Periodic Event-triggered Control Research Articles

Periodic event-triggered bipartite containment control for nonlinear multi-agent systems with iuput delay

This paper studies the periodic event-triggered bipartite containment control problem of multi-agent systems with unmeasurable states and input delays. To deal with the system input delay problem, a Pade approximation technique is introduced. By utilising the sampled output of the system, a fuzzy state observer is constructed to estimate the unknown state. A periodic event-triggered mechanism is designed, which can effectively reduce the usage of communication resources. Compared with the traditional event-triggered control manner, a periodic event-triggered control manner only monitors the preset threshold condition at the sampling instant to determine whether to update the current control signal, which can automatically guarantee the minimum lower bound of the execution interval, avoiding the occurrence of Zeno behaviour. Stability analysis verifies that all signals in the closed-loop system are bounded, and the bipartite tracking error can converge to a small neighbourhood of the origin. Finally, a practical example further verifies the effectiveness of the designed control scheme.

Periodic and Dynamic Periodic Event-Triggered Control for Nonlinear Cyber-Physical Systems Under DoS Attacks via a Hybrid System Approach

This paper is focused on the problem of periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks and exogenous disturbances. The analysis relies on a new model to design periodic event-triggered control and dynamic periodic event-triggered control schemes such that the nonlinear CPSs are resilient to a class of malicious attacks which can be characterized by attacking frequency and attacking duration. By developing an average dwell-time automaton and a time-ratio monitor to describe frequency and duration of the DoS attacks, general hybrid dynamical frameworks are firstly proposed for event-triggered nonlinear CPSs. Based on the established models, novel Lyapunov functions are constructed. Furthermore, thanks to the Lyapunov-based approach, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -gain performance of the considered nonlinear CPSs under DoS attacks is analyzed. Finally, the feasibility of the theoretical findings is demonstrated by a numerical example.

A Stochastic Hybrid Framework for Event-Triggered Nonlinear Control Systems With Stochastic Denial of Service Attacks

In this paper, the stability problem for event-triggered nonlinear control systems is addressed in the presence of stochastic denial of service (DoS) attacks on the communication network. Dynamic event-triggered control (DETC) and periodic event-triggered control (PETC) are considered under the stochastic attacks. The stochastic attacks are modeled by a stochastic hybrid timer and a logic variable which is used to identify whether the network is attacked or not. Then the entire closed-loop system can be modeled into the framework of stochastic hybrid systems. Uniform global asymptotic stability in probability is concluded for the resulting stochastic system by proving that the equilibrium set is uniformly globally stable in probability and each neighborhood of the equilibrium set is uniformly globally recurrent. A nonlinear system example is provided to illustrate the effectiveness of the proposed results.

Periodic event-triggered formation control of multi-agent systems via complex Laplacian

Abstract The event-triggered formation control of first-order continuous multi-agent systems is studied based on complex Laplacian in this paper. Periodic event-triggered control is designed in which continuous communication between agents is not required. For each agent, two different triggering conditions are discussed. The first one relies on the inter-neighboring communication at each verification time, while the second one only need the broadcast states of neighbors at their triggering instants. According to the Lyapunov stability theory and algebraic graph theory, consensus conditions on the verification period and parameters in the triggering conditions are also provided. It is demonstrated that the maximum verification period under two triggering conditions are two times larger than the existing results. And a certain amount of communication between neighbors can be further reduced in the second one. Finally, the simulation examples prove the validity of the results proposed.

Output feedback consensus for input-delayed nonlinear multi-agent systems via event-triggered communication

This paper designs two periodic event-triggered control protocols to achieve the output feedback leaderless consensus for nonlinear multi-agent systems with uniform input delays, and leader-follower consensus with nonuniform input delays. The involved system permits uncertainties in input delays and inherent nonlinearities, which brings the challenge on the design of observers. To overcome this challenge, a compensator is constructed independent of nonlinearities and input delays for every agent. To guarantee the event-triggered communication among different agents, two new periodic triggering mechanisms are designed based on the discrete output information. Moreover, these triggering mechanisms naturally avoid constantly monitoring and the Zeno behavior since triggering conditions are only checked on sampling points. Specifically, the designed event-triggered output feedback control protocols achieve convergence not boundedness of consensus errors. Finally, two examples are listed to demonstrate the validity of the two event-triggered strategies.

Continuous and Periodic Event-Triggered Sliding-Mode Control for Path Following of Underactuated Surface Vehicles.

This article develops continuous and periodic event-triggered sliding-mode control (SMC) algorithms for path following of underactuated surface vehicles (USVs). Based on the SMC technology, a continuous path-following control law is designed. The upper bounds of quasi-sliding modes for path following of USVs are established for the first time. Subsequently, both continuous and periodic event-triggered mechanisms are considered and added into the proposed continuous SMC scheme. It is demonstrated that with appropriate selecting of control parameters, the use of hyperbolic tangent functions does not affect the boundary layer of quasi-sliding mode caused by event-triggered mechanisms. The proposed continuous and periodic event-triggered SMC strategies can make the sliding variables reach the quasi-sliding modes and stay in there. Moreover, energy consumption can be reduced. Stability analysis shows that the USV can follow a reference path by using the designed method. The simulation results show the effectiveness of the proposed control methods.

Predictor-Based Periodic Event-Triggered Adaptive Fuzzy Control for a Class of Nonlinear Systems

Predictor-Based Periodic Event-Triggered Adaptive Fuzzy Control for a Class of Nonlinear Systems

Dynamic Periodic Event-Triggered Control for Networked Control Systems Under Packet Dropouts

This article presents a co-design method of dynamic periodic event-triggering mechanism (DPETM) and output-based control law for networked control systems (NCSs) subject to inevitable imperfections such as limited network resources, exogenous disturbances and successive packet dropouts. The developed DPETM has the potential to make full use of scarce network resources compared to the periodic sampled-data control on the one hand, and is natural for practical digital platforms instead of a discretized version of continuous event-triggered control (CETC) one the other hand. In this paper, the whole closed-loop system is modeled a unified hybrid system by incorporating bilateral DPETM, successive packet dropouts effects and external disturbances, and an improved hybrid Lyapunov function is constructed for stability analysis. Based on the hybrid framework, some sufficient conditions are presented to guarantee <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{L}_2$</tex-math> </inline-formula> -stability of the system while tolerating a maximum allowable number of successive packet dropouts (MANSD). Furthermore, new linear matrix inequality (LMI) conditions for co-design of control law and triggering strategy are derived by introducing some constraints with the free variables and a modified Young’s inequality. In addition, this paper considers two scenarios relating to whether an acknowledgment scheme is employed or not. Finally, the effectiveness of the proposed method is verified by two illustrated examples and comparative studies. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —With the increasing requirement for reducing unnecessary waste of communication resources in modern industries, it is necessary to consider an alternative paradigm of the time-triggered control. In many digital control applications such as smart power grid, vehicle and remote surgery, the control tasks are often executed periodically, which makes it difficult for the theoretical results of CETC to be directly applied to practical digital platforms. The DPETM proposed in this paper, which only verifies the triggering conditions periodically at each sampling instant, is more suitable for practical digital platforms such as time-sliced embedded architectures compared to CETC. This paper investigates the stability problem for NCSs with DPETM subject to packet dropouts. Different from most of the existing literature on randomness of packet loss, this paper focuses on impact of the continuity of packet dropouts on system performance. Based on the hybrid framework and the Lyapunov approach, a co-design methodology of triggering condition and control law is proposed to ensure that the system satisfies the desired performance and can admit a MANSD.

Event-triggered output feedback control design for polynomial fuzzy systems

This paper presents a novel approach to event-triggered output feedback control of polynomial fuzzy systems that exhibit unmeasurable system states. To stabilize the system state, a fuzzy model-based event-triggered control scheme is proposed based on output measurement information. The transmission frequency is modulated using a periodic event-trigger protocol, which is scheduled by resorting to a set of historically released packets to ensure better dynamic performance. The event-triggering condition uses the current samples to determine the next trigger and also takes into account the triggering time-dependent gain parameter, thereby significantly reducing network burden. The proposed approach ensures the existence of both polynomial controller gain and event-triggered parameters by satisfying sufficient conditions based on the sum-of-squares approach and the polynomial fitting approximation algorithm. The addressed system’s stability conditions are solved using MATLAB SOSTOOLS. Three numerical examples, including an invented pendulum model, illustrate the superiority and applicability of the methodology. The main contributions of this work are the introduction of a triggering instant dependent periodic event-triggered output feedback control design, which reduces network traffic and enhances dynamic performance. The approach is validated through numerical examples, which demonstrate its superiority and applicability.

Aperiodic dynamic event-triggered control for linear systems: A looped-functional approach

The recent literature on event-triggered control has demonstrated the potential of dynamic periodic event-triggered control. Compared to continuous-time event-triggering rules, the benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon, which refers to the situation when there are an infinite number of updates in a bounded interval of time. The idea of periodic event-triggered control is to trigger the control law only at known allowable periodic sampling instants. In this paper, our objective is to relax the constraint on the periodicity of the allowable sampling instants and to adapt this framework to the dynamic event-triggered control, which has not been considered in the literature, as far as we are aware of. Following the successful efforts to assess the stability of aperiodic sampled-data control, here we propose a generic framework to emulate aperiodic dynamic event-triggered control law for linear systems, for which the allowable sampling instants are not necessarily equidistant. Such an analysis is made possible thanks to the looped-functionals framework, which gives the flexibility to consider the periodic/aperiodic static/dynamic event-triggered control in a single formulation. Finally, the efficiency of the proposed results is illustrated through the study of two academic examples.

A hybrid framework of dynamic periodic event-triggered networked control systems subject to time-varying delays

This paper investigates the dynamic output-feedback control for networked control systems (NCSs). The data transmissions in the sensor-to-controller and the controller-to-actuator channels are generated by the dynamic periodic event-triggering mechanism. Due to the existence of time-varying delays in the two channels, the updated data is received after a time delay. To cope with this problem, a hybrid dynamical framework of the NCSs is established. With the help of Lyapunov function-based approach, a new event-triggering condition is designed and sufficient conditions on input-to-state stability are derived. By introducing an auxiliary function, the obtained sufficient conditions are transformed into linear matrix inequalities and the explicit forms of the dynamic output-feedback controller gains are provided. Moreover, the upper bounds on the maximum allowable transfer intervals and the maximum allowable delays are derived. Finally, a numerical example illustrates the feasibility of the proposed method.

Chaos and Order in Event-Triggered Control

Event-triggered control (ETC) is claimed to provide significant reductions in sampling frequency when compared to periodic sampling, but little is formally known about its generated traffic. This work shows that ETC can exhibit very complex, even chaotic traffic, especially when the triggering condition is aggressive in reducing communications. First, by looking at the map dictating the evolution of states sampled, we characterize limit traffic patterns by observing invariant lines and planes through the origin, as well as their attractivity. Then, we present abstraction-based methods to compute limit metrics, such as limit average and limit inferior inter-sample time (IST) of periodic ETC (PETC), with considerations to the robustness of such metrics, as well as measuring the emergence of chaos. The methodology and tools allow us to find ETC examples that provably outperform periodic sampling in terms of average IST. In particular for PETC, we prove that this requires aperiodic or chaotic traffic.

Periodic Event-Triggered CACC and Communication Co-design for Vehicle Platooning

Cooperative Adaptive Cruise Control (CACC) based vehicle platooning can increase the safety and efficiency of traffic. This work looks into the communication and control problems of vehicle platooning, and proposes a control and communication co-design for CACC. First, an integrated radar system is presented. This system integrates sensing of relative position, speed, and communication between a predecessor and its follower. Second, a working scheme for the integrated radar system is presented. This scheme allows the radar systems to switch periodically between different working modes without interferences from other modes. Therefore, the relative position, speed, and communication can be asynchronously periodically updated to the controller. Third, a periodic event-triggered control approach is presented. This approach allows asynchronous periodic sampling of the output, and is deeply co-designed with the radar system and its working scheme. Delays are also considered in the control approach. The co-design CACC approach can guarantee the vehicle platoons to be string stable. A numerical example has shown the feasibility of the approach.

Periodic Event-Triggered Control for Networked Control Systems With External Disturbance and Input and Output Delays.

This article investigates the problem of periodic event-triggered output-feedback control for networked control systems in the presence of external disturbance and input and output delays. With the aid of the prediction technique, we first develop the predictor-based-extended state observer to reconstruct the system information, including the unknown state and disturbance. The periodic event-triggered output-feedback control law is then designed via the disturbance/uncertainty estimation and attenuation (DUEA) method, such that the communication times can be remarkably reduced and, at the same time, the disturbance rejection ability can be effectively enhanced. Under the predictor-based event-triggered control method, the influence of the time delays is effectively attenuated, and the effect of external disturbance is considerably attenuated due to the prediction technique and the DUEA method. By using the small-gain arguments, this article gives some sufficient stability conditions for the overall control system, and the explicit computations of sampling/updating period and time delays are presented as well. Finally, we employ a practical example and show some comparative simulation results to demonstrate the advantages of the predictor-based event-triggered control method proposed in this article.

Output-Based Dynamic Periodic Event-Triggered Control with Application to the Tunnel Diode System

Output-Based Dynamic Periodic Event-Triggered Control with Application to the Tunnel Diode System

Coordinated path following control for multi-unmanned surface vehicles with specified performance and periodic event-triggered mechanism

This paper addresses coordinated path following for underactuated multi-unmanned surface vehicles (MUSVs) with specified performance (SP) under the lumped disturbances, proposes a novel adaptive periodic event-triggered path following control strategy via relative threshold event-triggered mechanism. First, the MUSVs communicates through the directed topology cooperative control structure, and maintains a safe distance between each USV along one curve. Meanwhile, the transformed error function is applied to establish the position errors constraint, guaranteeing that the position error of each USV is confined within the specified performance in guidance system. Then, RBF neural network and adaptive parameter method are applied to estimate the lumped disturbances and its error boundary, which makes MUSVs’ coordinated system have strong anti-disturbance ability. Besides, periodic event-triggered control base on relative threshold is introduced, which not only reduces the update frequency of controller and energy consumption, also avoids Zeno behavior phenomenon. Stability analysis proves that coordinated path following control system is uniformly ultimately bounded. Comparative simulations reveal the effectiveness of the coordinated path following control scheme.

Adaptive prescribed settling time periodic event-triggered control for uncertain robotic manipulators with state constraints

In this paper, an adaptive prescribed settling time periodic event-triggered control (APST-PETC) is investigated for uncertain robotic manipulators with state constraints. In order to economize network bandwidth occupancy and reduce computational burden, a periodic event-triggered control (PETC) strategy is proposed to reduce the update frequency of the control signal and avoid unnecessary continuous monitoring. Besides, considering that the maneuverable space of the actual robotic manipulators is often limited, the barrier Lyapunov function (BLF) is applied to deal with the influence of the constraint characteristics on the robotic manipulators. Further, based on the one-to-one nonlinear mapping function of the system tracking error, an adaptive prescribed settling time control (APSTC) is designed to ensure that the system tracking error reaches the predetermined precision residual set within the prescribed settling time. Finally, theoretical analysis and comparative experiments are given to verify its feasibility.

Periodic event-triggered dynamic output feedback control for networked control systems subject to packet dropouts

This paper proposes a co-design method of dynamic output feedback control law and periodic event-triggered control (PETC) strategy to tolerate a maximum allowable number of successive packet dropouts (MANSDs) in networked control systems (NCSs). For the purpose of striking a balance between saving limited communication resources and reducing complexity of the transmission implementation, we present the periodic event-triggering mechanism (PETM), in which the triggering conditions only needs to be monitored at each event-verifying instant. In NCSs, packets often suffer from some interference in network transmission, such as packet losses. For packet dropouts, we introduce a dropout variable and model the whole closed-loop systems as a hybrid system. Furthermore, some stability conditions for co-design are given by a novel Lyapunov function and stability theorems of hybrid systems, and the explicit designs parameters of controller and triggering conditions are presented to ensure L2 stability. Finally, two illustrated examples are given to show the effectiveness of the proposed design methods.

Approximate Optimal Control for Nonlinear Systems With Periodic Event-Triggered Mechanism.

This article investigates the approximate optimal control problem for nonlinear affine systems under the periodic event triggered control (PETC) strategy. In terms of optimal control, a theoretical comparison of continuous control, traditional event-based control (ETC), and PETC from the perspective of stability convergence, concluding that PETC does not significantly affect the convergence rate than ETC. It is the first time to present PETC for optimal control target of nonlinear systems. A critic network is introduced to approximate the optimal value function based on the idea of reinforcement learning (RL). It is proven that the discrete updating time series from PETC can also be utilized to determine the updating time of the learning network. In this way, the gradient-based weight estimation for continuous systems is developed in discrete form. Then, the uniformly ultimately bounded (UUB) condition of controlled systems is analyzed to ensure the stability of the designed method. Finally, two illustrative examples are given to show the effectiveness of the method.

Data‐driven analysis and control of periodic event‐triggered continuous‐time systems

AbstractThis article is concerned with data‐driven analysis and controller design for continuous‐time sampled‐data systems. The linear system considered in this paper is controlled under the periodic event‐triggering transmission mechanism. Firstly, the periodic event‐triggered control (PETC) systems are modeled and analyzed by the time‐delay approach. And model‐based stability conditions are presented by invoking the Lyapunov stability approach. Secondly, based on the model‐based conditions and a popular data‐based representation, data‐based stability criteria are deduced by using only noisy data. The stability criteria guarantee the stability properties robustly for all unknown systems consistent with the measured data. The data‐driven estimation of the maximum detecting interval (MDI) is also obtained directly without model knowledge. Beyond that, the data‐based method for the controller design as well as computing a possibly large MDI under various triggering parameters is put forth. Finally, the effectiveness of the proposed methods is demonstrated by the numerical simulation and the hardware‐in‐the‐loop (HIL) experiment.