Stability of oscillations in low-order nonlinear systems

Loeb's criterion and the incremental-input describing function (IDF) stability technique are compared for general nonlinear second- and third-order systems. Situations in which the two stability techniques disagree are determined and studied in detail. The IDF stability technique is related directly to the variational approach for a general system, and Loeb's criterion is related to that for second-order systems. The IDF stability technique is shown to involve the approximation of time averaging in addition to the inherent describing function (DF) approximation. Discrepancies between the two are found to coincide with relatively poor DF approximations. One technique cannot be considered better than the other in applications-they should be used together for proper interpretation.     

多机器人主—从行星式编队控制

研究了二阶积分器描述的多机器人主—从行星式编队控制问题,提出了将多机器人编队分解为每个机器人对各自具有时变速度的虚拟机器人的跟踪控制,使得每个机器人相对于虚拟机器人的位置与速度跟踪误差收敛为零且彼此不相碰撞,此时编队系统收敛到理想队形.在统一的算法框架下,分别实现了跟随者以领航者为中心的公转运动编队(revolution formation,RF)模式和跟随者与领航者保持期望距离、期望速度的编队(desiredformation,DF)模式.公转运动编队(RF)模式适用于异构多机器人系统的环境探索任务;保持期望距离、期望速度的编队(DF)模式适用于自主水下机器人(AUV)、无人机(UAV)等合作与协调任务.应用李亚普诺夫稳定性理论对控制算法的稳定性进行了分析,并通过计算机仿真验证了该方法的有效性.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

具输入饱和因子的广义系统的镇定

广义系统的镇定问题是广义系统理论的基本问题之一.为了研究具输入饱和因子 的广义系统的镇定,首先利用代数方法,借助大系统分解原理,对具输入饱和因子的广义系统 进行综合,给出闭环系统渐近稳定的判别条件.其次,给出了闭环系统E一渐近稳定的概念,利 用广义Lyapunov函数方法,研究具输入饱和因子的广义系统,提出了合适的反馈控制,得到 了具输入饱和因子的广义系统E一渐近稳定的判别定理.     

Stability guaranteed auto-tuning algorithm of a time-delay controller using a modified Nussbaum function

Time-delay control (TDC) has been widely used to control various systems thanks to its simplicity and robustness. The control distribution matrix of TDC is assumed to be constant and tuned heuristically. However, the constant TDC control gain could degrade the system control performance and even cause the closed-loop system to become unstable when the system parameters are substantially changing, resulting in the violation of the stability criterion of TDC. We propose an algorithm for automatic tuning of the TDC gain in order to guarantee stability by using a modified Nussbaum function. Thus, the closed-loop system controlled by TDC with the modified Nussbaum function is proven to be semi-globally uniformly ultimately bounded. The auto-tuned gain satisfies the stability criterion of TDC and the proposed method can widen the range of implementable dynamic systems. Simulations are conducted to verify the simplicity, robustness, and guaranteed stability by auto-tuning of the proposed method.     

DF控制推理模型的研究

针对控制系统中对象的模糊性和动态性,基于动态模糊集(Dynamic Fuzzy Sets)及动态模糊逻辑(Dynamic FuzzyLogic)系统理论,给出DF控制推理模型的相关概念,如DF向量、DF语言变量、DF语言规则和DF蕴涵关系等,并在此基础上探讨基于DF语言规则的DF推理方法,最后通过实例说明这些概念和方法的应用。     

On Maximum Stability Margin Design of Nonlinear Uncertain Systems: Fuzzy Control Approach

This paper studies the maximum stability margin design for nonlinear uncertain systems using fuzzy control. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear uncertain system. Next, based on the fuzzy model, the maximum stability margin for a nonlinear uncertain system is studied to achieve as much tolerance of plant uncertainties as possible using a fuzzy control method. In the proposed fuzzy control method, the maximum stability margin design problem is parameterized in terms of a corresponding generalized eigenvalue problem (GEVP). For the case where state variables are unavailable, a fuzzy observer‐based control scheme is also proposed to deal with the maximum stability margin for nonlinear uncertain systems. Using a suboptimal approach, we characterize the maximum stability margin via fuzzy observer‐based control in terms of a linear matrix inequality problem (LMIP). The GEVP and LMIP can be solved very efficiently via convex optimization techniques. Simulation examples are given to illustrate the design procedure of the proposed method.     

改进的解码转发多跳中继系统及最优功率分配

多跳信道的中断性能较差,且节点接收设备上的多跳分集信道较为复杂。为此,基于解码转发多跳信道和多跳分集信道,提出一种改进的解码转发多跳中继系统,解决上述2种信道性能和复杂度的矛盾。推导中断概率的计算公式,以最小化系统中断概率为目标,利用拉格朗日乘子优化各节点的功率分配。仿真结果表明,改进系统能获得比传统多跳中继系统更低的中断概率,最优功率分配方案下系统的中断性能优于均匀功率分配方案,并且性能优势随跳数增加更为明显。     

Characteristic model based adaptive controller design and analysis for a class of SISO systems一类SISO系统基于特征模型的极点配置自适应控制设计与分析

The design of an adaptive controller and stability analysis of the corresponding closed loop system are discussed for a class of SISO systems based on the characteristic model method. The obtained characteristic model is a second-order slow time-varying linear system with a compress mapping function for the system modeling error. The pole placement method is used to design the controller, and sufficient conditions for the stability of the closed loop system are obtained based on the robust control theory of slow time-varying systems with perturbations. The effectiveness of the proposed method is illustrated by two numerical examples.     

Stabilization of singularly perturbed fuzzy systems

This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with H/sup /spl infin// control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all /spl epsiv//spl isin/(0,/spl epsiv//sup */) and the upper bound /spl epsiv//sup */ can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with H/sup /spl infin// control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval /spl epsiv//spl isin/[/spl epsiv/_,/spl epsiv/~]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes.     

短时延多包传输网络控制系统的稳定性分析

提出一种短时延多包传输网络控制系统的建模方法.把多包传输网络控制系统建模为具有一定切换规则的线性切换系统模型.利用切换系统理论和鲁棒稳定性理论，得到多包传输网络控制系统的渐近稳定性判据,并首次提出周期动态输出反馈镇定控制器的设计方法.最后通过数值算例证明文中结论的可行性和有效性.     

关于一类脉冲切换系统的鲁棒H∞控制

研究一类具有扰动的脉冲切换线性系统的鲁棒H控制问题.分别从系统的鲁棒稳定性及其鲁棒性能两方面进行分析.首先利用Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒渐近稳定的几个重要的充分条件,通过它很容易判断系统是否鲁棒稳定.进一步运用线性矩阵不等式(LMI)法对系统鲁棒性能进行分析,得到了一般系统的状态反馈矩阵和脉冲控制矩阵,并在此基础上得出了一个鲁棒H控制律.最后提出了一套基于MAT-LAB软件的鲁棒控制器的设计方法,并通过一个数值例子很好地验证了文中主要结论的有效性.     

Limit-cycle analysis of dynamic fuzzy control systems

The main purpose of this study is to predict limit cycles of a dynamic fuzzy control system by combining a stability equation, describing function and parameter plane. The stability of a linearized dynamic fuzzy control system is then analyzed using stability equations and the parameter plane method, with the assistance of a describing function method. This procedure identifies the amplitude and frequency of limit cycles that are clearly formed by the dynamic fuzzy controller in the parameter plane. Moreover, the suppression of the limit cycle by adjusting control parameters is proposed. Continuous and sampled-data systems are addressed, and the proposed approach can easily be extended to a fuzzy control system with multiple nonlinearities. Simulations are performed to demonstrate the effectiveness of the proposed scheme.     

关于Lurie型控制系统的鲁棒绝对稳定性

用Lyapunov函数法研究了区间Lurie型间接控制系统与直接控制系统的鲁棒绝对 稳定性,给出了系统鲁棒绝对稳定的充分条件.一个应用实例说明该方法的优越性.     

具有端点质量的一维波动方程半离散格式的一致指数稳定性

无穷维系统主要由偏微分方程描述, 可是大部分用偏微分方程描述的控制系统, 无论是单纯的数值实验还是需要应用到实际的问题中去, 都需要对方程进行有限数值离散. 本文考虑了端点带有质量的波动方程在边界反馈控制下半离散格式的一致指数稳定性. 首先, 原闭环系统通过降阶法变成低阶的等价系统, 通过一种间接Lyapunov函数方法证明了降阶等价的连续系统是一致指数稳定的. 其次, 对等价系统空间变量离散得到半离散的差分格式.平行于连续系统, 间接Lyapunov函数方法证明了半离散系统的一致指数稳定性. 数值实验证明了基于降阶法的一致指数稳定性和经典半离散格式的非一致指数稳定性.     

Observer-based synergetic adaptive neural network control for a class of discrete-time nonlinear systems with dead-zone

In this paper, the observer-based synergetic adaptive neural network control method is designed for a class of discrete-time systems with dead-zone. A macro-variable is introduced by a synergetic approach to control theory and neural networks are utilised to estimate unmeasured states and unknown functions in the system. Furthermore, by employing an adaptive design procedure and Lyapunov stability theory, the closed-loop system stability is guaranteed, and the desired system performance is achieved simultaneously. Finally, some simulation results are given to prove the validity of the developed control method.     

一类滞后型控制系统的鲁棒绝对稳定性

利用Lyapunov泛函以及区间矩阵的分析方法,讨论了一类滞后型控制系统的鲁棒绝 对稳定性问题,给出了系统鲁棒绝对稳定的一些实用的代数判据．     

一类不确定分数阶混沌系统同步的自适应滑模控制方法

针对一类系统不确定及受外界干扰的分数阶混沌系统,本文首先将分数阶微积分应用到滑模控制中,构造了一个具有分数阶积分项的滑模面.针对系统不确定及外界干扰项,基于分数阶Lyapunov稳定性理论与自适应控制方法,设计了一种滑模控制器以及分数阶次的参数自适应律,实现了两不确定分数阶混沌系统的同步控制,并辨识出相应误差系统中不确定项及外界干扰项的边界.在分数阶系统稳定性分析中使用的分数阶Lyapunov稳定性理论及相关函数都可以很好地运用到其它分数阶系统同步控制方法中.最后数值仿真验证了所提控制方法的可行性与有效性.     

Robust sliding mode control of uncertain nonlinear systems

A dynamic sliding mode controller design method is proposed for multiple input-output systems with additive uncertainties. A previous result on the stability of triangular systems is generalised to the case of uniform ultimate boundedness of controlled triangular systems. This is used to prove the stability of the overall closed-loop system. The uncertain system with appropriately chosen sliding mode control is shown to be ultimately bounded if the zero dynamics of the nominal system are uniformly asymptotically (exponentially) stable. The design method is demonstrated with two examples.     

一类具有Markov跳跃参数的不确定混合线性时滞系统鲁棒稳定性研究

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒稳定性问题．分别给出了非匹配条件下不确定部分范数上界已知时使混合线性系统以概率1渐近稳定的充分条件,和匹配条件下不确定部分范数上界未知时同样可以实现混合系统以概率1渐近稳定的鲁棒自适应控制设计方案．文章研究结果表明,此控制方案对混合线性时滞系统的不确定部分是有效的．