Event-based Control Research Articles

Event-triggered bipartite consensus to heterogeneous multiagent systems under DoS attacks: A fully distributed method

This paper studies event-triggered bipartite output consensus problem of heterogeneous multiagent systems under denial-of-service (DoS) attacks. A novel dynamic event-triggered scheme (DETS) is proposed, which, by introducing an extra dynamic function with time-varying coefficients into triggering conditions, can guarantee strictly positive minimum inter-event intervals no matter DoS attacks occur or not. An event-based resilient compensator with adaptive coupling coefficients is then designed to estimate leader's state, and a hybrid model with jump dynamics is constructed that can incorporate the estimation error, DETS, and DoS attacks, and is useful for convergence analysis. Then, a fully distributed observer-based control protocol is designed to regulate the bipartite output consensus. The main advantages of the proposed method include: 1) global information is not needed to implement the event-based control protocol; 2) strictly positive inter-event intervals are guaranteed even under DoS attacks. Finally, a numerical example is presented to testify the main results.

Identifying Arnold's tongue for digital oscillators through event-based control in phase-locked loops.

Digital phase-locked loops (PLLs) are essential feedback circuits for synchronizing signals in digital communication systems. While amplitude and phase vary continuously in analog oscillators, the amplitude remains constant in digital oscillators with dynamical variations manifesting exclusively through changes in the timing of signal transitions. In this work, we introduce a novel analytically solvable event-based model for phase-locking in digital PLLs that leverages the discrete nature of digital signals. By employing a sampled control strategy, we demonstrate one-to-one and higher ratios of frequency locking under positive and negative feedback. By discretizing the continuous control signal, we drive a discrete iterative map, which we then use to derive analytical expressions for bifurcation curves, analogous to Arnold's tongue in analog oscillators. This mathematical framework provides an analytical approach for the analysis of synchronization and phase-locking in digital oscillators. Furthermore, the event-based control presented in this work for digital oscillators paves the way for energy-efficient circuit design and optimized control strategies for future digital communication systems.

3D dynamics and control of a snake robot in uncertain underwater environment

Abstract The snake robot can be used to monitor and maintain underwater structures and environments. The motion of a snake robot is achieved by lateral undulation which is called the gait pattern of the snake robot. The parameters of a gait pattern need to be adjusted for compensating environmental uncertainties. In this work, 3D motion dynamics of a snake robot for the underwater environment is proposed with vertical motion using the buoyancy variation technique and horizontal motion using lateral undulation. “The neutral buoyant snake robot motion in hypothetical plane and added mass effect is negligible”, these previous assumptions are removed in this work. Two different control algorithms are designed for horizontal and vertical motions. The existing super twisting sliding mode control (STSMC) is used for the horizontal serpentine motion of the snake robot. The control law is designed on a reduced-ordered dynamic system based on virtual holonomic constraints. The vertical motion is achieved by controlling the mass variation using a pump. The water pumps are controlled using the event-based controller or Proportional Derivative (PD) controller. The results of the proposed control technique are verified with various external environmental disturbances and uncertainties to check the robustness of the control approach for various path following cases. Moreover, the results of STSMC scheme are compared with SMC scheme to check the effectiveness of STSMC. The practical implementation of the work is also performed using Simscape Multibody environment where the designed control algorithm is deployed on the virtual snake robot.

On robustification of digital event-based controllers for control-affine nonlinear systems

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

A Bandwidth-Conscious Event-Based Control Approach to Secondary Frequency Regulation Under Vehicle-to-Grid Service

A Bandwidth-Conscious Event-Based Control Approach to Secondary Frequency Regulation Under Vehicle-to-Grid Service

Adaptive Input Delay Compensation Under Event-Based Control Signal Implementation

Adaptive Input Delay Compensation Under Event-Based Control Signal Implementation

Model-independent event-based consensus of multiple Euler-Lagrange systems with input disturbances

This paper investigates leaderless consensus (LLC) and leader-follower consensus (LFC) issues of multiple Euler-Lagrange systems (MELSs) with uncertain system parameters and input disturbances. Firstly, by utilizing event-based control strategy, event-based consensus protocols are proposed to achieve LLC and LFC, respectively. Then, to confirm that no Euler-Lagrange (EL) system will exhibit Zeno behavior under the above event-based consensus protocols, we show that the low bound of event-triggering interval is strictly positive for any time instants. Distinct with the existing related works, the proposed event-triggered consensus protocols only rely on local sampled state, and are irrelevant to the system parameters. Finally, some simulation examples are presented to illustrate the feasibility of the proposed event-based consensus algorithms.

Characterization of multi-channel denial-of-service

The embedded closed-loop in integrated systems can be compromised when attackers execute a successful malicious attack. Hence, over the past decade, interest in enhancing the safety of Cyber-Physical Systems (CPSs) has risen. This article examines the resilient control problem for CPSs with numerous transmission channels under Denial-of-Service (DoS). To begin with, a partial observer technique is developed in response to the Multi-Channel DoS (MCDoS) condition. Secondly, the changing frequency of MCDoS is characterized while maintaining the Input-to-State Stability (ISS) of the closed-loop system. Next, an event-based control strategy is developed to address Full-Scale DoS (FSDoS). Finally, the optimal control parameters are designed to make the system resilient against maximum MCDoS changing frequency.

Leader-Following Consensus of Multi-Agent Systems via Fully Distributed Event-Based Control

Leader-Following Consensus of Multi-Agent Systems via Fully Distributed Event-Based Control

Dynamic Event-Triggered-Based Adaptive Finite-Time Neural Control for Active Suspension Systems With Displacement Constraint.

In this article, we give an event-based control algorithm for nonlinear active suspension systems (ASSs) with the vertical displacement constraint. For in-vehicle communication networks, the controller area network (CAN) is a widely used standard for interconnecting electronic control units (ECUs). The main task in this work is, thus, to reduce the communication burden on the CAN. To this end, we develop a dynamic event-triggered communication mechanism in ASSs. Meanwhile, in practice, the vehicle safety is degraded when the body vibration exceeds the allowable maximum. Thus, the vertical displacement of ASSs should be constrained within a reliable range. For this purpose, we present a novel finite-time integral barrier Lyapunov function (FTIBLF), which not only guarantees that the vertical displacement constraint bounds are not violated, but also enables the position of the suspension to be stabilized in the neighborhood of a desired position in finite settling time. Furthermore, neural networks (NNs) are utilized to identify the unknown nonlinear characteristics in ASSs subjected to the modeling error and unknown mass. As a result, we propose an adaptive neural control technique based on the dynamic event-triggered condition, which helps to improve the ride comfort while ensuring the driving safety and handling stability. Finally, simulation results are provided to verify the validity of the presented methodology.

On the digital event-based control for nonlinear time-delay systems with exogenous disturbances

In this paper, the stabilization problem of nonlinear time-delay systems in presence of known exogenous disturbances and by means of quantized sampled-data event-based controllers is investigated. In particular, nonlinear systems with state delays are studied. Known exogenous disturbances affecting the plant dynamics are considered in order to address, for instance, tracking control problems commonly studied by considering the stabilization problem of the corresponding tracking error system in which the chosen reference signal appears as a known exogenous signal. The stabilization in the sample-and-hold sense theory is used as a tool to provide sufficient conditions for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the quantized sampled-data implementation of continuous-time controllers, updated through a proposed event-based mechanism, guarantees the semi-global practical stability property, with arbitrarily small final target ball of the origin, of the related closed-loop system. A spline approximation methodology is used in order to: (i) cope with the problem of the possible non-availability in the buffer of suitable past values of the system variables needed for the digital implementation of the controller; (ii) consider approximations related to the hardware implementation of the signal describing the known exogenous disturbance (e.g., the chosen reference signal). The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results, one of which concerning a single-link flexible joint robot arm with time delays.

Guaranteed cost tracking control of constrained input nonlinear uncertain systems using event-based ADP

This article investigates the guaranteed cost robust tracking control problem of nonlinear systems subjected to input constraint and unmatched uncertainty. The event-based adaptive dynamic programming (ADP) approach is utilized to address this problem. First, the tracking error and reference trajectory are combined to form an augmented uncertain system. Then, by decomposing the uncertainty into the matched and unmatched parts, the original tracking problem is converted into the optimal regulation problem of an auxiliary system. The cost function for the auxiliary system is defined, and the associated Hamilton–Jacobi–Bellman (HJB) equation is solved using a single critic neural network (NN). Moreover, a novel event-triggering rule is formulated, and it is shown that the designed event-based controller guarantees that the tracking error is uniformly ultimately bounded. The derivation of event-based guaranteed cost and its relation with the time-based counterpart is presented. The exclusion of the infamous Zeno behavior is guaranteed. The uniform ultimate boundedness of the critic weight estimation error is shown. Finally, the effectiveness of the proposed event-triggered ADP method is illustrated through simulations of the spring–mass–damper system and Van der Pol’s oscillator with unmatched uncertainty.

Dynamic Event-Sampled Control of Interconnected Nonlinear Systems Using Reinforcement Learning.

We develop a decentralized dynamic event-based control strategy for nonlinear systems subject to matched interconnections. To begin with, we introduce a dynamic event-based sampling mechanism, which relies on the system's states and the variables generated by time-based differential equations. Then, we prove that the decentralized event-based controller for the whole system is composed of all the optimal event-based control policies of nominal subsystems. To derive these optimal event-based control policies, we design a critic-only architecture to solve the related event-based Hamilton-Jacobi-Bellman equations in the reinforcement learning framework. The implementation of such an architecture uses only critic neural networks (NNs) with their weight vectors being updated through the gradient descent method together with concurrent learning. After that, we demonstrate that the asymptotic stability of closed-loop nominal subsystems and the uniformly ultimate boundedness stability of critic NNs' weight estimation errors are guaranteed by using Lyapunov's approach. Finally, we provide simulations of a matched nonlinear-interconnected plant to validate the present theoretical claims.

Event-Based Output Quantized Synchronization Control for Multiple Delayed Neural Networks.

This article concentrates on the global exponential synchronization problem of multiple neural networks with time delay by the event-based output quantized coupling control method. In order to reduce the signal transmission cost and avoid the difficulty of obtaining the systems' full states, this article adopts the event-triggered control and output quantized control. A new dynamic event-triggered mechanism is designed, in which the control parameters are time-varying functions. Under weakened coupling matrix conditions, by using a Halanay-type inequality, some simple and easily verified sufficient conditions to ensure the exponential synchronization of multiple neural networks are presented. Moreover, the Zeno behaviors of the system are excluded. Some numerical examples are given to verify the effectiveness of the theoretical analysis in this article.

Interleaved Periodic Event-Triggered Communications-Based Distributed Formation Control for Cooperative Unmanned Surface Vessels.

This article addresses the distributed formation control issue of cooperative unmanned surface vessels (USVs) under interleaved periodic event-triggered communications. First, an adaptive event-based control protocol is designed, where the event-based neural network (NN) scheme is developed to compensate for uncertain model dynamics. Upon the designed control protocol, an interleaved periodic event-triggered mechanism (IPETM) is subsequently proposed to achieve the communication objective. Unlike the common continuous event-triggered methods and periodic event-triggered methods, in which multiple nodes are allowed to trigger their events at the same time, the proposed IPETM ensures that USVs detect their events at different times to avoid the simultaneous event triggering of different nodes. By this virtue, traffic jamming in common wireless environments can be prevented, such that potential communication delays and faults are naturally avoided. In addition, the event detecting instants of the presented IPETM are also discrete and periodic, such that it can be performed under low-computational frequencies. Through Lyapunov-based analysis, it is verified that all closed-loop signals can converge to an arbitrary small compact set with exponential convergence rates. Simulation results demonstrate the effectiveness and superiority of the proposed control scheme.

Robustness study for networked event-based control system under Regular Quantization with Hysteresis sampling

Robustness study for networked event-based control system under Regular Quantization with Hysteresis sampling

On the robustification of digital event-based stabilizers for nonlinear time-delay systems

In this paper, the robust stabilization problem by means of quantized sampled-data event-based (QSE) controllers is investigated for nonlinear systems affected by state delays and unknown disturbances. In particular, a methodology for the design of robust QSE stabilizers is provided for control-affine nonlinear systems affected by unknown actuation disturbances and unknown measurement errors. Firstly, the notion of Steepest Descent Feedback (SDF), continuous or not, is suitably revised in order to deal with the robustification of event-based controllers. Then, Input-to-State Stability (ISS) redesign methodologies are used to provide the robustification term which is added to the SDF at hand in order to arbitrarily attenuate the effects of unknown external disturbances affecting the considered control scheme. A spline approximation approach is used in order to cope with the problem of the possible non-availability in the buffer of suitable past values of the system state required for the correct application of the proposed robust QSE controller. It is proved that there exist a suitably fast sampling and an accurate quantization of the input/output channels such that: the robust QSE implementation of SDFs, continuous or not, ensures the semi-global practical stability of the related closed-loop system, regardless of the above disturbances, provided that the observation errors affects marginally the new added control term. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results.

Self-triggered formation control for multi-spacecraft attitude coordination with communication delays

This article addresses the event-triggered formation control problem for multi-spacecraft systems subject to time-varying delays. Firstly, a formation attitude dynamics model considering communication delays is proposed, and two auxiliary trigger instants are designed to transform the event-based control problem subject to delays into the conventional event-triggered control problem. Next, a nonlinear observer based on the triggering information of neighbors is developed to estimate the lumped nonlinear term. To avoid continuous communication, a dynamic event-based formation control strategy is proposed based on the nonlinear observer. To avoid continuous computation of the trigger mechanism, a self-triggered function is developed based on the current trigger information. Moreover, the system is Zeno-free under the proposed event-based control algorithms. Finally, simulation results show that compared with the dynamic triggering function, the self-triggered function avoids continuous computation and improves the control accuracy by nearly one order of magnitude while increasing communication frequency by 67.8 %.

Event-based adaptive fuzzy tracking control for nonlinear systems with input magnitude and rate saturations

In this paper, an event-based adaptive fuzzy tracking control strategy for a class of uncertain nonlinear systems with limited control input and its rate of change is proposed. The unknown nonlinear function of the considered system is approximated by a fuzzy logic system (FLS). Furthermore, an event-triggered control method is developed to save the computing resources, in which the controller parameters are adaptively adjusted by a fuzzy controller. Moreover, it is proved by designing the Lyapunov function that the event-based controller can ensure that all signals of the controlled system are bounded. In addition, the tracking error can converge to a preset domain. Meanwhile, two practical simulations are given to demonstrate the effectiveness of the proposed method.

A fully distributed event-Triggered control approach to leader-following consensus of multiagent systems

This paper investigates the leader-following consensus problem for general linear multiagent systems under a fully distributed manner. To avoid using the global information of the communication network, two node-based adaptive parameters are designed and introduced to the fully distributed event-based control law. Such a protocol is more scalable and flexible for large-scaled and complex networked system, such as microgrids or multiple unmanned vehicles. A novel event-triggered rule is presented, and an internal dynamic variable is introduced in it to further cut down the triggering times and save the communication resources. A well-designed Lyapunov function candidate is constructed to not only ensure the convergence of the close-looped systems but also avoid using the eigenvalue of Laplacian matrix in the dynamic variable. Moreover, it is proved that the designed event-triggered conditions can avoid the Zeno behaviour. Finally, a simulation example based on a group of unmanned intelligent vehicle systems is provided to demonstrate the validity of the designed control method.