基于逼近误差调节的髋关节康复机器人自适应模糊容错控制算法的研究

针对基于人体生物动力学设计的一种髋关节康复机器人,在模型参数不确定的情况下,研究执行器故障容错控制问题.根据人体髋关节活动特点,给出了康复训练中期望跟踪轨线的数学表达式;对康复机器人的旋转驱动器提出了基于分层模糊系统的间接型自适应容错控制算法,对4个线性驱动器给出了直接型自适应模糊容错控制算法.该方法对逼近误差估计值在线调节,用此估计值设计补偿控制项以减小逼近误差对跟踪精度的影响.基于Lyapunov理论,对所设计的控制方案作了稳定性分析.此外,还给出了矩阵Lyapunov方程解的特征值的性质,为减小跟踪误差提供了理论依据.仿真结果表明所提出的控制方案可使髋关节康复机器人圆满完成训练任务.     

具有控制输入约束的轮式移动机器人轨迹跟踪最优保性能控制

针对考虑模型不确定性因素影响及控制输入约束的轮式移动机器人的轨迹跟踪问题,文章提出了一种具有控制输入约束的轨迹跟踪最优保性能控制器.依据实际机器人与虚拟机器人的相对位姿关系建立轨迹跟踪误差动态模型.采用平衡点线性化方法将非线性形式的轨迹跟踪误差动态模型转换为线性形式的轨迹跟踪误差动态模型.通过线性矩阵不等式处理方法,给出了具有鲁棒性能上界的最优保性能控制器的存在条件及设计方法.仿真及实验结果表明,文章所提控制器能较好抑制模型不确定性的影响,提高移动机器人的轨迹跟踪性能和鲁棒性.     

基于Udwadia-Kalaba方法的并联机器人鲁棒伺服约束控制

针对2自由度冗余驱动并联机器人轨迹跟踪控制问题,提出了一种基于Udwadia Kalaba方程的鲁棒伺服控制方法.在负载、外部干扰以及制造误差的影响下,无法得到机器人精确、完整的运动模型,导致机器人控制性能变差.为解决这类不确定性带来的影响,提出了一种鲁棒控制方法.该方法通过保证系统的一致有界性和一致最终有界性,使系统能够精确跟踪理想约束轨迹.此外,该方法采用Udwadia Kalaba方程,求解控制过程中满足系统理想约束所需要的约束力.Udwadia Kalaba方程不需要Lagrange乘子或伪广义速度等辅助变量,可以同时处理完整约束和非完整约束,且可以获得满足轨迹约束的约束力解析解.利用Lyapunov函数对该鲁棒控制方法的稳定性进行了理论证明,并且通过仿真实验,验证了该鲁棒控制方法能够在非理想条件下实现给定轨迹的高精度跟踪控制.     

具有外部干扰的连续时间线性系统鲁棒最优开环解耦控制

针对具有外部干扰的一类连续时间线性系统,将开环解耦控制和无限时间最优跟踪控制相结合,提出了一种鲁棒最优开环解耦控制方法.首先,通过引入中间虚拟变量,对系统进行开环解耦;其次,将解耦后的系统看做被控对象的广义系统,针对标称广义系统设计了无限时间最优跟踪控制方法;最后分析了该最优跟踪控制器与具有外部干扰的广义系统组成的闭环广义系统的鲁棒性.仿真结果表明所提方法的有效性以及与经典的无限时间最优跟踪控制控制方法相比的优越性.     

卫星姿态跟踪的间接自适应模糊预测控制

对含模型不确定性和未知干扰的卫星姿态系统提出了具有间接自适应模糊补偿的广义预测跟踪控制方法. 首先基于卫星姿态动力学模型设计了非线性广义预测控制律, 再利用自适应模糊系统逼近预测控制律中的模型不确定项, 使得所得到的预测控制算法可实施.证明了当卫星姿态模型中不确定项满足一定条件时, 所设计的控制律可使卫星姿态跟踪误差收敛到原点的小邻域内,并仿真结果验证了所提出方法的有效性.     

基于四元数方法的绳系机器人姿态控制

为进一步提升空间绳系机器人在轨服务能力，研究了空间绳系机器人抓捕目标后的复合体姿态控制问题.首先，基于四元数原理，描述了空间绳系机器人在抓捕目标后组成的复合体姿态，建立了空间绳系机器人系统的动力学方程；其次，针对带约束的动力学控制方程，结合投影技术和Runge Kutta方法，构造了一种保四元数范数的显式投影方法；最后，通过数值实验，验证了所提出数值方法的有效性，同时分析了采用系绳和推力器同时控制，采用系绳、推力器相互切换控制，以及单独采用推力器进行控制这3种方式对空间绳系机器人抓捕目标后的复合体姿态的控制效果和能量消耗.     

非完整性多体编队运动的一种无源化控制方法

讨论了非完整性多体编队运动问题．首先利用动态反馈将单个体的动力学模型线性化为2个三阶输入输出积分链的形式;然后提出一种带有单个体间阻尼注入的非连续分布式控制律,并利用Liapunov方法证明了在该控制律作用下闭环系统的渐进稳定性;最后通过一个平面机器人的编队运动仿真验证了所提方法的有效性．     

永磁同步电动机的转速跟踪控制

研究永磁同步电动机的转速控制问题.对于参数不确定,输出受限的永磁同步电动机系统,提出转速跟踪控制方法.利用神经网络逼近电动机系统中的复杂非线性函数,采用自适应控制,动态面控制技术,设计控制器实现电动机的转速跟踪控制器.文中提出的控制策略不仅能够克服电机参数的不确定性和负载扰动,而且避免了传统反步设计方法存在的"复杂性爆炸"问题.基于Lyapunov稳定性理论,证明闭环系统具有半全局稳定性,转速跟踪误差收敛于原点的极小邻域内.仿真结果验证了所提控制方法的有效性.     

不确定电液位置伺服系统的自适应终端滑模控制

为了解决非线性、不确定电液伺服系统的位置跟踪控制问题,提出了一种基于反步法的自适应终端滑模控制方法.该方法将自适应控制和终端滑模方法结合在一起,一方面,提出的自适应控制律可以对电液伺服系统中的不确定性参数进行有效在线估计和补偿;另一方面,通过引入误差吸引子到滑模趋近律中得到变系数趋近律,设计的终端滑模控制律不仅能够消除普通终端滑模控制律中的非奇异项,还大大降低了滑模面的抖震.最终,根据Lyapunov稳定性理论,位置跟踪误差的有限时间稳定性得以严格证明.将该方法与积分反步滑模控制和线性滑模控制方法进行了对比研究,仿真结果验证了该方法在电液伺服系统位置跟踪控制方面良好的鲁棒性和跟踪精度.     

一类模糊T-S模型互联系统的自适应容错跟踪控制

针对一类带有执行器故障的T-S模糊互联的容错跟踪控制问题,提出了一种模糊自适应容错控制器。该控制器由一个模糊控制器和一个自适应控制器组成,模糊控制器能够保证系统没有故障时闭环系统渐近稳定,而自适应控制器能够补偿系统的执行器故障。所提出的容错控制方法不但使得闭环系统渐近稳定、系统的输出渐近跟踪给定的参考信号,并获得H∞控制性能。最后应用Lyapunov函数和线性矩阵不等式的方法,给出和证明了带有执行器故障的T-S模糊互联系统的稳定的充分条件。仿真结果进一步验证了所提出方法的有效性。     

Null controllability and global blowup controllability of ordinary differential equations with feedback controls

This paper concerns the problem of feedback null controllability and blowup controllability with feedback controls for ordinary differential equations. First, we study the feedback null controllability on a time-varying ordinary differential system by unbounded feedback operators. Then, the global exact blowup controllability with feedback controls is derived on a time-invariant ordinary differential system. Finally, we obtain the approximate null controllability by bounded feedback operators, and get the approximate blowup controllability with feedback controls for ordinary differential equations.     

Optimal syntheses for infinite-dimensional linear delayed state-output systems: A semicausality approach

Quadratic optimal control synthesis for infinite-dimensional delayed dynamical systems with output time delay involved in the cost functional is described. By introducing a truncation operator and associated semicausal trajectory, a new dynamical optimality principle was established. The closed-loop optimal control is given in three parts as a linear feedback: real-time state feedback, retarded state integral feedback, and initial data feedback which effects only a small time interval. The main feedback operator can be determined by solving a linear Fredholm integral equation.This research was supported by the National Science Foundation under Grant No. 8607687 and the Airforce Office of Scientific Research under Grant No. 860088.     

Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability

We study semiconductor ring lasers subject to delayed optical feedback from one or two short external cavities. In case of two cavities we consider the feedback strengths and phases to be either symmetric or asymmetric feedback. When feedback is symmetric, the laser operates in a bi-directional continuous wave or periodic regime for most parameter values. Only for some small parameter regions complex dynamics, such as quasi-periodicity and chaos are obtained. When the feedback is asymmetric complex dynamical regimes, including chaos, are obtained in large parameter regions. We explain complex dynamical regimes obtained in both symmetric and asymmetric feedback cases by linear stability of the stationary solutions calculated using DDE-BIFTOOL.     

广义分布参数系统的状态反馈稳定性问题(1)

关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值.     

Endogenous fields enhanced stochastic resonance in a randomly coupled neuronal network

Endogenous field, evoked by structured neuronal network activity in vivo, is correlated with many vital neuronal processes. In this paper, the effects of endogenous fields on stochastic resonance (SR) in a randomly connected neuronal network are investigated. The network consists of excitatory and inhibitory neurons and the axonal conduction delays between neurons are also considered. Numerical results elucidate that endogenous field feedback results in more rhythmic macroscope activation of the network for proper time delay and feedback coefficient. The response of the network to the weak periodic stimulation can be notably enhanced by endogenous field feedback. Moreover, the endogenous field feedback delay plays a vital role in SR. We reveal that appropriately tuned delays of the feedback can either induce the enhancement of SR, appearing at every integer multiple of the weak input signal’s oscillation period, or the depression of SR, appearing at every integer multiple of half the weak input signal’s oscillation period for the same feedback coefficient. Interestingly, the parameters of low-passed filter which is used in obtaining the endogenous field feedback signal play a subtle role in SR.     

A necessary and sufficient condition for a class of nonsingular Galois NFSRs

Let n be a positive integer. An n-stage Galois NFSR is nonsingular if and only if the output sequences of each bit register are purely periodic. It is well known that a Galois NFSR used to build a stream cipher should be nonsingular. Recently, a useful concept that is the simplified feedback function is proposed for a Galois NFSR, which is a vectorial Boolean function. Generally, for a Galois NFSR, its simplified feedback function has less nonlinear terms than its traditional feedback function, and so is easier to analyze. Moreover, it has been shown that the nonsingularity of a Galois NFSR is decided by the invertibility of its simplified feedback function. Based on this observation, in this paper, we present a necessary and sufficient condition for the nonsingularity of a class of Galois NFSRs such that every component of its simplified feedback is linear or has a common nonlinear term.     

Boundary feedback stabilization of Boussinesq equations

The aim of this work is to design oblique boundary feedback controller for stabilizing the equilibrium solutions to Boussinesq equations on a bounded and open domain in R~2. Two kinds of such feedback controller are provided, one is the proportional stabilizable feedback control, which is obtained by spectrum decomposition method, while another one is constructed via the Ricatti operator for an infinite time horizon optimal control problem.An example of periodic Boussinesq flow in 2-D channel is also given.     

Application of stochastic artsteins theorem to feedback stablization

The stochastic Artstein's theorem is applied to derive sufficient conditions for dynamic asymptotic stabilization in probability by means of a feedback integrator for a class of nonlinear stochastic differential systems. A stabilizing feedback law is deduced from a control Lyapunov function     

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.