一类MIMO继电反馈系统极限环的全局稳定性

研究了分散继电反馈系统极限环的全局稳定性问题.主要思想是将所研究的极限环的全局稳定性问题转化为不确定离散系统的渐近稳定性问题.并给出了判定稳定性的充分条件.结果表明,在某些约束条件下,所有系统轨迹最终进入并停留在某一特定区域,而且趋于极限环.数值例子仿真验证了提出的方法的有效性.     

基于不变集的一类混合系统的稳定性

利用混合Ｐｅｔｒｉ网为混合系统建模,探讨了基于不变集混合系统在Ｌｙａｐｕｎｏｖ意义下关于恢复半径的稳定性概念,并给出利用Ｌｙａｐｕｎｏｖ函数法判定混合系统稳定性、一致稳定和渐近稳定的充分条件。     

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。     

实时离散事件系统的动态反馈控制

本文研究了一类含确定性状态时间的实时离散事件系统的动态反馈控制问题.基于一定语言的实时可控性的概念,证明了对给定实时离散事件系统G,存在完备监控器φ使L(φ/Gr)=K的充分必要条件是K是闭及实时可控的,并得到了有关实时监控问题解存在的充要条件.     

Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws

It is well-known that a suitably designed unpowered mechanical bipedrobot can walk down an inclined plane with a steady periodicgait. The energy required to maintain the motion comes from theconversion of the biped's gravitational potential energy as itdescends. Investigation of such passive natural motions maypotentially lead us to strategies useful for controlling activewalking machines as well as to understand human locomotion.In this paper we demonstrate the existence and the stability ofsymmetric and asymmetric passive gaits using a simple nonlinear bipedmodel. Kinematically the robot is identical to a double pendulum(similar to the Acrobot and the Pendubot) and is able to walk withthe so-called compass gait. Using the passivebehavior as a reference we also investigate the performance ofseveral active control schemes. Active control can enlarge the basinof attraction of passive limit cycles and can create new gaits.     

面向自动化装配的一类智能混杂系统

针对混杂系统理论和方法尚不能处理不确定性以及意外事件的发生等问题,将已有的智能理论和混杂系统理论进行有机结合,是一项有效的解决途径。在分析自动化装配中连续和离散变量组成混杂系统基础上,提出了集成装配计划和调度的一类智能混杂系统,给出了智能决策接口以及和智能技术的互连,分析了基于模糊神经网络和粗糙集的智能解决策略,使一类混杂系统具有智能决策功能。通过对一自动化装配实例建立极大代数模型和神经网络的仿真实验,验证了系统分析方法的可行性和有效性。     

Optimal Control of Switching Surfaces in Hybrid Dynamical Systems

This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system's mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics. The work of Boccadoro has been partially supported by MIUR under Grant PRIN 2003090090. The work of Wardi has been partly supported by a grant from the Georgia Tech Manufacturing Research Center. The work of Egerstedt has been partly supported by the National Science Foundation under Grant \# 0237971 ECS NSF-CAREER, and by a grant from the Georgia Tech Manufacturing Research Center.     

The Krakovskii-LaSalle Invariance Principle for a Class of Unilateral Dynamical Systems

This paper is devoted to the study of the extension of the invariance lemma to a class of hybrid dynamical systems, namely evolution variational inequalities. Applications can be found in models of electrical circuits with ideal diodes or oligopolistic market equilibrium.Acknowledgements. This work was partially supported by the European project SICONOS IST2001-37172.     

The Exponential Stability for a Class of Hybrid Systems

The exponential stability with a nonsmooth Lyapunov function for a class of hybrid systems is studied in this paper. First, a sufficient condition is derived that has to be satisfied by the feedback control for the hybrid systems. Then, for the special case where the Lyapunov function involved is a kind of nonsmooth function, the maximum of finitely many smooth functions (for short, max‐type function), the stability of a hybrid system is considered, and a convenient criterion to determine the stability of the system is established. Finally, a numerical method of determining the control input value is developed.     

一类混合动态系统的能控性和能观性研究

针对一类混合动态系统———周期型线性切换系统, 给出系统能控性、能观性的充分必要条件, 并通过例子加以验证.     

一类随机混杂系统的鲁棒方差控制

对一类结构参数不完全已知的Markov跳变参数系统, 研究使得闭环系统的稳态状态方差小于某个给定的上界, 同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题. 运用线性矩阵不等式(Linear matrix inequality, LMI)方法, 对系统进行了方差分析, 给出并证明了控制器存在的条件, 进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示. 通过建立一个具有LMI约束的凸优化问题, 给出了最小方差鲁棒控制器的设计方法. 最后仿真结果表明了该方法的有效性.     

一类混合动态系统的能控性和能观性研究

针对一类混合动态系统--周期型线性切换系统,给出系统能控性、能观性的充分必要条件,并通过例子加以验证.     

一类混杂系统的建模与控制器设计

研究一类离散事件系统和连接时间系统相混合的混杂系统建模与控制器设计问题。首先用不同的模型方法建立混杂系统的层次模型，分析连续时间系统状态空间的离散化和系统的可控性；在此基础上利用ＤＥＳ监控理论设计控制器，以规范系统的时域和逻辑行为。最后的示例表明了层次模型与控制算法的有效性。     

一类混杂系统的广义Petri网模型

提出一种含有变形连续时不变系统状态方程的广义Petri网,并用它为一类混杂系统建模:宏观为Petri网;微观为变形的线性时不变状态方程.同时研究了所提出的混合状态的演变规则、运行轨迹和状态方程.     

A Limit Law for Outputs in Random Recursive Circuits

We study the structure of uniform random binary recursive circuits. We show that a suitably normalized version of the number of outputs converges in distribution to a normal random variate. We also discuss the connection of the number of outputs to a non-classical urn model, and our investigation provides a first solved instance of this new class of urns. Received September 6, 2000; revised October 5, 2000.     

基于数据驱动的一类复杂系统动态特性分析

针对一类复杂的无法对其机理建模的离散时间系统,根据采集的两年工艺参数数据,结合复杂工艺特点,提出了基于数据驱动的系统动态特性建模方法,构建了时间序列受控回归滑动平均(CARMA)胞映射模型。在模型结构确定的基础上,采用改进的量子行为粒子群优化(IQPSO)算法对系统参数进行辨识。算法通过设计新的粒子更新式增加了粒子的多样性,避免了算法的早熟收敛;算法通过在后期将搜索到的最优值传递给神经元作为初始权值,利用神经元增强算法的局部搜索能力,实现了算法探索与开发的平衡,达到对模型参数进行快速精确辨识的目的。在转化为状态空间模型基础上,根据胞映射理论对系统进行了稳定性分析,通过对胞映射作图快速获得平衡胞,利用动态优化原理,找到所有的周期胞和吸引域,达到对系统稳定性分析的目的。利用现场工艺数据进行仿真,结果证明了所提方法的有效性。     

A Converse Lyapunov Theorem for a Class of Dynamical Systems which Undergo Switching

The authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields. They allow switching between members of the family of vector fields to be completely random. The focus of this paper is to prove a converse Lyapunov theorem for this class of systems.     

一类混杂系统建模和优化控制的研究

为解决混杂系统优化控制的计算复杂性问题,针对结合逻辑规则的工业过程混杂模型,采用结合约束程序的混合整数非线性规划算法,求解这种混杂模型的优化控制。计算实例表明,通过混杂建模方法,可以充分利用工业对象的机理模型以及操作工经验或专家经验,建立系统的更精确模型;结合约束程序混合整数非线性规划算法可以较迅速地求解混杂模型优化控制问题,从而使该方法可以用于工业过程实时控制中。     

利用临界点聚类的平面向量场极限环的检出及可视化

检出和可视化极限环已经成为向量场拓扑分析中日益重要的研究课题．提出了一个基于临界点聚类的检出算法,将向量场的全部临界点以几何距离为相似性判据聚类成一棵二叉树,通过只检查临界点指数和为＋1的少数树结点,以及在算法中增加检测和剔除中心型闭轨的部分,获得了比Wischgoll算法更好的结果．