Self-triggered Control Scheme Research Articles

Exponential synchronization of complex networks via intermittent dynamic event-triggered control

In this paper, the exponential synchronization in mean square (ESMS) of complex networks (CNs) under intermittent dynamic event-triggered control strategy (IE-TCS) is discussed. Compared with the existing literature, the intermittent control strategy (ICS) proposed is awakened when a certain situation occurs rather than periodically, which can better improve the control efficiency. The average control rate in this paper is more flexible. Furthermore, we give a positive lower bound for the event-triggered intervals to ensure that Zeno behavior does not occur. Combining the graph-theoretic approach with the Lyapunov method, some criteria for ESMS are obtained. In particular, we also discuss the ESMS of non-strongly connected CNs under IE-TCS. Besides, we combine the self-triggered control strategy (S-TCS) with the ICS, which is called the intermittent S-TCS, to study the ESMS of CNs. For practicability, the theoretical results are applied to research the ESMS of the microgrid system, and some relevant sufficient conditions are derived. Eventually, numerical simulations are put forward to verify the effectiveness of theoretical results.

Formula omitted] containment control for multi-unmanned aerial vehicle systems: A self-triggered control scheme

This paper is concerned with the containment control problem for multi-unmanned aerial vehicle (multi-UAV) systems with data transmission among agents during a limited-bandwidth network. A good deal of data transmitted during a limited-bandwidth network may result in data collision, which brings negative effects on controller design and containment tracking implementation. To reduce the network load during data transmission, a consensus condition and a triggering subsidiary condition are first proposed to realize the containment tracking with H∞ performance by using the triggered states. Then a self-triggered scheme is established under a multi-agent framework, in which the next triggering instant is calculated beforehand by using the past states. Combined with the self-triggered scheme, a containment controller is obtained via solving the derived consensus condition, which ensures that follower UAVs are driven into a convex set surrounded by leader UAVs. Finally, the validity of the self-triggered containment control method is proved through a simulation experience.

Fully Distributed Event/Self-Triggered Bipartite Output Formation-Containment Tracking Control for Heterogeneous Multiagent Systems.

This article considers the bipartite time-varying output formation-containment tracking control issue for general linear heterogeneous multiagent systems with multiple nonautonomous leaders, where the full states of agents are not available. Both cooperative interaction and antagonistic interaction between neighboring agents are taken into account. First, an observer is constructed using the output information to observe the state information. Then, based on the information between neighboring agents, an independent asynchronous fully distributed event-triggered bipartite compensator is put forward to estimate the convex hull spanned by the states of multiple leaders. Note that the compensator does not require to use of any global information. Subsequently, a formation-containment tracking control strategy based on the observer and compensator and an algorithm to determine its control parameters are given. The Zeno behavior is further proved to be excluded in any finite time. In addition, a novel self-triggered control strategy based only on the sampled information at triggering instants is also formulated, which avoids continuous communication among agents. Finally, a numerical example is given to validate the effectiveness and performance of the proposed control strategies.

Event-Based Fixed-Time Secure Cooperative Control for Nonlinear Cyber-Physical Systems Under Denial-of-Service Attacks

This paper investigates the problem of the fixed-time secure cooperative control for a class of nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. First of all, an event-based data transmission scheme is proposed to solve the fixed-time secure leader-following consensus in the occurrence of connective-preserved DoS attacks. Besides, a novel measurement error is developed to avoid Zeno behavior. However, the initial communication topology may inevitably be disconnected by malicious adversaries. To solve this difficulty, a new fixed-time secure observer is designed to estimate the leader information. Moreover, a self-triggered control strategy is proposed, which not only avoids the continuous communication but also restores the secure leader-following consensus subject to connective-preserved/broken DoS attacks. Then the characteristic of the allowable connective-preserved/broken DoS attacks can be obtained. Finally, simulation results show the effectiveness of the proposed method.

Integrated learning self-triggered control for model-free continuous-time systems with convergence guarantees

This paper presents an integrated self-triggered control strategy with convergence guarantees for model-free continuous-time systems using reinforcement learning. To consider the control cost and triggering consumption in the self-triggered scheme simultaneously, an integrated cost function is proposed. With this integrated cost function, the trade-off between the triggering occupation and control performance could be adjusted according to different requirements. Then, the actor-critic framework of reinforcement learning is employed to learn the control inputs and triggering intervals by minimizing the corresponding integrated cost function. Considering the divergent characteristics between the control inputs and triggering intervals, two different actors are utilized to learn the triggering strategy and control policy, respectively. Also, the convergence of the developed model-free self-triggered control learning algorithm is proved to ensure the limited learning duration of both the control policy and triggering strategy. The proposed framework can be used to design self-triggered controllers for a wide range of engineering systems with unknow dynamics, including control of aircraft, robots, chemical processes, and other automated systems. Finally, the effectiveness and superiorities of the proposed method are verified by an illustrative example.

Self-triggered coordination of distributed renewable generators for frequency restoration in islanded microgrids: A low communication and computation strategy

Microgrid provides a promising solution to consume more distributed renewable energies. To coordinate the increasingly developed distributed renewable generators in a high flexibility and high efficiency way, distributed event-triggered mechanisms have been widely investigated in the literature to reduce the communication requirement and hence improve the control performance of microgrids. However, most of the event-triggered mechanisms mandate continuous calculation of complicated triggering conditions, which may in turn impose the computation burden of the controller and increase additional energy cost. To this end, this paper presents a distributed self-triggered control strategy for the frequency restoration in islanded microgrids with the aid of a linear clock. With this self-triggered solution, each distributed generator’s controller decides its own control and communication actions based on monitoring the linear clock, which excludes continuous calculation of any triggering conditions. Thus, the communication and computation costs can be reduced simultaneously. Moreover, Zeno behavior can be naturally excluded by the above design. The results of theoretical analysis and simulations show that the proposed distributed self-triggered control scheme can effectively coordinate distributed renewable generators with very low communication and computation requirements. Therefore, this research can improve the coordination efficiency of microgrids greatly, which is very useful for guiding the efficient operation of large-scale distributed renewable generators.

Self-Triggered Adaptive Dynamic Programming for Model-Free Nonlinear Systems via Generalized Fuzzy Hyperbolic Model

For nonlinear systems, a novel adaptive dynamic programming (ADP) algorithm of self-triggered control (STC) strategy is proposed. This is a novel attempt to introduce self-triggering into the ADP algorithm. First, an identifier based on a generalized fuzzy hyperbolic model (GFHM) is established, which only uses input–output data to reconstruct the unknown system, thus reducing the requirements for system dynamics. Then, the critic neural network (NN) adjusts continuously, while actor NN updates the control strategy only at triggering instants. The event-triggered control (ETC) reduces the use of control resources and improves the anti-interference capability. However, it requires dedicated hardware to monitor whether triggering rules are violated, which is not feasible on most general-purpose devices. Hence, we propose a novel technique, which uses the current state of the device to determine the state measurement at the next moment, calculate the control law, and then abandon persistently monitoring of the plant. This technique is called STC. Finally, the closed-loop system is guaranteed to be ultimate uniform boundedness (UUBs). Furthermore, a simulation example is given.

Self-triggered multi-mode control of Markovian jump systems

This paper is concerned with the problem of self-triggered multi-mode control for a class of Markovian jump systems, in which the system states are transmitted to the controller via a communication network with limited bandwidth. In order to achieve the desired performance of the closed-loop system via utilizing a controller with fewer modes, a mode monitoring mechanism related to the system modes is employed to describe the jumping characteristics among different controller modes. Based on the mode monitoring mechanism, a multi-mode controller is constructed, in which the number of controller modes may be fewer than the one of system modes. Moreover, a self-triggered strategy is developed to reduce network loads, according to which the next triggering instant on state transmission is calculated via the past and current transmitted states at the triggering instants. By introducing a sufficiently small scalar, a solving algorithm is proposed for obtaining the self-triggered multi-mode controller gains to ensure the stochastic stability of the closed-loop system with the given L2 gain performance. Finally, the simulation results are provided to illustrate the proposed self-triggered control scheme.

Self-triggered scheduling for the stabilization of impulsive Boolean control networks

This paper investigates the self-triggered control scheduling in order to stabilize impulsive Boolean control networks (IBCNs) towards the desired state. Compared with the event-triggered control strategy, self-triggered control scheduling has the ability to determine the next update time of feedback controller in advance by resorting to network states and control input at the current sampled time. Moreover, by establishing the Lyapunov theory for IBCNs, two necessary and sufficient conditions are accordingly derived for the global stabilization of IBCNs in the hybrid domain and in the time domain. Subsequently, we design a flexible self-triggered control scheme with the aim of stabilizing IBCNs to a pre-assigned state in the time domain and in the hybrid domain, respectively. Finally, we apply this control strategy in a biological example to demonstrate the feasibility of theoretical results.

Self-triggered control of probabilistic Boolean control networks: A reinforcement learning approach

In this work, strategies to devise an optimal feedback control of probabilistic Boolean control networks (PBCNs) are discussed. Reinforcement learning (RL) based control is explored in order to minimize model design efforts and regulate PBCNs with high complexities. A Q-learning random forest (QLRF) algorithm is proposed; by making use of the algorithm, state feedback controllers are designed to stabilize the PBCNs at a given equilibrium point. Further, by adopting QLRF stabilized closed-loop PBCNs, a Lyapunov function is defined, and a method to construct the same is presented. By utilizing such Lyapunov functions, a novel self-triggered control (STC) strategy is proposed, whereby the controller is recomputed according to a triggering schedule, resulting in an optimal control strategy while retaining the closed-loop PBCN stability. Finally, the results are verified using computer simulations.

Wide-area damping power system control based on robust self-triggered model predictive control

Unavoidable random disturbances during the operation of large-scale interconnected power systems may undermine their stability. To prevent this problem, we propose a damping control method based on robust self-triggered model predictive control. First, we linearize the power system model and determine the controller installation location and feedback signal through geometric measurements. Subsequently, the model order is reduced by applying Schur method for balanced truncation. According to the assumed distribution and boundary range of random disturbance, the multi-cell robust predictive control minimax optimization problem described by the vertex is established. By deriving the upper bound of the maximum problem, the minimax problem is transformed into minimizing the upper bound problem to deal with the uncertain problem, which is transformed into linear matrix inequality for controller design. Finally, we introduce a self-triggered control strategy that avoids solving a constrained optimization problem at every time step. This strategy reduces the number of controller responses and resource requirements for sampling and communication, thereby improving computational efficiency. Selecting the two zone four-machine system as the test system, the simulation results demonstrate that the proposed control strategy can effectively eliminate the effect of random disturbances on the stable operation of power systems, improve the damping characteristics of power systems, and suppress low-frequency oscillations.

Resilient predictive control strategy of cyber–physical systems against FDI attack

Self-triggered control strategy has been widely applied in cyber–physical systems, which are unavoidable to suffer various malicious cyber-attacks. This paper is aimed at solving the cyber security problem of self-triggered model predictive control in cyber–physical systems under false data injection attack, and a resilient control strategy is proposed based on control signal reconstruction. Firstly, the continuous control signal is discretely sampled at the controller side, and the key data samples are determined and protected. Then, the discretised control samples are transmitted through the network channel, based on which the control signal is reconstructed at the controlled system side according to a preset mode. It is further theoretically proved that the control signals reconstructed from the critical control samples can guarantee the feasibility and stability of the control system against the FDI attacks. Finally, a simulation verification on a robot system is conducted to verify the effectiveness of the proposed algorithm.

Dynamic self-triggered control for nonlinear systems with delays

Self-triggered control (STC) is a resource efficient approach to determine sampling instants for Networked Control Systems (NCS). Recently, a dynamic STC strategy based on hybrid Lyapunov functions for nonlinear NCS has been proposed in Hertneck and Allgöwer (2021b), however with limitation to NCS without transmission delays. In this paper, we extend this strategy for nonlinear NCS with transmission delays. The capability to handle systems with delays makes it possible to use the resulting dynamic STC mechanism in many practical scenarios where instant transmissions without delays cannot be guaranteed. The proposed dynamic STC mechanism guarantees stability despite bounded transmission delays. The effectiveness of the mechanism is illustrated with a numerical example and compared to state-of-the art literature.

Secure Synchronization for Cyber-Physical Complex Networks Based on Self-Triggering Impulsive Control: Static and Dynamic Method

This paper investigates a self-triggered control scheme for a class of cyber-physical complex networks under deception attacks. The false data generated by attacks in both sensor-to-controller channels and controller-to-actuator channels are assumed to obey the Bernoulli distribution. By jointly combining distributed impulsive control scheme, time-varying impulsive effects and self-triggered strategy, a novel distributed self-triggered impulsive controller is elaborately designed. By integrating the definition of average impulsive gain, the contradiction analysis and Lyapunov stability theorem, sufficient conditions are derived for ensuring the secure synchronization within a given error bound. In addition, for further decreasing the triggering frequency and energy consumption, the advanced dynamic self-triggered criteria are obtained. It is worth mentioning that the updating laws adopted for dynamic self-triggered protocol in this paper is non-monotonic, which benefits to deal with the bounded synchronization. Finally, two numerical simulations are given to illustrate the feasibility of derived results.

Integral-Type Edge-Event- and Edge-Self-Triggered Synchronization to Multi-Agent Systems with Lur’e Nonlinear Dynamics

This paper proposes event- and self-triggered control strategies to achieve distributed synchronization for multiple Lur’e systems with unknown static nonlinearities. Firstly, the integral-type edge-event-triggered function is designed here without Zeno behaviors. Compared to the traditional event-triggered schemes, the considered algorithm has the advantages of reducing controller update frequency and sensor energy consumption. Then, the integral-type self-triggered is further investigated, which implements discontinuous monitoring and discontinuous agent listening. Finally, numerical simulations verified the effectiveness and superiority of our policies.

A Zeno-Free Self-Triggered Approach to Practical Fixed-Time Consensus Tracking With Input Delay

This article considers the practical fixed-time self-triggered consensus tracking problem of delayed multiagent networks (MANs) subject to external disturbances under undirected topology and directed topology. The fixed-time consensus implies that the consensus is reached in a finite time and the convergence time is independent of initial conditions under the nonlinear consensus protocols. A self-triggered control (STC) strategy is developed based on the event-triggered control (ETC) strategy. For the ETC strategy, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid a nondifferential problem and Zeno behavior. To avoid continuous monitoring, the STC strategy is presented. Furthermore, the minimal interevent interval is strictly positive, which implies that no Zeno behavior occurs in the STC strategy. Finally, a numerical example is presented to verify the availability of the algorithms.

Self-Triggered Scheduling for Boolean Control Networks

It has been shown that self-triggered control has the ability to deal with cases with constrained resources by properly setting up the rules for updating the system control when necessary. In this article, self-triggered stabilization of the Boolean control networks (BCNs), including the deterministic BCNs, probabilistic BCNs, and Markovian switching BCNs, is first investigated via the semitensor product of matrices and the Lyapunov theory of the Boolean networks. The self-triggered mechanism with the aim to determine when the controller should be updated is provided by the decrease of the corresponding Lyapunov functions between two consecutive samplings. Rigorous theoretical analysis is presented to prove that the designed self-triggered control strategy for BCNs is well defined and can make the controlled BCNs be stabilized at the equilibrium point.

Periodic event‐triggered and self‐triggered control of singular system under stochastic cyber‐attacks

The periodic event-triggered control (PETC) and self-triggered control (STC) for networked singular systems under denial-of-service (DoS) attack and deception attack are studied. Due to the fact that DoS attack is able to prevent the control input from transmitting and deception attack falsifies the control input as a non-linear disturbance, a closed-loop system is constructed with different control inputs based on the switched system method. Next, the attention is focused on the design of PETC and STC schemes. PETC scheme adopts the input delay approach to transform the closed-loop system into a switched singular time-delay system and adjusts the triggering intervals by the frequency and duration of cyber-attacks. STC scheme relies on a reduced-order system derived from the original singular system and utilises the current sampled information to predict the next triggering instant. Then, exponential stability criteria are derived by codesigning the triggering parameter and controller gain. Finally, a small-signal version of the structure-preserving power network model is given to demonstrate the effectiveness of the proposed methods.

Fixed-Time Leader–Follower Consensus of Networked Nonlinear Systems via Event/Self-Triggered Control

This brief addresses the fixed-time event/self-triggered leader-follower consensus problems for networked multi-agent systems subject to nonlinear dynamics. First, we present an event-triggered control strategy to achieve the fixed-time consensus, and a new measurement error is designed to avoid Zeno behavior. Then, two new self-triggered control strategies are presented to avoid continuous triggering condition monitoring. Moreover, under the proposed self-triggered control strategies, a strictly positive minimal triggering interval of each follower is given to exclude Zeno behavior. Compared with the existing fixed-time event-triggered results, we propose two new self-triggered control strategies, and the nonlinear term is more general. Finally, the performances of the consensus tracking algorithms are illustrated by a simulation example.

Self-Triggered Consensus of Vehicle Platoon System With Time-Varying Topology.

This paper focuses on the consensus problem of a vehicle platoon system with time-varying topology via self-triggered control. Unlike traditional control methods, a more secure event-triggered controller considering the safe distance was designed for the vehicle platoon system. Then, a Lyapunov function was designed to prove the stability of the platoon system. Furthermore, based on the new event-triggered function, a more energy efficient self-triggered control strategy was designed by using the Taylor formula. The new self-triggered control strategy can directly calculate the next trigger according to the state information of the last trigger. It avoids continuous calculation and measurement of vehicles. Finally, the effectiveness of the proposed two self-triggered control strategies were verified by numerical simulation experiments.