Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.     

Fuzzy control of thyristor-controlled series compensator in power system transients

Power system transient stability is one of the most challenging technical areas in electric power industry. Thyristor-controlled series compensation (TCSC) is expected to improve transient stability and damp power oscillations. TCSC control in power system transients is a nonlinear control problem. This paper presents a T–S-model-based fuzzy control scheme and a systematic design method for the TCSC fuzzy controller. The nonlinear power system containing TCSC is modelled as a fuzzy “blending” of a set of locally linearized models. A linear optimal control is designed for each local linear model. Different control requirements at different stages during power system transients can be considered in deriving the linear control rules. The resulting fuzzy controller is then a fuzzy “blending” of these linear controllers. Quadratic stability of the overall nonlinear controlled system can be checked and ensured using H^∞ control theory. Digital simulation with NETOMAC software has verified that the fuzzy control scheme can improve power system transient stability and damp power swings very quickly.     

STABILITY OF LOTKA-VOLTERRA COOPERATION SYSTEM WITH SINGLE FEEDBACK CONTROL

In this paper,a Lotka-Volterra cooperation system with single feedback control is proposed and studied.We investigate the local stability and the global stability of the system.Our study shows that with suitable restriction on the coefficients of the feedback control variable,the system can still remain globally stable or become extinct,which shows that the feedback control variable plays a very important role in the dynamics behaviors of the system.     

Lyapunov stability for impulsive control affine systems

This article studies several notions of Lyapunov stability for impulsive control affine systems in the setting of nonautonomous dynamical systems. It presents some relations between the stability of an impulsive control affine system and the stability of its adjacent control system. Stability of compact sets and their components are specially investigated. Lyapunov functionals are employed to characterize each type of stability of closed sets.     

Decentralized event-based control: Stability analysis and experimental evaluation

Event-based control aims at reducing the amount of information which is communicated between sensors, actuators and controllers in a networked control system. The feedback link is only closed at times at which an event indicates the need for an information update to retain a desired performance. Between consecutive event times the control loop acts as a continuous system, whereas at the event times it performs a state jump. Thus, the event-based control loop belongs to the class of hybrid dynamical systems. In this paper a new method for decentralized event-based control is proposed. Two methods are presented for the stability analysis of the decentralized event-based state feedback control of physically interconnected systems. The comparison principle leads to a stability criterion that provides an upper bound for the coupling strength for which the stability of the uncoupled event-based control loops implies ultimate boundedness of the interconnected event-based system. It is shown that ultimate boundedness of the event-based state-feedback loop is implied by the asymptotic stability of the continuous state-feedback system. Furthermore, it is explained how the number of events can be reduced by estimating the interconnection signals between the subsystems and two different estimation methods are proposed. The derived methods are demonstrated for a thermofluid process by simulation and experiments.     

网络化非周期采样控制系统的主动时间滞后控制:随机脉冲切换系统方法

研究了一类带有随机丢包的非周期采样网络化控制系统的镇定问题.不同于传统观点往往将时滞看作系统稳定性的消极因素,考虑时间滞后对系统稳定性的积极影响,并提出一个新颖的主动时间滞后控制方法来镇定该系统.为了分析时间滞后控制的积极作用并获得较低保守性的结论,首先把带随机丢包的非周期采样系统建模为带固定切换率的随机脉冲切换系统,...     

基于营养动力学的广义捕食者—食饵—生物残体系统的变结构控制

利用变结构控制理论研究了一个基于营养动力学的广义捕食者一食饵一生物残体系统的变结构控制问题.首先,给出了基于营养动力学的广义捕食者一食饵一生物残体系统的正则平衡点的稳定性条件;同时利用广义系统理论研究了基于营养动力学的广义捕食者一食饵一生物残体系统的正则化问题,得到了其可正则化条件;最后,对其实施控制,并利用变结构控制理论,实现了基于营养动力学的广义捕食者一食饵一生物残体系统的稳定化,保持了系统的持续生存.     

具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.     

Model-reference control of chaotic systems

In this paper, the problem of controlling chaotic systems is studied. A control law is introduced for a chaotic system to follow a desired reference system. The control strategy is developed within the general framework of the nonlinear model-reference control systems. Lyapunov stability is used to ensure the global stability of the error dynamics represents the difference between the desired and chaotic systems.     

未知死区输入高阶关联大系统的全局稳定分散控制

针对一类具有未知非线性死区输入的高阶关联大系统,设计了一种新的分散控制方法。该方法基于模糊滑模控制原理,确保所设计的分散控制器能使各个子系统仅根据自己的信息就能确定相应的控制量,真正实现分散控制。Lyapunov稳定理论分析证明了闭环系统的全局稳定性,跟踪误差收敛到零,并且给出了全局一致终结有界的相关界。仿真结果表明了所设计方法的有效性。     

控制系统的广义传递函数和运动稳定性判定方法的改进

本文给出了控制系统的广义传递函数和它的连续性的定义.利用广义传递函数作为工具,建立了一组判定运动稳定性的定理,从而把对一个控制动力学系统特性的了解建立在这个系统的被观测过程之中,简化了运动稳定性问题的判定方法.     

Periodic solution of a chemostat model with variable yield and impulsive state feedback control

In this paper, a chemostat model with variable yield and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.     

Stability analysis for networked control systems with sampling,transmission protocols and input delays

In this paper, the stability problem is investigated for networked control systems. Input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols are considered. A unified framework based on the hybrid systems with memory is proposed to model the whole networked control system. Hybrid systems with memory are used to model hybrid systems affected by delays and permit multiple jumps at a jumping instant. The stability analysis depends on the Lyapunov–Krasovskii functional approaches for hybrid systems with memory and the proposed stability theorem does not need strict decrease of the Lyapunov–Krasovskii functional during jumps. Based on the developed stability theorems, stability conditions for networked control systems are established. An explicit formula is given to compute the maximal allowable transmission interval. In the special case that the networked control system contains linear dynamics, an explicit Lyapunov functional is constructed and stability conditions in terms of linear matrix inequalities (LMI) are proposed. Finally, an example of a chemical batch reactor is given to illustrate the effectiveness of the proposed results.     

Delay-dividing approach for absolute stability of Lurie control system with mixed delays

This paper studies the absolute stability problem for a Lurie control system with nonlinearity located in an infinite sector and finite one. By dividing the discrete delay interval into multiple segments and choosing proper Lyapunov functionals, some delay dependent stability criteria are derived to guarantee the stability of the Lurie control system. It is established theoretically that the criteria are less conservative than the previous ones. Numerical examples demonstrate the validity of the proposed criteria.     

Decentralized Model Predictive Control for Networks of Linear Systems with Coupling Delay

This paper presents a new dissipativity-based decentralized model predictive control strategy for networks of linear systems suffering from a bounded coupling delay. The notion of delay-robust dissipativity is introduced and applied to the development of interconnection stability conditions. The dissipation inequality of system trajectories is converted into a prognostic stability constraint for the optimization problem of model predictive control to guarantee the system stability. A recursive feasibility condition is derived for the constrained optimization problem, which is formulated in a semi-definite program. A numerical example of an interconnected three-unit process system is provided for illustrations.     

Stabilization of boundary control systems

Feedback stabilization of a linear hyperbolic boundary value control system is implemented. Consistent with finite dimensional control theory, the property of controllability of the control system yields the asymptotic stability of the feedback system.     

基于模糊双线性模型的非线性系统的跟踪控制

研究一种基于T-S模糊双线性系统的跟踪控制器设计及稳定性分析.使用分布并行补偿法(PDC)设计了模糊控制器,得到模糊双线性系统跟踪控制渐近稳定的充分条件,仿真结果验证了该方法改进了闭环系统的性能.     

函数空间多体挠性结构系统动力学、稳定性与控制的研究

利用现代数学方法,在函数空间中研究了一类无穷维系统动力学、稳定性与控制问题.首先提出并建立了具有阻尼、陀螺部件和约束阻尼的多拓扑结构多挠体分布参数系统动力学控制模型;其次给出并论证了多体挠性结构特征、系统分析结果--可控可观性充要条件、稳定性理论和系统的渐近性质.研究的结果扩充和发展了本领域关于多挠体系统动力学与控制的理论成果,具有重要的工程意义.     

碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。     

Chaos and optimal control of cancer self-remission and tumor system steady states

This paper is devoted to study the problem of optimal control of cancer self-remission and tumor unstable steady-states. The stability analysis of the biologically feasible equilibrium states is presented using a local stability approach. The system appears exhibit a chaotic behavior for some ranges of the system parameters. The necessary optimal control inputs for the asymptotic stability of the positive equilibrium states and minimizes the require performance measure are obtained as nonlinear function of the system densities. Analysis and extensive numerical examples of the uncontrolled and controlled systems were carried out for various parameters values and different initial densities.