Event‐triggered distributed constrained consensus

We consider a distributed consensus problem for continuous‐time multi‐agent systems with set constraints on the final states. To save communication costs, an event‐triggered communication‐based protocol is proposed. By comparing its own instantaneous state with the one previously broadcasted to neighbours, each agent determines the next communication time. Based on this event‐triggered communication, each agent is not required to continuously monitor its neighbours' state and the communication only happens at discrete time instants. We show that, under some mild conditions, the constrained consensus of the multi‐agent system with the proposed protocol can be achieved with an exponential convergence rate. A lower bound of the transmission time intervals is provided that can be adjusted by choosing different values of parameters. Numerical examples illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Event‐triggered control for networked Markovian jump systems

The problem of H_∞ control for networked Markovian jump system under event‐triggered scheme is studied in this paper. In order to reduce the utilization of limited network bandwidth, a dynamic discrete event‐triggered scheme to choose the transmitted data is designed. A Markovian jump time‐delay system model is employed to describe the event‐triggered scheme and the network related behavior, such as transmission delay, data package dropout, and disorder. Furthermore, a sufficient condition is derived to guarantee that the resulting closed‐loop system is stable and has a prescribed performance index. A co‐design method for the H_∞ controller and the event‐triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example. Copyright © 2014 John Wiley & Sons, Ltd.     

Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

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.     

Event‐triggered constrained control of positive systems with input saturation

This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.     

Event‐triggered output synchronization of heterogeneous multi‐agent systems

This paper proposes a control architecture that employs event‐triggered control techniques to achieve output synchronization of a group of heterogeneous linear time‐invariant agents. We associate with each agent an event‐triggered output regulation controller and an event‐triggered reference generator. The event‐triggered output regulation controller is designed such that the regulated output of the agent approximately tracks a reference signal provided by the reference generator in the presence of unknown disturbances. The event‐triggered reference generator is responsible for synchronizing its internal state across all agents by exchanging information through a communication network linking the agents. We first address the output regulation problem for a single agent where we analyze two event‐triggered scenarios. In the first one, the output and input event detectors operate synchronously, meaning that resets are made at the same time instants, while in the second one, they operate asynchronously and independently of each other. It is shown that the tracking error is globally bounded for all bounded reference trajectories and all bounded disturbances. We then merge the results on event‐triggered output regulation with previous results on event‐triggered communication protocols for synchronization of the reference generators to demonstrate that the regulated output of each agent converges to and remains in a neighborhood of the desired reference trajectory and that the closed‐loop system does not exhibit Zeno solutions. Several examples are provided to illustrate the advantages and issues of every component of the proposed control architecture. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered adaptive backstepping control for parametric strict‐feedback nonlinear systems

This paper proposes a novel adaptive backstepping control method for parametric strict‐feedback nonlinear systems with event‐sampled state and input vectors via impulsive dynamical systems tools. In the design procedure, both the parameter estimator and the controller are aperiodically updated only at the event‐sampled instants. An adaptive event sampling condition is designed to determine the event sampling instants. A positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. The closed‐loop stability of the adaptive event‐triggered control system is rigorously proved via Lyapunov analysis for both the continuous and jump dynamics. Compared with the periodic updates in the traditional adaptive backstepping design, the proposed method can reduce the computation and the transmission cost. The effectiveness of the proposed method is illustrated using 2 simulation examples.     

Event‐based distributed robust synchronization control for multiple Euler‐Lagrange systems without relative velocity measurements

This paper focuses on the event‐based distributed robust leaderless synchronization control for multiple Euler‐Lagrange systems with directed communication topology that contains a directed spanning tree. Update frequency of the system is reduced by taking advantages of the event‐triggered approach, which can help extend the service life of the controller. Robust control theory is employed to guarantee the synchronization stability of the networked Euler‐Lagrange systems when unmodeled dynamics occur. The cost on the distributed synchronization protocol design can be saved due to the relaxation of the requirement on relative velocity measurements. Furthermore, our results are more practical because unknown disturbance is taken into consideration. In addition, it can be rigorously analyzed that each agent can exclude the undesired Zeno behavior. Some simulation examples are provided in the end to demonstrate the effectiveness of the proposed event‐based distributed robust control algorithm.     

Event‐triggered Control of Linear Systems with Saturated Inputs

This paper investigates the event‐triggered control of linear systems with saturated state feedback and saturated observer‐based feedback, respectively. The problem of simultaneously deriving stabilizing event‐triggered controllers and tackling saturation nonlinearity is cast into a standard linear matrix inequalities problem. Key topics are studied, such as event‐triggered observer design and event‐triggered saturated observer‐based feedback synthesis. Important issues are touched on, including the existence of the positive lower bound for inter‐event times, and self‐triggered algorithms.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Event‐triggered optimal tracking control of nonlinear systems

We propose a novel event‐triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event‐triggered controller. Because the actor network updates only when an event occurs, we shall use a zero‐order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed‐loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one‐link rigid robot under gravitation field, and a controlled Van‐der‐Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered UKF for nonlinear dynamic systems with packet dropout

In this paper, the event‐triggered nonlinear filtering problem is investigated for nonlinear dynamic systems over a wireless sensor network with packet dropout. Measurements are transmitted to a remote estimator only when a specific event happens for a reduction of communication cost. An event‐triggered unscented Kalman filter related to trigger threshold is derived. It is shown that the prediction error covariance of the proposed filter is bounded and converges to a steady value if the threshold and packet dropout rate are small enough. Sufficient conditions are obtained to ensure stochastic stability of the filter, where a critical value of the threshold exists. Two examples are given to illustrate the effectiveness of the proposed filter. Copyright © 2017 John Wiley & Sons, Ltd.     

Event‐triggered control design for nonlinear systems with actuator failures and uncertain disturbances

Traditional adaptive event‐triggered design methods compensated for the event‐triggered error are not direct, and the stability analysis of resulting close‐loop systems is rather complicated. To alleviate the above restrictions, we propose a direct and simple event‐triggered co‐design method to solve the tracking control problem for parameter strict‐feedback systems with actuator faults and uncertain disturbances. By introducing a compensating terms in a smooth function form of a conventional control law and certain positive integrable functions, the effects of actuator faults and event‐triggered error can be compensated completely. Such a direct design method has the following features: (i) a direct compensation of the event‐triggered error is achieved without introducing any extra design parameters; (ii) it is not necessary to know any bound information on the parameters of event‐triggered threshold, and global asymptotic tracking control of the overall closed‐loop system is achieved; and (iii) the resulting stability criteria of the proposed event‐triggered control design are much simpler and easier to fulfill by virtue of the introduced co‐design method. Simulations are then carried out to validate the proposed schemes.     

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.     

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

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.     

Event‐triggered cascade high‐gain observer and its application

In this article, we consider the event‐triggered cascade high‐gain observer (ETCHGO) for a class of nonlinear systems. By cascading lower dimensional observers, we design a cascade high‐gain observer together with a Zeno‐free event‐triggered mechanism to estimate the state of the plant. We show that the ETCHGO has the same steady‐state performance as the continuous‐time cascade high‐gain observer, that is, there is a finite time after which the estimation error will not exceed the given threshold, and moreover, the finite time and the threshold can be made sufficiently small by adjusting some design parameters. We also investigate an ETCHGO with saturation, which will reduce the peaking value while maintaining the steady‐state estimation performance. Furthermore, we use the ETCHGO with saturation to solve the output feedback stabilization problem for a class of nonlinear systems. An example is given to illustrate our results.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.