无动力双足步行机器人控制策略与算法

本文研究无动力双足步行机器人的建模、分析与控制问题. 基于能量的控制增加了机器人行走极限环的稳定性、鲁棒性, 扩大了极限环的收敛域; 角度不变控制使机器人的稳定行走步态摆脱了地面倾斜角度的限制; 把基于能量的控制与角度不变控制结合起来, 可以实现在不同倾斜角度地面上行走模式的切换. 基于能量的行走平均速度控制方法在平均速度与目标能量之间建立了联系, 能使机器人的行走产生新的稳定步态. 最后, 对无动力双足步行机器人的研究前景做了展望.     

延迟离散神经网络动态特征的矩阵判据S

该文利用延迟离散网络的状态转移方程与矩阵不等式的等价性研究网络的动力学性质.对于具有任意连接权阵的网络,文章给出了周期为1和2的极限环存在的一些条件.同时,对于周期为1,2和4的一些特殊极限环给出了存在的条件,还得到了网络不存在任何不动点的充分条件,即只有极限环的充分条件.计算机模拟实验表明其结果是正确的.     

极限环高阶分岔控制

分岔控制是非线性动力学研究的重要问题之一.Hopf分岔的控制与反控制已经得到较多的研究,但其二次分岔,特别是由一系列高阶分岔形成的分岔序列的控制,已有的工作还极少.对某存在极限环复杂分岔序列的二自由度非线性自治系统,通过与受共振激励的单自由度非线性系统耦合,成功抑制了系统中极限环高次分岔.为分岔序列的非线性控制提供了一个简单的例子.     

延迟离散神经网络动态特征的矩阵判据

该文利用延迟离散网络的状态转移方程与矩阵不等式的等价性研究网络的动力学性质.对于具有任意连接权阵的网络,文章给出了周期为1和2的极限环存在的一些条件.同时,对于周期为1,2和4的一些特殊极限环给出了存在的条件,还得到了网络不存在任何不动点的充分条件,即只有极限环的充分条件.计算机模拟实验表明其结果是正确的.     

卫星姿态控制性能优化仿真研究北大核心CSCD

在气浮式模拟平台的地面模拟卫星的位姿控制问题的研究中,为提高地面模拟卫星的位姿控制精度及收敛速度,解决超调和振荡等问题,通过对传统极限环形状的优化设计,提出了双极限环相对位姿控制算法。首先,建立了地面模拟卫星的位姿控制系统数学模型。然后,基于相平面最优控制,通过使相点收敛于原点将传统的极限环变为经过原点的双极限环,并提出了采用双极限环的相平面控制策略,对相点的运动路径进行了理论分析,证明了控制算法的收敛性,得到了双极限环控制算法可以有效提高控制精度、减小超调的结论。最后开展数值仿真工作,通过对比双极限环控制方法和相平面最优控制方法的控制性能,验证了改进方法的有效性。     

伪振子分析法的证明及其在高阶Hopf分岔中的应用

采用由闭轨分岔出极限环的思路给出了伪振子分析法的严格证明,所得结果推广了伪振子分析法的主要结论,使其能够应用于高阶Hopf分岔问题,其中分岔周期解的稳定性分析需要高于三次的非线性项.论文给出两个数值算例检验了伪振子分析法的有效性.     

多自由度 Van der Pol 型系统振幅增大控制

研究多自由度Van der Pol型非线性振动系统振幅增大的控制,设计反馈控制器,用数值方法对控制系统的幅值进行了计算,绘制了在不同控制参数下,系统响应的时间历程曲线和极限环.研究表明通过调整控制参数,能够增大极限环的幅值,有工程应用价值,对高维系统的分岔控制研究有一定的理论意义.     

倒立摆系统中强化学习的极限环问题

倒立摆系统是强化学习的一种重要的应用领域。首先分析指出在倒立摆系统中,常用的强化学习算法存在着极限环问题,算法无法正确收敛、控制策略不稳定。但是由于在简单的一级倒立摆系统中算法的控制策略不稳定的现象还不明显,因此极限环问题常常被忽视。针对强化学习算法中极限环问题,提出基于动作连续性准则的强化学习算法。算法采用修正强化信号和改进探索策略的方法克服极限环对倒立摆系统的影响。将提出的算法用于二级倒立摆的实际系统控制中,实验结果证明算法不仅能成功控制倒立摆,而且可以保持控制策略的稳定。     

一类切换系统极限环的反馈镇定研究

利用多Lyapunov函数法讨论一类切换系统极限环的反馈镇定问题．首先给出切换系统极限环的有界状态反馈、有界输出反馈以及动态反馈镇定定理；然后利用Jurdjevic—Quinn方法给出反馈控制器的具体形式，并证明了在给定反馈控制器的作用下，切换系统的极限环渐近稳定．仿真例子验证了结论的正确性．     

建立Hopfield网络的一般方法

讨论了用离散的带反馈的Hopfield网络的极限环来表达概念,以及在给定不动点、极限 环或迭代序列等限制下,用线性规划和遗传算法通过求解不等式组一般性地建立Hopfield网 络的方法,从而也解决了网络联结的稀释问题.最后给出了几个实例,     

Feedback equivalence and global stabilization of nonstationary discrte systems

A problem is considered for the global stabilization of nonstationary nonlinear discrete systems without outputs. Here, the key instant is the establishment of equivalence of an arbitrary discrete system and a lossless system with the use of the appropriate feedback. The construction of control laws is performed on the basis of new methods for investigating the stability of nonautonomous systems of difference equations, using the theory of limit systems and Lyapunov limit functions.     

On the modelling and solving of the truss design problem with global stability constraints

The goal of this paper is to find a computationally tractable formulation of the optimum truss design problem involving a constraint on the global stability of the structure. The stability constraint is based on the linear buckling phenomenon. We formulate the problem as a nonconvex semidefinite programming problem and briefly discuss an interior point technique for the numerical solution of this problem. We further discuss relation to other models. The paper is concluded by a series of numerical examples.     

Global stability analysis of fuzzy path tracking using frequency response

This paper studies the stability of fuzzy path tracking of autonomous vehicles. This problem lies in the generation of the steering commands for a vehicle to follow a given path autonomously. In this control loop, both the plant and the fuzzy controller are nonlinear. Due to this nonlinearity, complex behavioral phenomena can occur, giving rise to the loss of global stability. The extension of conventional frequency response methods for the stability analysis of the nonlinear fuzzy path-tracking control loop is proposed. Simulation experiments show the validity of the proposed method in three different cases: stable origin and unstable limit cycle, delay-induced Hopf bifurcation, and delay-induced unstable limit cycle.     

Describing function analysis of uncertain fuzzy vehicle control systems

In this paper, some useful frequency domain methods including describing function, parameter space, and Kharitonov approach are applied to analyze the stability of an uncertain fuzzy vehicle control system for limit cycle prediction. A systematic procedure is proposed to solve this problem. The fuzzy controller can be linearized by the use of classical describing function firstly. By doing so, it is feasible to treat the stability problem of a fuzzy control system as linear one. In order to consider the robustness of a fuzzy vehicle control system, parameter space method and Kharitonov approach are then employed for plotting the stability boundaries. Furthermore, the effect of transport delay is also addressed. More information of limit cycles can be obtained by this approach. This work shows that the limit cycles caused by a static fuzzy controller can be easily suppressed if the system parameters are chosen carefully.     

On the analysis of nonlinear nilpotent switched systems using the Hall–Sussmann system

We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system, the nilpotent Hall–Sussmann system. Furthermore, local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems. We derive several new results revealing the elegant Lie-algebraic structure of the nilpotent Hall–Sussmann system.     

Realistic and stable animation of cloth

Researchers have proposed various techniques for cloth simulation in the last decades. The crucial problem in interactive animation for cloth is how to speed up simulation with a stable system. In this paper, we describe a realistic and stable scheme for cloth simulation based on mass‐spring system. This scheme modifies semi‐implicit integration used in cloth simulation system with an efficient damping method. Semi‐implicit integration methods have been widely used in dynamic simulation because of acceptable speed and stability. However, internal damping forces are generated with respect to rotational rigid motions, which are only depending on relative velocities. Undesirable change in global movement of dynamic cloth could result in damping artifact. We replace the internal damping forces with an optimal damping method which is based on iterative spring damping but the limit can be computed directly. The method provides simple damping parameter estimation and guarantees conservation of global movement. As a result, complex clothes can be realistically and stably simulated in real time. Copyright © 2015 John Wiley & Sons, Ltd.     

多关节机器人的自适应模糊滑模控制

针对多关节机械臂轨迹跟踪控制,提出了一种基于全局快速终端滑模面的自适应模糊滑模控制方法。该方法通过设计合适的自适应律,采用模糊自适应控制调节滑模控制的切换控制增益,实现了对建模误差和不确定干扰的自动跟踪,削弱了抖振。系统不需要对建模误差和干扰进行预估计,并且通过对控制器结构的简化,降低了模糊控制器的维数,减少了计算量。利用李亚普诺夫定理证明了控制系统的稳定性,仿真结果表明了其有效性。     

Reset control systems with reset band: Well-posedness,limit cycles and stability analysis

Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed, for example, the anticipation of the reset condition with the so-called reset band. There is a lack of analysis tools for reset systems with reset band. In this paper we address this problem by means of Poincaré maps (PM). It is shown how PM can predict the existence and stability of limit cycles, and give also information on pathologies such as Zenoness, and provide parameter ranges where the system is guarded against those behaviors and thus global asymptotical stability (GAS) is guaranteed.     

A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics.     

Control and Stability Analysis of Limit Cycles in a Hopping Robot

A new stabilizing nonlinear controller for the vertical motion of an electrically actuated hopping robot is introduced and analyzed. The approach starts by finding reference limit cycles from the "passive dynamics" of a mass-spring system. The controller then modulates the system dynamics via the leg actuator during the stance phase to force the system trajectory to converge to this reference limit cycle. The controlled system dynamics is a continuous yet nonsmooth vector field. A piecewise-continuous Lyapunov function and the general forms of Lasalle's invariance and domain of attraction theorems are used to prove global asymptotic stability of the desired limit cycles. It is also shown that the derived passive dynamic cycles are indeed the positive limit sets of the controlled system. The rate of convergence can be adjusted but is limited by actuator constraints.