Event‐triggered MPC design for distributed systems toward global performance

This paper studies the coordination control problem of stabilizing large‐scale dynamically coupled systems via a novel event‐triggered distributed model predictive control (DMPC) approach. In order to achieve global performance, certain constraints relevant to the triggering instant are imposed on the DMPC optimization problem, and triggering mechanisms are designed by taking into account coupling influences. Specifically, the triggering conditions derived from the feasibility and stability analysis are based on the local subsystem state and the information received from its neighbors. Based on these triggering mechanisms, the event‐triggered DMPC algorithm is built, and a dual‐mode strategy is adopted. As a result, the controllers solve the optimization problem and coordinate with each other asynchronously, which reduces the amount of communication and lowers the frequency of controller updates while achieving global performance. The recursive feasibility of the proposed event‐triggered DMPC algorithm is proved, and sufficient parameter conditions about the prediction horizon and the triggering threshold are established. It shows that the system state can be gradually driven into the terminal set under the proposed strategy. Finally, an academic example and a realistic simulation problem to the water level of a 4‐tank system are provided to verify the effectiveness of the proposed algorithm.     

Distributed event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under a directed graph. We propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter‐event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.     

基于事件触发非线性多智能体系统的固定时间一致性

本文研究了在有向拓扑下,带有非线性动力学多智能体系统的固定时间一致性问题.提出了一种新的基于事件触发机制的非线性控制策略,对于每个智能体给出了基于状态信息的事件触发条件,当状态误差满足所给条件时才触发事件,能有效的减小系统的能量耗散和控制器的更新频次.利用Lyapunov稳定性理论和代数图论,证明在该控制策略下,多智能体系统在固定时间能实现领导跟随一致性,且不存在Zeno行为.相较于有限时间一致性策略,采用固定时间一致性策略系统的收敛时间不再依赖于系统的初始状态.最后,仿真实例验证了理论结果的有效性.     

Distributed MPC of polytopic uncertain systems: handling quantised communication and packet dropouts

In this paper, we study the distributed model predictive control (MPC) of polytopic uncertain systems with quantised communication and packet dropouts. The model of the whole plant is divided into a certain number of incomplete subsystems. Due to the nature of the distributed control structure, there is generally a lack of information about the state of the overall system. Each subsystem shares its information with neighbour subsystems via reliable connection. Distributed MPC controllers are designed for each subsystem by solving the linear matrix inequalities optimisation problem. The distributed state feedback laws are quantised and transmitted via communication network. An iterative algorithm is presented to make coordination among distributed state feedback laws. The communication is assumed to be affected by random packet dropouts in a representation of Bernoulli distributed white sequences with known conditional probabilities. A case study is carried out to demonstrate the effectiveness of the proposed distributed MPC technique.     

Decentralized summation‐based triggering mechanism for Lipschitz nonlinear systems

In this paper, a decentralized event‐based triggering mechanism for a class of nonlinear control systems is studied. It is assumed that the measurement sensors are geographically distributed and so local event generator modules are employed. Then, a novel periodic triggering condition is proposed for each module, which can potentially reduce the information exchange between subsystems compared with traditional control approaches, while maintaining closed‐loop asymptotic stability. The triggering condition parameters are designed through a convex optimization problem with LMI constraints. Finally, simulations are carried out to illustrate the performance of the introduced scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

An adaptive event‐triggering scheme for networked interconnected control system with stochastic uncertainty

This paper investigates the problem of adaptive event‐triggering scheme for networked interconnected systems to relieve the burden of the network bandwidth. The data releasing is triggered by an adaptive event‐triggering device. The triggering condition depends on the state information at both the latest releasing instant and the current sampling instant. The threshold of the triggering parameter is achieved online rather than a predetermined constant. Taking the network‐induced delays and the coupling delays of the subsystems into account, together with the hybrid adaptive event‐triggering scheme and the stochastic uncertainty, we propose an unified model of the networked interconnected system. Sufficient conditions for the mean square stability and stabilization of the interconnected systems are developed by using Lyapunov–Krasovskii functional approach. A co‐designed method is put forward to obtain the controller gains and the weight of the triggering condition simultaneously. Finally, an example is provided to demonstrate the design method. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Event‐triggered fault‐tolerant control and scheduling codesign for nonlinear networked control systems with medium‐access constraint and packet disordering

This paper studies an event‐triggered communication, scheduling, and fault‐tolerant control codesign method for nonlinear networked control systems with medium‐access constraint, delay, and packet disordering using an adaptive approximation method and adaptive technique. By considering nonlinear dynamics and controller reconfiguration, a novel event‐triggering scheme with an adjustable triggering condition and adaptive triggering thresholds is proposed. The stochastic event‐driven actuator scheduling is investigated without the assumption that the controller can access the current modes of the actuators. By considering the Markovian delay and focusing on the transmitter node, a new packet reordering approach is used to cope with packet disordering. This paper proposes an active fault‐tolerant control method, in which the nominal controller is redesigned for the postfault plant by using the fault information provided by an estimator. It is proven that the estimation error of the estimator is uniformly bounded, the reconfigurable controller and event‐trigger ensure the boundedness in probability of the state tracking error before and after the fault occurrence in the presence of medium‐access constraint, delay, and packet disordering while reducing communication load. The effectiveness of the proposed method is demonstrated in the numerical example.     

A novel event‐triggered extended state observer for networked control systems subjected to external disturbances

In this paper, the event‐triggered‐based state estimation problem is investigated for a class of nonlinear networked control systems subjected to external disturbances. A novel event‐triggered extended state observer (ESO) is utilized to estimate the so‐called total disturbance, and an output predictor is adopted for the proposed ESO between two consecutive transmission instants. It is also worth pointing out that, in the newly proposed ESO, an event‐triggered mechanism is adopted to update the measurement signal so as to save the communication resource. The sufficient conditions are provided such that the estimation error dynamics is exponentially ultimately bounded. Furthermore, it is proven that the Zeno behavior does not exist for the event‐triggering rules. A number of numerical simulations are conducted to verify the validity of the theoretical results.     

Event‐triggered output consensus for heterogeneous multiagent systems with fixed and switching directed topologies

This paper studies the event‐triggered output consensus problem of heterogeneous linear multiagent systems characterized via fixed and switching directed graphs. With proper state‐dependent triggering functions, two new event‐triggered output consensus control schemes are proposed for each agent to achieve consensus. Notably, under the proposed control protocols, continuous communication among agents is not required in both controllers updating and triggering threshold detection, which means being completely continuous communication free. The communication instances are reduced significantly, and the periodic or high‐frequency communication is restrained. It is also ensured that events cannot be triggered infinitely in finite time (ie, the Zeno behavior is elegantly avoided). Meanwhile, the simulation examples are given to illustrate the theoretical analysis.     

Observer-based event-triggered distributed model predictive control for a class of nonlinear interconnected systems

In this paper, an observer-based event-triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event-triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event-triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed-loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.     

Periodic event-triggering in distributed receding horizon control of nonlinear systems

How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.     

Distributed tracking control of uncertain mechanical systems with velocity constraints

This paper considers the leader‐following control problem of multiple mechanical systems with uncertainty and velocity constraints. So as to deal with the velocity constraints, a reduction procedure is applied to transform the model of each system to a cascaded system. With the aid of the cascade structure of each system and the properties of linear time‐varying systems, distributed robust feedback controllers are proposed such that the state of each follower system asymptotically converges to the state of a leader system with the aid of neighbors' information. So as to reduce the cost of the communication between systems, an event‐triggered leader‐following control problem is also considered, and event‐triggered distributed controllers are proposed. As an application of the proposed results, formation control of wheeled mobile robots is considered, and distributed controllers are obtained with the aid of the results in Theorems 1 and 2. Simulation results show the effectiveness of the proposed results. Copyright © 2017 John Wiley & Sons, Ltd.     

Event-triggered robust model predictive control of continuous-time nonlinear systems

The event-triggered control is of compelling features in efficiently exploiting system resources, and thus has found many applications in sensor networks, networked control systems, multi-agent systems and so on. In this paper, we study the event-triggered model predictive control (MPC) problem for continuous-time nonlinear systems subject to bounded disturbances. An event-triggered mechanism is first designed by measuring the error between the system state and its optimal prediction; the event-triggered MPC algorithm that is built upon the triggering mechanism and the dual-mode approach is then designed. The rigorous analysis of the feasibility and stability is conducted, and the sufficient conditions for ensuring the feasibility and stability are developed. We show that the feasibility of the event-triggered MPC algorithm can be guaranteed if, the prediction horizon is designed properly and the disturbances are small enough. Furthermore, it is shown that the stability is related to the prediction horizon, the disturbance bound and the triggering level, and that the state trajectory converges to a robust invariant set under the proposed conditions. Finally, a case study is provided to verify the theoretical results.     

Event‐based asynchronous communication and sampled control for synchronization of multiagent networks with input saturation

This paper investigates the problem of event‐based synchronization of linear dynamical networks subject to input saturation. The asynchronous neighboring information transmission is triggered by distributed events. The sampled control technique is utilized to exclude both the internal Zeno behavior of each agent and the network Zeno behavior attributed to neighboring agents. Allowing the input saturation to be attained, an event‐based global synchronization algorithm is proposed for multiagent networks with neutrally stable dynamics. For general linear networks, an event‐triggered control protocol is designed using the modified algebraic Riccati equation, with a low‐gain cooperative control law proposed to achieve semiglobal synchronization. A numerical example is presented to illustrate the theoretical results.     

事件触发双模分布式预测控制

本文针对有界扰动作用下的线性离散大系统,提出了事件触发双模分布式预测控制设计方法.利用输入状态稳定性(input-to-state stability,ISS)理论建立了仅与子系统自身信息相关的事件触发条件.只有子系统满足相应的事件触发条件,才进行状态信息的传输和分布式预测控制优化问题的求解,并与邻域子系统交互最优解作用下的关联信息.当子系统进入不变集时,采用状态反馈控制律进行镇定,并与进入不变集的邻域子系统不再交互信息.分析了算法的递推可行性和系统的闭环稳定性,给出了扰动的上界.最后,通过车辆控制系统对算法进行仿真验证,结果表明,本文提出的方法能够有效降低优化问题的求解次数和关联信息的交互次数,节约计算资源和通信资源.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.     

Finite ‐gain problem for networked control systems with delays via event‐triggered control

By using the integrals of the signals to construct the triggering condition, integral‐based event‐triggered control can relax the requirement of persistent decrease on the Lyapunov function and, then, may yield better sampling performance. This paper studies the disturbance rejection problem for the integral‐based event‐triggered control systems with transmission delays and observer‐based output feedbacks. An integral‐based triggering condition is employed to generate the events. Two asynchronous models are implemented in the different sides of the networks. The model in the observer node is used to detect the events, whereas the model in the controller node is used to calculate the control signals. This structure contributes to avoiding the Zeno behavior, and then, an estimation on the lower bound of the interevent times is provided. Moreover, the criteria on the parameter in the triggering condition and on the bounds of the transmission delays are given to guarantee the desired disturbance rejection performance. Finally, a numerical example is provided to illustrate the efficiency and feasibility of the obtained results.