 终端代价函数和局部稳定控制器的一种方法, 在此基础上可方便地得到非线性模型预测控制终端域. 一个具体的数值算例验证了算法的有效性.     

模拟反馈联想记忆的吸引域和指数收敛速度的估计及其应用

本文得到了若干关于模拟反馈联想记忆各记忆模式的吸引域及其中每一点趋向相应记忆模式的指数收敛速度的估计结果，它们可用于高效模拟反馈联想记忆的性能评价以及综合过程．     

An estimation of the domain of attraction for recurrent neural networks with time-varying delays

Based on Lyapunov–Krasovskii functional or Lyapunov–Razumikhin functional method and invariant set principle, we presented a new method to estimate the domain of attraction for general recurrent neural networks with time-varying delays. Convex optimization method is proposed to enlarge and estimate the domain of attraction. Local exponential stability conditions are derived, which can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can be easily checked in both analysis and design.     

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature.     

Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.     

Estimating the domain of attraction for uncertain polynomial systems

Estimating the Domain of Attraction (DA) of equilibrium points is a problem of fundamental importance in systems engineering. Several approaches have been proposed for the case of known polynomial systems allowing one to find the Largest Estimate of the DA (LEDA) for a given Lyapunov Function (LF). However, the problem of estimating the Robust DA (RDA), that is the DA guaranteed for all possible uncertainties in an uncertain system, it is still an unsolved problem. In this paper, LMI methods are proposed for estimating the RDA in the case of systems depending polynomially in the state and in the uncertainty which is supposed to belong to a polytope. Specifically, the issue of computing the Robust LEDA (RLEDA), that is the intersection of all LEDAs, is considered for common and parameter-dependent LFs, providing constant and parameter-dependent lower bounds. The computation of approximations with simple shape of the RLEDA in the case of parameter-dependent LFs is also discussed.     

Semiglobal stability of saturated linear PID control for robot manipulators

This paper addresses the position regulation problem of robot manipulators under control input constraints. It is proven that the robot system under a saturated linear PID control is semiglobally asymptotically stable, if the torque bounds are larger than gravitational torques, and if the proportional gain is large enough and the integral gain is small enough.The stability analysis makes use of singular perturbation tools and the results are illustrated via numerical simulations.     

Delay-range-dependent control synthesis for time-delay systems with actuator saturation

The control synthesis problem for a class of linear time-delay systems with actuator saturation is investigated in this paper. The time delay is considered to be time-varying and has lower and upper bounds. A delay-range-dependent approach is adopted and the corresponding existence conditions of the stabilizing state-feedback controller are derived in terms of LMIs. An estimate for the domain of attraction of the origin can be obtained for the underlying systems with different time-delay ranges. Two numerical examples are presented to show the effectiveness and less conservatism of the developed theoretical results.     

Estimating the domain of attraction for non-polynomial systems via LMI optimizations

This paper proposes a strategy for estimating the domain of attraction (DA) for non-polynomial systems via Lyapunov functions (LFs). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst-case remainders in truncated Taylor expansions. Moreover, a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen LF, and another condition is provided for establishing whether such an estimate has been found. The proposed strategy can readily be exploited with variable LFs in order to search for optimal estimates. Lastly, it is worth remarking that no other method is available to estimate the DA for non-polynomial systems via LMIs.     

Estimation of optimal feet forces and joint torques for on-line control of six-legged robot

The present study aims to estimate optimal feet forces and joint torques necessary for real-time control of a six-legged robot. Two approaches have been developed, such as minimization of norm of feet forces and minimization of norm of joint torques using the least squared method. Results of these two approaches have been compared with each other, and with those of available literature. As both of these approaches are found to be computationally fast, these are suitable for real-time control of the six-legged robot.     

On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

This paper investigates the estimation of domain of attraction for nonlinear port-controlled Hamiltonian (PCH) systems with actuator saturation (AS).Several conditions are established under which an el...