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.

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.

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.

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.

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.

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.

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper investigates the robust cooperative output regulation problem for a class of heterogeneousuncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizingthe internal model approach and the adaptive control technique, a distributed adaptive internal model isconstructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed ofa distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggeringmechanism is proposed, in which each agent updates its control input at its own triggering time instants. It isshown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solvedwithout requiring either the global information associated with the communication topology or the bounds ofthe uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided toillustrate the effectiveness of the proposed control strategy.

Formation-Containment Control Using Dynamic Event-Triggering Mechanism for Multi-Agent Systems

The paper proposes a novel approach for formationcontainment control based on a dynamic event-triggering mechanism for multi-agent systems.The leader-leader and follower-follower communications are reduced by utilizing the distributed dynamic event-triggered framework.We consider two separate sets of design parameters:one set comprising control and dynamic event-triggering parameters for the leaders and a second set similar to the first one with different values for the followers.The proposed algorithm includes two novel stages of codesign optimization to simultaneously compute the two sets of parameters.The design optimizations are convex and use the weighted sum approach to enable a structured trade-off between the formation-containment convergence rate and associated communications.Simulations based on non-holonomic mobile robot multi-agent systems quantify the effectiveness of the proposed approach.

Dynamic Event-Triggered Scheduling and Platooning Control Co-Design for Automated Vehicles Over Vehicular Ad-Hoc Networks

This paper deals with the co-design problem of event-triggered communication scheduling and platooning control over vehicular ad-hoc networks(VANETs)subject to finite communication resource.First,a unified model is presented to describe the coordinated platoon behavior of leader-follower vehicles in the simultaneous presence of unknown external disturbances and an unknown leader control input.Under such a platoon model,the central aim is to achieve robust platoon formation tracking with desired inter-vehicle spacing and same velocities and accelerations guided by the leader,while attaining improved communication efficiency.Toward this aim,a novel bandwidth-aware dynamic event-triggered scheduling mechanism is developed.One salient feature of the scheduling mechanism is that the threshold parameter in the triggering law is dynamically adjusted over time based on both vehicular state variations and bandwidth status.Then,a sufficient condition for platoon control system stability and performance analysis as well as a co-design criterion of the admissible event-triggered platooning control law and the desired scheduling mechanism are derived.Finally,simulation results are provided to substantiate the effectiveness and merits of the proposed co-design approach for guaranteeing a trade-off between robust platooning control performance and communication efficiency.

Dynamic event-triggered formation control of second-order nonholonomic systems

In this paper,the formation control problem of secondorder nonholonomic mobile robot systems is investigated in a dynamic event-triggered scheme.Event-triggered control protocols combined with persistent excitation(PE)conditions are presented.In event-detecting processes,an inactive time is introduced after each sampling instant,which can ensure a positive minimum sampling interval.To increase the flexibility of the event-triggered scheme,internal dynamic variables are included in event-triggering conditions.Moreover,the dynamic event-triggered scheme plays an important role in increasing the lengths of time intervals between any two consecutive events.In addition,event-triggered control protocols without forward and angular velocities are also presented based on approximate-differentiation(low-pass)filters.The asymptotic convergence results are given based on a nested Matrosov theorem and artificial sampling methods.

Consensus Control of Multi-Agent Systems Using Fault-Estimation-in-the-Loop:Dynamic Event-Triggered Case

The paper develops a novel framework of consensus control with fault-estimation-in-the-loop for multi-agent systems(MASs)in the presence of faults.A dynamic event-triggered protocol(DETP)by adding an auxiliary variable is utilized to improve the utilization of communication resources.First,a novel estimator with a noise bias is put forward to estimate the existed fault and then a consensus controller with fault compensation(FC)is adopted to realize the demand of reliability and safety of addressed MASs.Subsequently,a novel consensus control framework with fault-estimation-in-the-loop is developed to achieve the predetermined consensus performance with the l_(2)-l_(∞)constraint by employing the variance analysis and the Lyapunov stability approaches.Furthermore,the desired estimator and controller gains are obtained in light of the solution to an algebraic matrix equation and a linear matrix inequality in a recursive way,respectively.Finally,a simulation result is employed to verify the usefulness of the proposed design framework.

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.

Event-Triggered Sliding Mode Control for Trajectory Tracking of Nonlinear Systems

In this paper, an event-triggered sliding mode control approach for trajectory tracking problem of nonlinear input affine system with disturbance has been proposed. A second order robotic manipulator system has been modeled into a general nonlinear input affine system. Initially, the global asymptotic stability is ensured with conventional periodic sampling approach for reference trajectory tracking. Then the proposed approach of event-triggered sliding mode control is discussed which guarantees semi-global uniform ultimate boundedness. The proposed control approach guarantees non-accumulation of control updates ensuring lower bounds on inter-event triggering instants avoiding Zeno behavior in presence of the disturbance. The system shows better performance in terms of reduced control updates, ensures system stability which further guarantees optimization of resource usage and cost. The simulation results are provided for validation of proposed methodology for tracking problem by a robotic manipulator. The number of aperiodic control updates is found to be approximately 44% and 61% in the presence of constant and time-varying disturbances respectively.

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.

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.

Data-Driven Control of Distributed Event-Triggered Network Systems

The present paper deals with data-driven event-triggered control of a class of unknown discrete-time interconnected systems(a.k.a.network systems).To this end,we start by putting forth a novel distributed event-triggering transmission strategy based on periodic sampling,under which a model-based stability criterion for the closed-loop network system is derived,by leveraging a discrete-time looped-functional approach.Marrying the model-based criterion with a data-driven system representation recently developed in the literature,a purely data-driven stability criterion expressed in the form of linear matrix inequalities(LMIs)is established.Meanwhile,the data-driven stability criterion suggests a means for co-designing the event-triggering coefficient matrix and the feedback control gain matrix using only some offline collected state-input data.Finally,numerical results corroborate the efficacy of the proposed distributed data-driven event-triggered network system(ETS)in cutting off data transmissions and the co-design procedure.