Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network.It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network.For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed.In an event-triggered system, when an error signal exceeds a specified time-varying threshold, it indicates the occurrence of a typical event.The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed.Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs.A simulation example is finally used to verify that the effectiveness of such a control strategy can enhance the system performance.

Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints

This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregular constraints are considered and a constraints switching mechanism(CSM)is introduced to circumvent the difficulties arising from irregular output constraints.Based on the CSM,a new class of generalized barrier functions are constructed,which allows the control results to be independent of the maximum and minimum values(MMVs)of constraints and thus extends the existing results.Finally,we proposed a novel dynamic constraint-driven event-triggered strategy(DCDETS),under which the stress on signal transmission is reduced greatly and no constraints are violated by making a dynamic trade-off among system state,external constraints,and inter-execution intervals.It is proved that the system output is driven to close to the reference trajectory and the semi-global stability is guaranteed under the proposed control scheme,regardless of the external irregular output constraints.Simulation also verifies the effectiveness and benefits of the proposed method.

Achieving Given Precision Within Prescribed Time yet With Guaranteed Transient Behavior via Output Based Event-Triggered Control

It is interesting yet nontrivial to achieve given control precision within user-assignable time for uncertain nonlinear systems.The underlying problem becomes even more challenging if the transient behavior also needs to be accommodated and only system output is available for feedback.Several key design innovations are proposed to circumvent the aforementioned technical difficulties,including the employment of state estimation filters with event-triggered mechanism,the construction of a novel performance scaling function and an error transformation.In contrast to most existing performance based works where the stability is contingent on initial conditions and the maximum allowable steady-state tracking precision can only be guaranteed at some unknown(theoretically infinite)time,in this work the output of the system is ensured to synchronize with the desired trajectory with arbitrarily pre-assignable convergence rate and arbitrarily pre-specified precision within prescribed time,using output only with lower cost of sensing and communication.In addition,all the closed-loop signals are ensured to be globally uniformly bounded under the proposed control method.The merits of the designed control scheme are confirmed by numerical simulation on a ship model.

State-dependent event-triggered control of multi-agent systems

Event-triggered control has been recent/y proposed as an effective strategy for the consensus of multi-agent systems. We present an improved distributed event-triggered control scheme that remedies a shortcoming of some previous event- triggered control schemes in the literature. This improved distributed event-triggered method has no need for continuously monitoring each agent＇ neighbors. Moreover, each agent in the multi-agent systems will not exhibit the Zeno behavior. Numerical simulation results show the effectiveness of the proposed consensus control.

Synchronization of Markovian jumping complex networks with event-triggered control

This paper investigates event-triggered synchronization for complex networks with Markovian jumping parameters.Nonlinear dynamics with Markovian jumping parameters is considered for each node in a complex network. By utilizing the proposed event-triggered strategy, and based on the Lyapunov functional method and linear matrix inequality technology,some sufficient conditions for synchronization of complex networks are derived whether the transition rate matrix for the Markov process is completely known or not. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.

PC synchronization of a class of chaotic systems via event-triggered control

The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated.For cooperative-competitive network,two different control protocols,fixed-time group consensus and fixed-time eventtriggered group consensus,are designed.It is demonstrated that there is no Zeno behavior under the designed eventtriggered control.Meanwhile,it is proved that for an arbitrary initial state of the system,group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory.Finally,a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.

Time-varying formation for general linear multi-agent systems via distributed event-triggered control under switching topologies

This paper investigates the time-varying formation problem for general linear multi-agent systems using distributed event-triggered control strategy.Different from the previous works,to achieve the desired time-varying formation,a distributed control scheme is designed in an event-triggered way,in which for each agent the controller is triggered only at its own event times.The interaction topology among agents is assumed to be switching.The common Lyapunov function as well as Riccati inequality is applied to solve the time-varying formation problem.Moreover,the Zeno behavior of triggering time sequences can be excluded for each agent.Finally,a simulation example is presented to illustrate the effectiveness of the theoretical results.

Function Observer Based Event-triggered Control for Linear Systems with Guaranteed L_∞-Gain

This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results. © 2014 Chinese Association of Automation.

Quantization and Event-Triggered Policy Design for Encrypted Networked Control

This paper proposes a novel event-driven encrypted control framework for linear networked control systems(NCSs),which relies on two modified uniform quantization policies,the Paillier cryptosystem,and an event-triggered strategy.Due to the fact that only integers can work in the Pailler cryptosystem,both the real-valued control gain and system state need to be first quantized before encryption.This is dramatically different from the existing quantized control methods,where only the quantization of a single value,e.g.,the control input or the system state,is considered.To handle this issue,static and dynamic quantization policies are presented,which achieve the desired integer conversions and guarantee asymptotic convergence of the quantized system state to the equilibrium.Then,the quantized system state is encrypted and sent to the controller when the triggering condition,specified by a state-based event-triggered strategy,is satisfied.By doing so,not only the security and confidentiality of data transmitted over the communication network are protected,but also the ciphertext expansion phenomenon can be relieved.Additionally,by tactfully designing the quantization sensitivities and triggering error,the proposed event-driven encrypted control framework ensures the asymptotic stability of the overall closedloop system.Finally,a simulation example of the secure motion control for an inverted pendulum cart system is presented to evaluate the effectiveness of the theoretical results.

Mixed H_(∞)/Passive Exponential Synchronization for Delayed Memristive Neural Networks with Switching Event-Triggered Control

This paper is devoted to event-triggered synchronization of delayed memristive neural networks with H∞and passivity performance.The aim is to guarantee the exponential synchronization and mixed H∞and passivity control for memristive neural networks by using event-triggered control.Firstly,a switching system is constructed under the event-triggered control strategy.Then,by adopting a piece-wise Lyapunov functional,a sufficient condition is established for the exponential synchronization and mixed H_(∞)and passivity performance.Moreover,an event-triggered controller design scheme is proposed using matrix decoupling method.Finally,the effectiveness of the designed controller is exemplified by a numerical example.

Distributed Event-triggered Control for Frequency Restoration in Islanded Microgrids with Reduced Trigger Condition Checking

For islanded microgrids(MGs),distributed control is regarded as a preferred alternative to centralized control for the frequency restoration of MGs.However,distributed control with successive communication restricts the efficiency and resilience of the control system.To address this issue,this paper proposes a distributed event-triggered control strategy for the frequency secondary control in islanded MGs.The proposed event-triggered control is Zeno behavior free and enables each DG to update and propagate its state to neighboring DGs only when a specific“event”occurs,which significantly reduces the communication burden.Compared with the existing event-triggered control,a trigger condition checking period of the proposed event-triggered control is provided to reduce the computation burden when checking the trigger condition.Furthermore,using the aperiodicity and intermittent properties of the communication,a simple detection principle is proposed to detect and isolate the compromised communication links in a timely and economic fashion,which improves the resilience of the system against FDI attacks.Finally,the control effectiveness of the proposed control scheme is validated by the simulation results of the tests on an MG with 4 DGs.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Dynamic Event-Triggered Consensus Control for Input Constrained Multi-Agent Systems With a Designable Minimum Inter-Event Time

This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.

Adaptive Event-Triggered Time-Varying Output Group Formation Containment Control of Heterogeneous Multiagent Systems

In this paper,a class of time-varying output group formation containment control problem of general linear hetero-geneous multiagent systems(MASs)is investigated under directed topology.The MAS is composed of a number of tracking leaders,formation leaders and followers,where two different types of leaders are used to provide reference trajectories for movement and to achieve certain formations,respectively.Firstly,compen-sators are designed whose states are estimations of tracking lead-ers,based on which,a controller is developed for each formation leader to accomplish the expected formation.Secondly,two event-triggered compensators are proposed for each follower to evalu-ate the state and formation information of the formation leaders in the same group,respectively.Subsequently,a control protocol is designed for each follower,utilizing the output information,to guide the output towards the convex hull generated by the forma-tion leaders within the group.Next,the triggering sequence in this paper is decomposed into two sequences,and the inter-event intervals of these two triggering conditions are provided to rule out the Zeno behavior.Finally,a numerical simulation is intro-duced to confirm the validity of the proposed results.

Novel Adaptive Memory Event-Triggered-Based Fuzzy Robust Control for Nonlinear Networked Systems via the Differential Evolution Algorithm

This article mainly investigates the fuzzy optimization robust control issue for nonlinear networked systems characterized by the interval type-2(IT2)fuzzy technique under a differential evolution algorithm.To provide a more reasonable utilization of the constrained communication channel,a novel adaptive memory event-triggered(AMET)mechanism is developed,where two event-triggered thresholds can be dynamically adjusted in the light of the current system information and the transmitted historical data.Sufficient conditions with less conservative design of the fuzzy imperfect premise matching(IPM)controller are presented by introducing the Wirtinger-based integral inequality,the information of membership functions(MFs)and slack matrices.Subsequently,under the IPM policy,a new MFs intelligent optimization technique that takes advantage of the differential evolution algorithm is first provided for IT2 TakagiSugeno(T-S)fuzzy systems to update the fuzzy controller MFs in real-time and achieve a better system control effect.Finally,simulation results demonstrate that the proposed control scheme can obtain better system performance in the case of using fewer communication resources.

Dynamic Event-triggered Control and Estimation: A Survey

The efficient utilization of computation and communication resources became a critical design issue in a wide range of networked systems due to the finite computation and processing capabilities of system components(e.g., sensor, controller) and shared network bandwidth. Event-triggered mechanisms(ETMs) are regarded as a major paradigm shift in resource-constrained applications compared to the classical time-triggered mechanisms, which allows a trade-off to be achieved between desired control/estimation performance and improved resource efficiency. In recent years, dynamic event-triggered mechanisms(DETMs) are emerging as a promising enabler to fulfill more resource-efficient and flexible design requirements. This paper provides a comprehensive review of the latest developments in dynamic event-triggered control and estimation for networked systems. Firstly, a unified event-triggered control and estimation framework is established, which empowers several fundamental issues associated with the construction and implementation of the desired ETM and controller/estimator to be systematically investigated. Secondly, the motivations of DETMs and their main features and benefits are outlined. Then, two typical classes of DETMs based on auxiliary dynamic variables(ADVs) and dynamic threshold parameters(DTPs) are elaborated. In addition, the main techniques of constructing ADVs and DTPs are classified, and their corresponding analysis and design methods are discussed. Furthermore, three application examples are provided to evaluate different ETMs and verify how and under what conditions DETMs are superior to their static and periodic counterparts. Finally, several challenging issues are envisioned to direct the future research.

Distributed Periodic Event-Triggered Optimal Control of DC Microgrids Based on Virtual Incremental Cost

This article presents a distributed periodic eventtriggered(PET)optimal control scheme to achieve generation cost minimization and average bus voltage regulation in DC microgrids.In order to accommodate the generation constraints of the distributed generators(DGs),a virtual incremental cost is firstly designed,based on which an optimality condition is derived to facilitate the control design.To meet the discrete-time(DT)nature of modern control systems,the optimal controller is directly developed in the DT domain.Afterward,to reduce the communication requirement among the controllers,a distributed event-triggered mechanism is introduced for the DT optimal controller.The event-triggered condition is detected periodically and therefore naturally avoids the Zeno phenomenon.The closed-loop system stability is proved by the Lyapunov synthesis for switched systems.The generation cost minimization and average bus voltage regulation are obtained at the equilibrium point.Finally,switch-level microgrid simulations validate the performance of the proposed optimal controller.

Bipartite Consensus of Linear Multi-Agent Systems by Distributed Event-Triggered Control

For multi-agent systems with competitive and collaborative relationships,signed graph can more intuitively express the characteristics of their interactive networks.In this paper,the bipartite consensus is investigated for multi-agent systems with structurally balanced signed graph.In order to reduce actuation burden in dynamical network environment,the event-triggering strategy is applied to bipartite consensus protocol for the multi-agent systems.The triggered condition for each agent is designed by using its own information and transmitted information of its neighbors at sampling instant and make the number of triggers of the whole systems be reduced.Based on the distributed eventtriggered control,some sufficient conditions are derived to guarantee the leaderless and leader-following bipartite consensus.Finally,some numerical examples are shown to demonstrate the effectiveness of the theoretical results.

Event-triggered control for containment maneuvering of second-order MIMO multi-agent systems with unmatched uncertainties and disturbances

This paper is concerned with distributed containment maneuvering of second-order Multi-Input Multi-Output(MIMO)multi-agent systems with non-periodic communication and actuation.The agent is subject to unmatched nonlinear dynamics and external disturbances.Event-triggered containment maneuvering control methods is developed based on a modular design.Specifically,an estimator module is constructed based on neural networks and the nonperiodic obtained follower information through event-triggered communication.Next,a controller module is designed by using the identified information from the estimator module and a third-order linear tracking differentiator.An event-triggered mechanism is introduced for updating the actuator.Then,a path update law is designed based on the non-periodic leader information through event-triggered communication.The closed-loop system cascaded by the estimation subsystem and control subsystem is proved to be input-to-state stable,and Zeno behavior is excluded in the control process.The proposed method is capable of reducing the consumption of communication and actuation.A simulation example is provided to substantiate the effectiveness of the proposed event-triggered control method for distributed containment maneuvering of second-order MIMO multi-agent systems.