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.

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.

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.

Finite-time decentralized event-triggered state estimation for coupled neural networks under unreliable Markovian network against mixed cyberattacks

This article investigates the issue of finite-time state estimation in coupled neural networks under random mixed cyberattacks,in which the Markov process is used to model the mixed cyberattacks.To optimize the utilization of channel resources,a decentralized event-triggered mechanism is adopted during the information transmission.By establishing the augmentation system and constructing the Lyapunov function,sufficient conditions are obtained for the system to be finite-time bounded and satisfy the H∞ performance index.Then,under these conditions,a suitable state estimator gain is obtained.Finally,the feasibility of the method is verified by a given illustrative example.

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.

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.

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.

Set-Membership Filtering Approach to Dynamic Event-Triggered Fault Estimation for a Class of Nonlinear Time-Varying Complex Networks

The present study addresses the problem of fault estimation for a specific class of nonlinear time-varying complex networks,utilizing an unknown-input-observer approach within the framework of dynamic event-triggered mechanism(DETM).In order to optimize communication resource utilization,the DETM is employed to determine whether the current measurement data should be transmitted to the estimator or not.To guarantee a satisfactory estimation performance for the fault signal,an unknown-input-observer-based estimator is constructed to decouple the estimation error dynamics from the influence of fault signals.The aim of this paper is to find the suitable estimator parameters under the effects of DETM such that both the state estimates and fault estimates are confined within two sets of closed ellipsoid domains.The techniques of recursive matrix inequality are applied to derive sufficient conditions for the existence of the desired estimator,ensuring that the specified performance requirements are met under certain conditions.Then,the estimator gains are derived by minimizing the ellipsoid domain in the sense of trace and a recursive estimator parameter design algorithm is then provided.Finally,a numerical example is conducted to demonstrate the effectiveness of the designed estimator.

Event-triggered H_(∞) PI state estimation for delayed switched neural networks

On state estimation problems of switched neural networks,most existing results with an event-triggered scheme(ETS)not only ignore the estimator information,but also just employ a fixed triggering threshold,and the estimation error cannot be guaranteed to converge to zero.In addition,the state estimator of non-switched neural networks with integral and exponentially convergent terms cannot be used to improve the estimation performance of switched neural networks due to the difficulties caused by the nonsmoothness of the considered Lyapunov function at the switching instants.In this paper,we aim at overcoming such difficulties and filling in the gaps,by proposing a novel adaptive ETS(AETS)to design an event-based H_(∞)switched proportional-integral(PI)state estimator.A triggering-dependent exponential convergence term and an integral term are introduced into the switched PI state estimator.The relationship among the average dwell time,the AETS and the PI state estimator are established by the triggering-dependent exponential convergence term such that estimation error asymptotically converges to zero with H_(∞)performance level.It is shown that the convergence rate of the resultant error system can be adaptively adjusted according to triggering signals.Finally,the validity of the proposed theoretical results is verified through two illustrative examples.

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.

Adaptive H_(∞) event-triggered load frequency control in islanded microgirds with limited spinning reserve constraints

Using an islanded microgrid(MG)with large-scale integration of renewable energy is the most popular way of solving the reliable power supply problem for remote areas and critical electrical users.However,compared with traditional power systems,the limited spinning reserves and network communication bandwidth may cause weak frequency stability in the presence of stochastic renewable active outputs and load demand fluctuations.In this paper,an adap-tive event-triggered control(ETC)strategy for a load frequency control(LFC)system in an islanded MG is proposed.First,a bounded adaptive event-triggered communication scheme is designed.This not only saves on network resources,but also ensures that the control center has a sensitive monitoring ability for the MG operating status when the frequency deviations have been effectively damped.Secondly,by fully considering the spinning reserve con-straints and uncertain communication delays,the LFC system is described as a nonlinear model with saturation terms.Design criteria for ETC parameters are strictly deduced based on Lyapunov stability theory.Finally,an ETC parameter optimization algorithm based on random direction search is developed to reconcile the bandwidth occupancy and control performance.The effectiveness of the proposed method is verified in an MG test system.

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.

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.

Integral Event-Triggered Attack-Resilient Control of Aircraft-on-Ground Synergistic Turning System With Uncertain Tire Cornering Stiffness

This article proposes an integral-based event-triggered attack-resilient control method for the aircraft-on-ground(AoG) synergistic turning system with uncertain tire cornering stiffness under stochastic deception attacks. First, a novel AoG synergistic turning model is established with synergistic reverse steering of the front and main wheels to decrease the steering angle of the AoG fuselage, thus reducing the steady-state error when it follows a path with some large curvature. Considering that the tire cornering stiffness of the front and main wheels vary during steering, a dynamical observer is designed to adaptively identify them and estimate the system state at the same time.Then, an integral-based event-triggered mechanism(I-ETM) is synthesized to reduce the transmission frequency at the observerto-controller end, where stochastic deception attacks may occur at any time with a stochastic probability. Moreover, an attackresilient controller is designed to guarantee that the closed-loop system is robust L2-stable under stochastic attacks and external disturbances. A co-design method is provided to get feasible solutions for the observer, controller, and I-ETM simultaneously. An optimization program is further presented to make a tradeoff between the robustness of the control scheme and the saving of communication resources. Finally, the low-and high-probability stochastic deception attacks are considered in the simulations. The results have illustrated that the AoG synergistic turning system with the proposed control method follows a path with some large curvature well under stochastic deception attacks. Furthermore,compared with the static event-triggered mechanisms, the proposed I-ETM has demonstrated its superiority in saving communication resources.

Dynamic Event-Triggered Fixed-Time Consensus Control and Its Applications to Magnetic Map Construction

This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.

Region coverage control for multiple stratospheric airships with combined self-/event-triggered mechanism

The region coverage control problem of multiple stratospheric airships system is firstly addressed in this paper.Towards it,we propose a two-layer control framework with the artificial potential field(APF)-based region coverage control law and the adaptive tracking control law.The APF-based region coverage control law ensures the coverage task is achieved until every single stratospheric airship ends up performing station keeping where near the respective global minimum point,in which an innovative solution to the local minimum problem is put forward.The adaptive tracking control law is designed to realize motion control using tracking the desired velocity and angular velocity given by coverage control law,with the consideration of several practical control problems as unknown individual differences and external disturbances.To save resources,the combined self-/event-triggered mechanism designed therein significantly reduces the times of state information transmission and control law calculation.The effectiveness of the proposed control framework is verified through simulations.

Matrix pencil based robust control for feedforward systems with event-triggered communications and sensor/actuator faults

In this paper we address the issue of output-feedback robust control for a class of feedforward nonlinear systems.Essentially different from the related literature,the feedback/input signals are corrupted by additive noises and can only be transmitted intermittently due to the consideration of event-triggered communications,which bring new challenges to the control design.With the aid of matrix pencil based design procedures,regulating the output to near zero is globally solved by a non-conservative dynamic low-gain controller which requires only an a priori information on the upper-bound of the growth rate of nonlinearities.Theoretical analysis shows that the closed-loop system is input-to-state stable with respect to the sampled errors and additive noise.In particular,the observer and controller designs have a dual architecture with a single dynamic scaling parameter whose update law can be obtained by calculating the generalized eigenvalues of matrix pencils offline,which has an advantage in the sense of improving the system convergence rate.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

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.