Exponential stability of output‐based event‐triggered control for switched singular systems

This paper presents the exponential stability of output‐based event‐triggered control for switched singular systems. An event‐triggered mechanism is introduced based on measure output, by employing the Lyapunov functional method and average dwell time approach, some sufficient conditions for exponential stability of the switched singular closed‐loop systems are derived. Furthermore, dynamic output feedback controller parameters are obtained. Lastly, a numerical example is given to illustrate the validity of the proposed solutions.     

Dynamic Output Feedback Control for Systems Subject to Actuator Saturation via Event‐Triggered Scheme

In this paper, the event‐triggered dynamic output feedback control problem for linear systems with actuator saturation is investigated. Event‐triggered scheme only transmits the corresponding signal when the event‐triggered condition is violated. Due to its advantage of saving communication resources, it is utilized to design the dynamic output feedback controller. A criterion is established to guarantee the stability of the closed‐loop system by introducing an exponential term for the Lyapunov function, which corresponds to the exponential term in the event‐triggered condition. The explicit design of the coefficient matrices of the controller is presented. Furthermore, a lower bound of the inter‐event time is calculated to avoid Zeno behavior. An optimization algorithm is then formulated to maximize the estimation of the domain of attraction. Finally, a numerical example is given to illustrate the effectiveness of our methods and to show the trade‐off between the size of the domain of attraction and communication resources saving.     

Robust exponential stabilization for network-based switched control systems

It has become a common practice to employ networks in control systems for connecting controllers and sensors/actuators on controlled plants and processes. A network-based switched control system, as a special case of networked control systems, is studied. Such a system is represented with network-induced delays and packet dropout as a switched delay system. Sufficient conditions for robust exponential stability are derived for a class of switching signals with average dwell time. A stabilization design for continuous-time, linear switched plant with nonlinear perturbation under a given communication network via a hybrid state feedback controller is proposed. A hybrid controller design is network-dependent and given in terms of linear matrix inequalities.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

Fuzzy scheduling strategy for generalized switched server systems and its robustness over system heterogeneity

Generalized switched server system, a discretely controlled continuous‐time system, in which N tanks are used to represent N parallel entities, respectively, can be employed to address a class of load‐balancing problems. A tank‐pair model is a system that consists of two tanks and a single input single output controller, which regulates the inflows of the two tanks to acquire the two uniform levels under the specified inflow constraints. According to a quantized observation of the N tank levels, some discrete events are generated, and based on certain event feedback strategy, switching the location of the tank‐pair can control all the N tanks in a time‐sharing manner to acquire the N levels uniformity. Different from some existing scheduling strategies, this study proposes a fuzzy scheduling strategy (FSS) for such generalized switched server systems. Special measures are taken to reduce the N‐inputs two‐outputs fuzzy inference to a two‐inputs one‐output one, which greatly facilitates fuzzy scheduler design. Simulation results show that the proposed FSS strategy outperforms over the three existing scheduling strategies as a whole, and they also show that the proposed FSS strategy demonstrates high robustness over system heterogeneity. © 2009 Wiley Periodicals, Inc.     

网络控制系统的模型依赖平均驻留时间调度与控制

针对具有随机短时延的资源受限网络控制系统,提出了一种新的模型依赖平均驻留时间的调度策略与反馈控制联合设计方法.该调度策略由模型依赖平均驻留时间和动态试一次就丢弃(try-once-discard,TOD)调度策略共同决定,将系统建模成带有参数不确定性的离散切换系统,基于多Lyapunov函数方法及线性矩阵不等式(linear matrix inequality,LMI)技术,给出了使闭环系统指数稳定的控制器设计和TOD调度策略下的各模态平均驻留时间条件.该联合设计方法降低了保守性,在一定程度上减少了系统模态之间的切换频率.最后通过仿真验证所提方法的有效性.     

Hybrid Scheduling and Quantized Output Feedback Control for Networked Control Systems

A novel co-design scheme of hybrid scheduling strategy, adaptive logarithmic quantizer and dynamic robust H-infinity output feedback controller for a class of networked control system (NCS)with communication constraints and time delay is proposed. The hybrid scheduling scheme integrates dead zone scheduling and Try Once Discard (TOD) scheduling so as to get the stronger adaptability and flexibility than the single scheduling. In this scheme, dead zone scheduling which updates the threshold according to mode-dependent control strategy is used for single node of NCS to reduce the network bandwidth utilization while TOD scheduling is used for the whole node of NCS in order to meet the requirements of communication constraints and guarantee the overall system performance.We develop the integrated design for the hybrid scheduling strategy, adaptive quantizer and dynamic robust output feedback controller to maintain asymptotic stability of the closed-loop NCS by using the multiple-Lyapunov function and switched system theory. The proposed method can improve the the quality of service (QoS) meanwhile ensure the quality of control (QoC) of overall systems, which make a better trade-off between network utilization and control performance. An simulation example demonstrates the efficiency of the proposed method.     

具有执行器饱和的切换2-D系统事件触发控制

针对具有执行器饱和的切换2-D连续离散系统,提出了一种基于多Lyapunov函数法的事件触发控制方案。为了减少通信资源浪费和执行器的损耗,提出了一种事件触发机制。该触发机制考虑了执行器饱和特性,只有当执行器未饱和,且满足事件触发条件时,控制器才会更新。利用凸组合技术和多Lyapunov函数法,提出了一种状态依赖的切换信号与状态反馈控制器的设计方法,并对闭环系统的指数稳定性进行了分析,利用线性矩阵不等式技术导出了控制器增益矩阵存在的充分条件。利用Darboux方程的仿真算例验证了所提出的事件触发控制方案的有效性,仿真结果表明了在所设计的控制方案下,闭环系统的状态是指数收敛的,同时还能减少通信资源的浪费。     

Stabilization of linear discrete‐time networked control systems via protocol and controller co‐design

This paper investigates the stabilization problem for networked control systems (NCSs) with communication constraint and packet loss. The communication constraint considered is that only one network node is allowed to access a shared communication channel during one time‐slot, and a feedback control is performed with only partially available measurements and control inputs. By taking random packet loss into consideration, a stochastic switched system model is presented to describe the NCS. A sufficient condition is derived for the NCS to be mean‐square exponentially stable, and it is shown that the system performance specified by the exponential decay rate critically depends on the network accessing rates (NARs) of the network nodes and the packet loss probability. The state feedback controller and scheduling protocol, which allocates the NARs, are co‐designed such that the NCS achieves a minimal decay rate. Finally, an illustrative example is given to show the effectiveness of the proposed design approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Event‐triggered control for discrete‐time linear systems subject to bounded disturbance

This paper considers event‐triggering controller design for directly observable discrete‐time linear systems subject to bounded disturbances. The main control objective is diminishing the influence aroused by the disturbances despite a reduction of the communication. Criteria are given to design feedback controllers in order to guarantee that systems are uniformly ultimately bounded in an ellipsoidal‐positive invariant set, which is used as an estimate of control performance for disturbance rejection. An optimization for minimizing the ellipsoidal‐positive invariant set is achieved by synthesizing the feedback control gain and the given event‐triggering conditions in LMIs. The effectiveness and applicability of the controller are illustrated by simulations and experimental implementations. Copyright © 2015 John Wiley & Sons, Ltd.     

Consensus of multi‐agent systems with time‐varying topology: An event‐based dynamic feedback scheme

The event‐based control strategy is an effective methodology for reducing the controller update and communication over the network. In this paper, the event‐based consensus of multi‐agent systems with linear dynamics and time‐varying topology is studied. For each agent, a state‐dependent threshold with an exponentially decaying bound is presented to determine the event times, and a new event‐based dynamic feedback scheme is proposed. It is shown that the controller update for each agent is only dependent on its own event times, which reduces significantly the controller update or computation for each agent. Moreover, based on the event‐based dynamic feedback scheme and the event triggering function presented in this paper, the continuous communication among neighboring agents is avoided, and the Zeno‐behavior of the closed‐loop systems is excluded. A numerical example is given to illustrate the effectiveness of theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed event‐triggered containment control for dynamical multiagent networks

This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.     

一类非线性系统的控制器和观测器设计

研究一类非线性系统的全状态反馈控制问题、观测器设计问题及输出反馈控制设计问题.首先设计出非线性全状态反馈控制器,获得了系统指数镇定的充分条件.然后提出了非线性观测器,并证明了该观测器是指数稳定观测器.进一步,在控制器和观测器问题的充分条件满足的假设下,证明了提出的带估计状态的反馈控制能达到指数镇定.最后,仿真实例验证了所得结果的有效性.     

大型空间结构的动态输出变结构控制*

本文研究大型柔性空间结构作单轴大角度操纵时的状态估计及变结构控制方法。建立指数律的状态观测器实现了以较少传感器估计系统弹性振动模态的目的。利用状态观测器状态及系统输出变量反馈方法设计了大型空间结构的动态输出变结构控制律,针对一个实际模型仿真计算,得到了满意的结果。     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

IS A MIXED DESIGN OF OBSERVER‐CONTROLLERS FOR TIME‐DELAY SYSTEMS INTERESTING?

This paper deals with H∞ observer‐based feedback control for linear time‐delay systems, in the framework of delay independent stability. We will propose a new LMI solution to observer‐controller design that ensures a disturbance attenuation level for the controlled output as well as for the state estimation error, which is an open problem. This will be compared with a well‐known solution and with a usual strategy in control which consists in designing the observer and the controller separately. Our aim is to try to bring a positive answer to the following question: is there an interest to solve the problem in a single (unique) formulation or should we design separately the observer and the controller? An application to a wind tunnel model is provided to emphasize the interest of the given results, particularly in comparison with existing results on H∞ observer‐based control.     

State and mode feedback control strategy for discrete‐time Markovian jump linear systems with time‐varying controllable mode transition probability matrix

In this article, the state and mode feedback control strategy is investigated for the discrete‐time Markovian jump linear system (MJLS) with time‐varying controllable mode transition probability matrix (MTPM). This strategy, consisting of a state feedback controller and a mode feedback controller, is proposed to ensure MJLS's stability and meanwhile improve system performance. First, a mode‐dependent state feedback controller is designed to stabilize the MJLS based on the time‐invariant part of the MTPM such that it can still keep valid even if the MTPM is adjusted by the mode feedback control. Second, a generalized quadratic stabilization cost is put forward for evaluating MJLS's performance, which contains system state, state feedback controller, and mode feedback controller. To reduce the stabilization cost, a mode feedback controller is introduced to adjust each mode's occurrence probability by changing the time‐varying controllable part of MTPM. The calculation of such mode feedback controller is given based on a value‐iteration algorithm with its convergence proof. Compared with traditional state feedback control strategy, this state and mode feedback control strategy offers a new perspective for the control problem of general nonhomogeneous MJLSs. Numerical examples are provided to illustrate the validity of the proposed strategy.     

有时延和数据包丢失的网络控制系统控制器设计

在同时考虑网络诱导时延和数据包丢失的基础上,研究了动态输出反馈网络控制系统指数稳定性和控制器设计问题.基于一定的数据包丢失率和不大于一个采样周期的时延,将系统建模为结构事件率约束的异步动态系统.利用线性矩阵不等式方法推导出网络接通率约束的系统指数稳定的充要条件,给出了确保系统稳定的控制器设计方法.Matlab数值算例说明了研究结果是有效可行的.     

On feedback controllers

The two main results are the necessary and sufficient conditions for the existence of a causal and a strongly causal feedback controller which realizes a given behaviour on a given system. The proofs are constructive. If the given system is a discrete event system or an ordinary discrete event system, then a controller could also be a discrete event system or an ordinary discrete event system, respectively. The results are given using an algebraic approach to the modelling of general time systems introduced by the author.     

Novel results on nonfragile sampled‐data exponential synchronization for delayed complex dynamical networks

This article investigates exponential synchronization for complex dynamical networks (CDNs) with nonfragile sampled‐data feedback control. An important yet challenging problem that contains the time delays of the controller, the uncertainties occurrence and randomness of controller gain fluctuation due to the packet loss, and time delays during data transmission is to be solved. A novel Lyapunov‐Krasovskii functional (LKF) that allows for more free matrix terms and slacks certain one of the terms to nonpositive definite is first constructed based upon special refined block matrices. By employing the novel LKF and functional analysis theory, the nonfragile sampled‐data feedback controller is developed to guarantee the exponential synchronization of CDNs and make a more optimal bound estimation of the sampled period. Finally, compared simulation examples are performed as significant to demonstrate the effective performance and the superiority of the proposed methods.