Event‐triggered predictive control for networked control systems with network‐induced delays and packet dropouts

This paper presents an event‐triggered predictive control approach to stabilize a networked control system subject to network‐induced delays and packet dropouts, for which the states are not measurable. An observer‐based event generator is first designed according to the deviation between the state estimation at the current time and the one at the last trigger time. A predictive control scheme with a selector is then proposed to compensate the effect of network‐induced delays and packet dropouts. Sufficient conditions for stabilization of the networked control system are derived by solving linear matrix inequalities and the corresponding gains of the controller and the observer are obtained. It is shown that the event‐triggered implementation is able to realize reduction in communication and save bandwidth resources of feedback channel networks. A simulation example of an inverted pendulum model illustrates the efficacy of the proposed scheme.     

双率采样系统的基于观测器的网络化H∞控制

研究一类带有网络传输时滞和丢包的双率采样系统的网络化H∞控制问题. 假设对象状态变量被分成两个分向量, 同一分向量的状态变量由同一类传感器以相同周期采样, 且两类传感器的采样频率不同. 采样后的分向量分别通过非理想网络传输到控制器端. 考虑到双率采样、网络传输时滞和丢包现象, 引入同步观测器来估计对象状态并设计基于估计状态的控制器来镇定双率采样系统. 基于这个思路, 将双率采样的网络化控制系统建模为带有两个时变时滞的连续系统. 利用Lyapunov-Krasovskii泛函方法, 以矩阵不等式形式给出该系统的稳定性判据和控制器设计方法. 最后, 通过数值例子验证所提方法的有效性.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

具有长时延和丢包的网络控制系统稳定性分析

针对同时出现长网络诱导时延和丢包的网络控制系统,研究了带不确定性的网络控制系统的稳定性问题。基于一定的数据包丢失率,系统被建模成带结构事件率约束的异步动态系统。利用李亚普诺夫方法和线性矩阵不等式相关知识,结合异步动态系统的稳定性理论,推出了使不确定网络控制系统指数稳定的充分条件,并给出了保证系统指数稳定的数据传输成功率满足范围;最后利用MATLAB仿真的数值例子验证了此方法的有效性和可行性。     

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses

In this paper, the stochastic optimal control of linear networked control system (NCS) with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived. The proposed stochastic optimal control method uses an adaptive estimator (AE) and ideas from Q-learning to solve the infinite horizon optimal regulation of unknown NCS with time-varying system matrices. Next, a stochastic suboptimal control scheme which uses AE and Q-learning is introduced for the regulation of unknown linear time-invariant NCS that is derived using certainty equivalence property. Update laws for online tuning the unknown parameters of the AE to obtain the Q-function are derived. Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control signals converge to optimal or suboptimal control inputs. Simulation results are included to show the effectiveness of the proposed schemes. The result is an optimal control scheme that operates forward-in-time manner for unknown linear systems in contrast with standard Riccati equation-based schemes which function backward-in-time.     

基于T-S 模糊模型的一类非线性网络控制系统故障检测

针对同时存在网络时延和数据包丢失的网络环境,研究了一类非线性网络控制系统的鲁棒故障检测问 题．基于不确定T-S 模糊模型描述的非线性网络控制系统模型,完成了网络环境下鲁棒故障检测观测器的设计,使 得残差信号对故障敏感而对外部扰动具有鲁棒性．构造Lyapunov-Krasovskii 函数,并引入一个积分不等式,给出了 使得观测器误差动态系统渐近稳定的充分条件．采用线性矩阵不等式技术将鲁棒故障检测问题转化为具有线性矩阵 不等式约束的凸优化问题求解．仿真算例验证了上述方法应用于此类系统的故障检测的有效性．     

Guaranteed cost control of distributed parameter networked control systems with time‐varying delay

Distributed parameter networked control systems mean distributed parameter systems are controlled through a network, where the control loops are closed. In this paper, the problem of guaranteed cost and state feedback controller design is investigated for a class of distributed parameter networked control systems. With the network factors, such as transmission delays, data packet dropouts considered, the distributed parameter networked control system is modeled as a linear closed‐loop system with time‐varying delay and uncertain parameters. By selecting an appropriate Lyapunov‐Krasovskii function and using linear matrix inequality (LMI) approach, the controller is designed to render the system stable and it can keep the cost function less than a certain upper value. In addition, numerical simulation is included to demonstrate the theoretical results.     

具有双通道数据包丢失的Delta算子系统故障检测

研究同时存在双通道数据包丢失和时变时延的Delta算子网络控制系统（NCSs）故障检测问题.假定数据包丢失发生在控制器到执行器、传感器至控制器的数据传输过程中，并且利用两个相互独立的伯努利随机变量描述是否发生丢包.将上述的NCSs建模为网络切换系统，提出任意切换律下故障检测滤波器的设计方法.利用线性矩阵不等式（LMIs）方法、Lyapunov-Krasovskii泛函和平均驻留时间等得出所考虑的网络切换系统具备指数均方稳定性的充分条件.证明了所用的网络切换系统满足H_∞性能，并推导出了滤波器参数的显式表达.数值仿真结果验证了所提方法的有效性.     

A periodic approach for input‐delay problems: Application to network controlled systems affected by polytopic uncertainties

This paper deals with robust stability and stabilization of linear discrete‐time systems subject to uncertainties and network constraints. In network control systems, the control loop is closed over a network, which induces additional dynamics to the original control loop such as delays, sampling, and quantization among many others. This paper focuses on networked induced delays due to unreliable network for which packet losses may occur. An equivalent periodic‐like representation of the resulting system is proposed. This allows first to revisit existing results in this framework and second to take model uncertainties into account by analyzing the closed‐loop model by means of a recent method based on robust control for discrete‐time time‐varying systems. Stability analysis and dynamic state‐feedback stabilization are characterized via new conditions, whose conservatism is extensively discussed. Effectiveness of the proposed methodology is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Efficient routing redundancy design over lossy networks

In this paper, a wireless networked control system is made robust with respect to packet losses by exploiting routing redundancy. Multiple copies of sensing and actuation data are sent via different routing paths, associated to possibly different delays. Similar to linear network coding, such data are recombined as a weighted linear combination. A MIMO output‐feedback architecture is considered. A methodology that takes into account both the network parameters and the plant dynamics is proposed to set up an optimization problem to design network weights to satisfy a robustness metric based on the notion of asymptotic mean‐square stability. Such metric induces either an objective or a constraint function that is nonlinear. For this reason, an efficient suboptimal design methodology is also proposed. Finally, the solutions are compared with the optimal choice from the communication designer point of view, which is based on the minimization of the quadratic error induced by the network on the actuation signal. The suboptimal methodology is shown, by means of a nontrivial example, to give results extremely close to the optimum with a strongly reduced computation time. It is also shown that the optimal choice from the communication design point of view, which neglects the plant dynamics, does not guarantee stochastic stability.     

基于网络的运动控制系统预测控制研究

针对一类基于网络的运动控制系统中存在的时延和丢包问题进行研究。对于网络运动控制系统存在数据时延和丢包的情况,建立网络运动控制系统模型。在此模型下,对预测函数控制算法进行分析,设计了预测函数控制产生器和数据延时预测补偿器,并研究相应的补偿策略。仿真分析表明算法的合理性和有效性。     

网络传输迟延与丢包的补偿及系统稳定性分析

针对网络传输在控制系统中引发的问题，提出在控制器节点采用针对迟延和丢包的补偿估计器．以提高控制系统的性能。当迟延小于一个采样周期且数据包传输率已定时，将包含该补偿估计器的网络控制系统（CEDPNCS），描述为具有两个事件的异步动态系统，并推导出保证系统稳定的时变双线性矩阵不等式．仿真结果表明．所提出的方法能有效提高控制系统的性能．     

Quantitative analysis and synthesis for networked control systems with non‐uniformly distributed packet dropouts and interval time‐varying sampling periods

This paper is concerned with quantitative analysis and synthesis for a networked control system under simultaneous consideration of non‐uniformly distributed packet dropouts, interval time‐varying sampling periods and network‐induced delays. A new packet dropout separation method is proposed to separate packet dropouts from the lump sum of network‐induced delays and packet dropouts. An interval time‐varying sampling period approach, which is more general than a switched sampling period approach, is presented to model the variation of the sampling period. Then a packet dropout decomposition‐based Lyapunov functional is constructed to drive some stability criteria. Based on these stability criteria, a state feedback controller is designed to asymptotically stabilize the networked system in the sense of mean‐square. Numerical examples are given to illustrate the effectiveness of the obtained results. Copyright © 2013 John Wiley & Sons, Ltd.     

A new approach to network‐based H∞ control for stochastic systems

This paper deals with the problem of network‐based H_∞ control for a class of uncertain stochastic systems with both network‐induced delays and packet dropouts. The networked control system under consideration is represented by a stochastic model, which consists of two successive delay components in the state. The uncertainties are assumed to be time varying and norm bounded. Sufficient conditions for the existence of H_∞ controller are proposed to ensure exponentially stable in mean square of the closed‐loop system that also satisfies a prescribed performance. The conditions are expressed in the frame of linear matrix inequalities (LMIs), which can be verified easily by means of standard software. Two practical examples are provided to show the effectiveness of the proposed techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer‐Based H∞ Control for Continuous‐Time Networked Control Systems

This paper is concerned with the observer‐based H_∞ control for continuous‐time networked control systems (NCSs) considering packet dropouts and network‐induced delays. The packet dropouts and network‐induced delays in the sensor‐to‐controller (S‐C) channel and network‐induced delays in the controller‐to‐actuator (C‐A) channel are taken into full consideration. By taking the non‐uniform distribution characteristic of the arrival instants of actually adopted controller inputs into account, a new model for continuous‐time NCSs is established. To reduce the conservatism of modelling, a linear estimation‐based measurement output estimation method is introduced. Based on the newly established model and a Lyapunov functional, new controller design methods are proposed. A numerical example is given to illustrate the effectiveness and merits of the derived results.     

Real-time networked control of an industrial robot manipulator via discrete-time second-order sliding modes

This article presents the networked control of a robotic anthropomorphic manipulator based on a second-order sliding mode technique, where the control objective is to track a desired trajectory for the manipulator. The adopted control scheme allows an easy and effective distribution of the control algorithm over two networked machines. While the predictability of real-time tasks execution is achieved by the Soft Hard Real-Time Kernel (S.Ha.R.K.) real-time operating system, the communication is established via a standard Ethernet network. The performances of the control system are evaluated under different experimental system configurations using, to perform the experiments, a COMAU SMART3-S2 industrial robot, and the results are analysed to put into evidence the robustness of the proposed approach against possible network delays, packet losses and unmodelled effects.     

Robust H∞ control for networked systems with transmission delays and successive packet dropouts under stochastic sampling

This paper is concerned with the H_∞ performance analysis for networked control systems with transmission delays and successive packet dropouts under stochastic sampling. The parameter uncertainties are time‐varying norm‐bounded and appear in both the state and input matrices. If packet loss is considered the same as time delay, when models the networked control systems with successive packet dropouts and delays as ordinary linear system with input‐delay approach, due to sampling period is stochastic, then the delay caused by packet losses is a stochastic variable, which leads to difficulties in the stability analysis of the considered system. However, if we can transform the system with stochastic delay into a continuous system with stochastic parameter, we can solve the problem. In this paper, by assuming that the network packet loss rate and employing the information of probabilistic distribution of the time delays, the stochastic sampling system is transformed into a continuous‐time model with stochastic variable, which satisfies a Bernoulli distribution. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean‐square exponential stability of the system with an H_∞ performance. What's more, an H_∞ controller design procedure is then proposed, and a less conservative result is obtained by taking the probability into consideration. Finally, a numerical simulation example is employed to show the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

基于Kalman滤波的网络丢包补偿器

针对网络控制系统中普遍存在的连续丢包问题,建立了网络控制系统状态反馈丢包补偿模型,提出了1种基于Kalman滤波的连续丢包补偿器算法。把具有数据包连续丢失补偿的网络控制系统描述为具有3个事件的异步动态系统,并且给出了系统稳定性的证明。该补偿器具有较高的预测补偿和抗干扰能力。仿真结果表明卡尔曼滤波连续丢包补偿器算法的有效性。     

INTERNET‐BASED REAL‐TIME CONTROL ARCHITECTURES WITH TIME‐DELAY/PACKET‐LOSS COMPENSATION

The main objective of this paper is to demonstrate the feasibility of Internet‐based real‐time control. A novel client/server‐based architecture for Internet‐based supervisory control with a Common Gateway Interface/Hyper Text Markup Language (CGI/HTML) interface is presented. A real‐time operating environment was established for closed‐loop control over Ethernet. We conceived of an autoregressive (AR) prediction scheme and a novel compensation algorithm to compensate for network‐induced time delays and data‐packet losses simultaneously. We constructed an open‐loop unstable ball magnetic‐levitation (maglev) setup as a test bed to validate the two proposed control architectures. Experimental results proved the feasibility of Internet‐based real‐time control and verified the effectiveness of the proposed time‐delay/packet‐loss compensation algorithm in networked feedback control systems.     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.