Event-triggered Control Law Research Articles

Event-Triggered Dynamic Surface Control of an Underactuated Autonomous Surface Vehicle for Target Enclosing

This article addresses the event-triggered dynamic surface control of an underactuated autonomous surface vehicle with unknown kinetics for circumnavigating a dynamic target with unknown velocity. A modular design approach to the event-triggered dynamic surface control is proposed for target enclosing. In the estimator module, an extended state observer is employed for estimating the relative motion between the target and the surface vehicle. A fuzzy system is used for online modeling the unknown vehicle kinetics. In the controller module, an event-triggered dynamic surface control law is constructed by using the estimated relative velocities and vehicle kinetics in the estimator module. In the control law, a triggered mechanism is introduced to reduce the transmission load and the execution rate of actuators. Besides, the control inputs are bounded with the aid of a projection operator and saturated functions. The input-to-state stability of the closed-loop target enclosing system is proven through Lyapunov analysis. Simulation results substantiate the effectiveness of the event-triggered dynamic surface control method for circumnavigating a maneuvering target.

Event‐triggered distributed H ∞ control of physically interconnected mobile Euler–Lagrange systems with slipping, skidding and dead zone

This study addresses an event-triggered distributed ℋ ∞ control method by extending traditional zero-sum differential games for physically interconnected non-holonomic mobile mechanical multi-agent systems with external disturbance and slipping, skidding and dead-zone disturbances. Initially, a problem of physically interconnected kinematic and dynamic control is transformed into an equivalent problem of event-triggered distributed ℋ ∞ control. Subsequently, the traditional two-player zerosum differential game is extended to a three-player zero-sum differential game, where a new player is included to approximate the worst dead-zone disturbance. To find player policies, an event-triggering condition and an event-triggered control law are proposed via neural networks (NNs). Although an NN weight-tuning law is designed on the basis of adaptive dynamic programming techniques, it can relax identification procedures for unknown drift dynamics and persistent excitation conditions. It also guarantees that the closed system is stable and the cost function converges to the bounded ℒ 2 -gain optimal value, while the Zeno behaviour is excluded. Finally, the effectiveness of the proposed method is verified by an application to a dead-zone torque multi-mobile robot system through numerical simulations.

Event-Triggered Bipartite Consensus for Multiagent Systems: A Zeno-Free Analysis

In this article, the bipartite consensus of first-order multiagent systems with a connected structurally balanced signed graph is studied. To reduce the communications among agents, a distributed event-triggered control law is proposed, where the event-triggering condition of each agent only uses its own state and the sampled states of its neighbours, and no knowledge of the global network topology is required. By relating to the nonexistence of some finite-time convergence, a novel analysis is given to show that there is no Zeno behavior in the proposed event-triggered multiagent system. Then, from the Lyapunov stability theory and the algebraic graph theory, it is proved that all agents can reach agreement with an identical magnitude but opposite signs. Finally, a numerical example is given to illustrate the efficiency and feasibility of the proposed results.

Practical Prescribed-Time Event-Triggered Bipartite Consensus of Linear Multi-Agent Systems

In this paper, the practical prescribed-time bipartite consensus problem of linear multi-agent systems with a connected structurally balanced signed graph is investigated by using event-triggered mechanism. Novel event-triggered control law and triggering condition are proposed for each agent, in which the sampled states of agent and its neighbors are needed. By using the algebraic graph theory and Lyapunov stability theory, it is verified that the practical bipartite consensus can be achieved at fully prespecified time with an adjustable neighborhood range. Moreover, a theoretical discussion is provided to illustrate that Zeno behavior can be avoided during the whole time span. The feasibility of the presented control strategy is validated by a simulation result.

Robust Stabilization of a Class of Nonlinear Systems via Aperiodic Sensing and Actuation

This article proposes a framework to design a robust controller for a class of nonlinear networked control systems using aperiodic feedback information. Here, the nonlinearity and parameter variations of system model are considered as sources of uncertainty. To tackle the uncertainty in system dynamics, a linear robust control law is derived by applying the optimal control theory. Two different architectures of closed-loop systems are considered. In the first one, system and controller are not collocated; instead they are interconnected by means of a shared communication network. In the second architecture, system, controller and actuator are all collocated with their respective outputs available at all time-instead, sensors and controller are connected through a shared communication channel. In both architectures, the feedback loop is closed through the network. Owing to its shared nature, the network may suffer from bandwidth limitations. To save the network bandwidth, state and input information are transmitted aperiodically within the feedback loop. With this aim, the paper adopts an event-triggered control technique so as to reduce the transmission overhead. Applying Input-to-State Stability theory, we derive two different event-triggered robust control laws that stabilize the uncertain nonlinear system. Finally, we show that the designed event-triggered controllers satisfy the trade-off between control performance and saving in network bandwidth in the presence of uncertainty. The developed control algorithm is implemented and validated through numerical simulations.

Event-triggered Control for Heterogeneous Discrete-time Multi-agent Systems Subject to Uncertainties and Noises

This paper investigates the event-triggered control problem of heterogeneous discrete-time multi-agent systems (MASs) subject to uncertainties and noises. Based upon the output regulation theory, a new distributed event-triggered control scheme is proposed to reduce communication burden and attenuate effects of stochastic noises. Two types of event-triggered control laws based on dynamic state feedback and dynamic output feedback are designed, respectively. Moreover, to compensate parameter uncertainties, a p-copy internal model is synthesized into the designed controllers. It is shown that all tracking errors are exponentially ultimately bounded in the mean square sense regardless of uncertainties and noises. Several examples are finally given to demonstrate the validity of main results.

Adaptive Fuzzy Event-Triggered Control for Stochastic Nonlinear Systems With Full State Constraints and Actuator Faults

In this paper, an adaptive fuzzy output feedback control problem is investigated for a class of stochastic nonlinear systems in which the fuzzy logic systems are adopted to approximate the unknown nonlinear functions. A reduced-order observer and a general fault model are designed to observe the unavailable state variables and describe the actuator faults, respectively. An event-triggered control law is developed to reduce the communication burden from the controller to the actuator. Meanwhile, the barrier Lyapunov functions are constructed to guarantee that all the states of the stochastic nonlinear system are not to violate their constraints. Furthermore, an observer-based adaptive fuzzy event-triggered control strategy is proposed for the full-state-constrained nonlinear system with actuator faults based on backstepping technique, which can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

Event-triggered backstepping control for attitude stabilization of spacecraft

To decrease the communication frequency between the controller and the actuator, this paper addresses the spacecraft attitude control problem by adopting the event-triggered strategy. First of all, a backstepping-based inverse optimal attitude control law is proposed, where both the virtual control law and the actual control law are respectively optimal with respect to certain cost functionals. Then, an event-triggered scheme is proposed to realize the obtained inverse optimal attitude control law. By designing the event triggering mechanism elaborately, it is guaranteed that the trivial solution of the closed-loop system is globally exponentially stable and there is no Zeno phenomenon in the closed-loop system. Further, the obtained event-triggered attitude control law is modified and extended to the more general case when the disturbance torque cannot be ignored. It is proved that all states of the closed-loop system are bounded, the attitude error can be made arbitrarily small ultimately by choosing appropriate design parameters and the Zeno phenomenon is excluded in the closed-loop system. In the proposed event-triggered attitude control approaches, the control signal transmitted from the controller to the actuator is only updated at the triggered time instant when the accumulated error exceeds the threshold defined elaborately. Simulation results show that by using the proposed event-triggered attitude control approach, the communication burden can be significantly reduced compared with the traditional spacecraft control schemes realized in the time-triggered way.

Distributed Optimal Coordination for Heterogeneous Linear Multiagent Systems With Event-Triggered Mechanisms

This note considers the distributed optimal coordination (DOC) problem for heterogeneous linear multiagent systems. The local gradients are locally Lipschitz and the local convexity constants are unknown. A control law is proposed to drive the states of all agents to the optimal coordination that minimizes a global objective function. By exploring certain features of the invariant projection of the Laplacian matrix, the global asymptotic convergence is guaranteed utilizing only local interaction. The proposed control law is then extended with event-triggered communication schemes, which removes the requirement for continuous communications. Under the event-triggered control law, it is proved that no Zeno behavior is exhibited and the global asymptotic convergence is preserved. The proposed control laws are fully distributed, in the sense that the control design only uses the information in the connected neighborhood. Furthermore, to achieve the DOC for linear multiagent systems with unmeasurable states, an observer-based event-triggered control law is proposed. A simulation example is given to validate the proposed control laws.

Event-Triggered Robust Output Regulation of Uncertain Linear Systems With Unknown Exosystems

This article studies the robust output regulation problem (RORP) for a class of uncertain linear systems with unknown exosystems via event-triggered control (ETC). Compared with existing related works, the system matrix of the exosystem under consideration is allowed to contain unknown parameters. Based on an adaptive internal model, an ETC strategy composed of an event-triggered adaptive output feedback control law and an output-based event-triggering mechanism is proposed such that the RORP is solved. It is shown that under the proposed ETC strategy, the tracking error converges to zero asymptotically in spite of the unknown exosystem, and meanwhile the occurrence of Zeno behavior is prevented. Finally, two examples are provided to illustrate the effectiveness of the proposed control strategy.

Adaptive Fuzzy Event-Triggered Control for Leader–Following Consensus of High-Order Nonlinear Systems

This article is concerned with the adaptive fuzzy event-triggered control for leader-following consensus of high-order nonlinear systems under directed communication topologies. Utilizing fuzzy logic systems to model the uncertain dynamics of the followers, a novel adaptive fuzzy event-triggered control law is presented, and a distributed event-trigger condition is proposed, simultaneously. The developed adaptive fuzzy event-triggered control is carried out by the violation of the designed event-trigger condition, which can realize ultimate state synchronization with bounded tracking errors. Moreover, the data transmissions and the frequency of the control law updates can be significantly reduced compared with the control law with fixed sampling period. In addition, it is proved that the Zeno behavior is excluded in the proposed control scheme. Finally, a simulation example is provided to illustrate the obtained theoretical results.

Fully Distributed Event-triggered Semi-global Consensus of Multi-agent Systems with Input Saturation and Directed Topology

This paper studies the consensus problem of multi-agent systems with input saturation and directed communication topology, by utilizing the low-gain feedback method and the event-triggered control laws. Two event-triggered control laws, the centralized and the distributed laws, are proposed to guarantee semi-global consensus of the multi-agent systems. Then, a sufficient condition is presented to prove strictly positive low bound of inner-event time, i.e., the Zeno behavior can be avoided. Finally, the effectiveness of the proposed event-triggered laws is further verified by an example.

Distributed Event-Triggered Secondary Voltage Control for Microgrids With Time Delay

We consider the distributed secondary voltage control problem for microgrids subject to delays in a connected communication topology. For each distributed generator (DG), a distributed event-triggered control law, which uses its own voltage and those of its neighbors, along with a strategy for its triggering, are designed. Under these distributed event-triggered control laws, the magnitudes of the output voltages of all DGs can be synchronized to their reference value subject to a bounded time-varying delay that can be arbitrarily large, and no Zeno behavior will occur. The simulation results illustrate the theoretical conclusions.

Event-triggered uniform ultimate bound control for linear systems with time-varying delay

This paper investigates an effective event-triggered control for linear systems with time-varying delay. For reducing the sampled data transmission amount, a novel event-trigger is proposed wherein a state-independent threshold is involved. For guaranteeing uniformly ultimately bounded stability, an event-triggered feedback control law is proposed. By aid of a new free-weight matrix technique, the event-trigger and control co-design method is conveniently obtained. By pre-specifying the threshold of the event-trigger, the event-triggered frequency and the ultimate state convergence region can be simultaneously regulated. In addition, the convergence rate of closed-loop system is pre-specifiable as well. More significantly, the minimal event-triggering time interval is given. During that time interval, the event-trigger can not be violated, thus the Zeno phenomena is excluded naturally. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Event-triggered global stabilization of general linear systems with bounded controls

This paper studies the problem of global stabilization of general linear systems using event-triggered bounded controls. The system dynamics is decomposed into single input subsystems with various dynamic characteristics. Based on the dynamics of the subsystems, both an event-triggered state feedback law and an event-triggered output feedback law are constructed. Event-triggering updating strategies for the two control laws are designed accordingly. These event-triggered control laws are shown to achieve global asymptotic stabilization. The absence of the Zeno behavior is also established. The validity of the theoretical results is illustrated by numerical simulation.

Distributed Dynamic Event-Triggered Control for Cooperative Output Regulation of Linear Multiagent Systems.

This paper investigates the cooperative output regulation problem for heterogeneous linear multiagent systems under fixed communication graphs via event-triggered control. A fully distributed event-triggered dynamic output feedback control law is proposed based on the feedforward design approach. At the same time, a fully distributed dynamic event-triggering mechanism is designed so that each agent can determine when to broadcast its information to its neighbors. Compared with existing related results, both the control law and the event-triggering mechanism in this paper are independent of any global information. It is shown that with the proposed dynamic event-triggered control strategy, the cooperative output regulation problem can be solved in a fully distributed manner by intermittent communication. Moreover, Zeno behavior can be strictly ruled out for each agent. Finally, the effectiveness of the proposed dynamic event-triggered control strategy is validated by a numerical example.

Dynamic Event-Triggered and Self-Triggered Control for Multi-agent Systems

We propose two novel dynamic event-triggered control laws to solve the average consensus problem for first-order continuous-time multiagent systems over undirected graphs. Compared with the most existing triggering laws, the proposed laws involve internal dynamic variables, which play an essential role in guaranteeing that the triggering time sequence does not exhibit Zeno behavior. Moreover, some existing triggering laws are special cases of ours. For the proposed self-triggered algorithm, continuous agent listening is avoided as each agent predicts its next triggering time and broadcasts it to its neighbors at the current triggering time. Thus, each agent only needs to sense and broadcast at its triggering times, and to listen to and receive incoming information from its neighbors at their triggering times. It is proved that the proposed triggering laws make the state of each agent converge exponentially to the average of the agents’ initial states if and only if the underlying graph is connected. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Event-triggered fault tolerant control for spacecraft formation attitude synchronization with limited data communication

This paper investigates the leader-following attitude consensus problem of a group of n-th spacecrafts with actuator fault and limited data communication, where the event-triggered based sending mechanism is considered to decrease communication burthen. In this design, unknown actuator faults and external disturbances are considered, and an event-triggered based adaptive distributed cooperative attitude control law is developed to solve the multiple spacecrafts formation control problem. It is shown that leader-following attitude synchronization can be achieved under the designed event-triggered control law. Finally, a simulation example is provided to illustrate the effectiveness of the proposed attitude coordination control techniques.

Event-Triggered Leader-Following Consensus for Nonlinear Multiagent Systems Subject to Actuator Saturation Using Dynamic Output Feedback Method

This paper addresses the distributed event-triggered consensus problem for a class of nonlinear multiagent systems subject to actuator saturation. A new distributed event-based dynamic output feedback controller is put forward via the relative output measurements of neighboring agents. It removes the impractical assumptions that the controllers for agents have to update continuously and the observers embedded in agents have to share information with their neighbors, thus the energy consumptions of agents are significantly reduced. Two event-triggered strategies for the cases with and without continuous communication among neighboring agents are established. Sufficient conditions are derived in terms of matrix inequalities to guarantee the exponential leader-following consensus. The problem of designing a distributed event-triggered control law such that the domain of attraction for consensus errors is enlarged, formulated, and solved as an optimization problem with matrix inequality constraints. Simulation results are given to verify the effectiveness of the theoretical results.

Formation-containment control of networked Euler–Lagrange systems: An event-triggered framework

To improve the concurrency of leaders’ formation and followers’ containment, a difficult problem of designing the formation controller and the containment controller simultaneously should be addressed for networked systems. Motivated by this, this paper presents an even-triggered control framework for networked Euler–Lagrange systems to achieve formation-containment control even in the presence of uncertain parameters. An event-triggered formation controller is firstly designed for leaders to achieve the desired configuration. An event-triggered containment control law is then developed to guarantee that all the followers can converge to the convex hull formed by leaders. The key feature of the containment control law is that it does not necessitate any relative velocity information with respect to neighbor followers. Each controller’s gains are adaptively tuned using only local information. The parametric uncertainties are accommodated by using the adaptive updating law. Zeno behaviors of the triggering time sequences are also excluded. As a result, the communication burden of formation-containment system can be reduced. Numerical simulation is finally presented to verify the effectiveness of the proposed event-triggered formation-containment control framework.