Event-triggered Control Systems Research Articles

Optimizing control efficiency in discrete-time multi-agent systems via event-triggered containment techniques combining disturbance handling and input delay management

The goal of this paper is to mitigate disturbances and input delays while optimizing controller actuation updates for discrete-time multi-agent systems through the use of an event-triggered confinement control system, especially in resource-constrained scenarios. This approach when combined with event-triggered control techniques, then every follower in the system adjusts its condition at specified times based on an event-triggered condition that is suggested. The containment control system issue in the presence of disturbances and input delays was tackled by using both decentralized and centralized event-triggered control systems. Using matrix theory and the Lyapunov technique, convergence analysis is conducted to show that the proposed strategy stays free of zeno phenomena. Numerical boosts are used to further illustrate the impact of theoretical results.

An event triggered control scheme for enhanced production of Escherichia coli and biomass concentration during fed-batch cultivation

Control of a bioprocess is a challenging task mainly due to the nonlinearity of the process, the complex nature of microorganisms, and variations in critical parameters such as temperature, pH, and agitator speed. Generally, the optimum values chosen for critical parameters during Escherichia coli (E.coli) K-12fed-batch fermentation are37 ᵒC for temperature, 7 for pH, and 35 % for Dissolved Oxygen (DO). The objective of this research is to enhance biomass concentration while minimizing energy consumption. To achieve this, an Event-Triggered Control (ETC) scheme based on feedback-feed forward control is proposed. The ETC system dynamically adjusts the substrate feed rate in response to variations in critical parameters. We compare the performance of classical Proportional Integral (PI) controllers and advanced Model Predictive Control (MPC) controllers in terms of bioprocess yield. Initially, the data are collected from a laboratory-scaled 3L bioreactor setup under fed-batch operating conditions, and data-driven models are developed using system identification techniques. Then, classical Proportional Integral (PI) and advanced Model Predictive Control (MPC) based feedback controllers are developed for controlling the yield of bioprocess by manipulating substrate flow rate, and their performances are compared. PI and MPC-based Event Triggered Feed Forward Controllers are designed to increase the yield and to suppress the effect of known disturbances due to critical parameters. Whenever there is a variation in the value of a critical parameter, it is considered an event, and ETC initiates a control action by manipulating the substrate feed rate. PI and MPC-based ETC controllers are developed in simulation, and their closed-loop performances are compared. It is observed that the Integral Square Error (ISE) is notably minimized to 4.668 for MPC with disturbance and 4.742 for MPC with Feed Forward Control. Similarly, the Integral Absolute Error (IAE) reduces to 2.453 for MPC with disturbance and 0.8124 for MPC with Feed Forward Control. The simulation results reveal that the MPC-based ETC control scheme enhances the biomass yield by 7 %, and this result is verified experimentally. This system dynamically adjusts the substrate feed rate in response to variations in critical parameters, which is a novel approach in the field of bioprocess control. Also, the proposed control schemes help reduce the frequency of communication between controller and actuator, which reduces power consumption.

Strengthening stability with centralized event-triggered control system with the disturbances and artificial time delay in wireless connected vehicle platooning (CVSs)

This paper addresses the difficulties with connected vehicle systems (CVSs), particularly with vehicle platooning, are examined in this paper. For leader and follower-connected vehicles, the control protocol (which includes artificial delays, disturbances and proportional gains) is implemented. With tracking error systems, system dynamics are modelled while taking outside influences into consideration. Using creative thinking, a centralized event-triggered control system is implemented to maximize fleet wide communication updates. System stability is guaranteed by this centralized method in combination with quadratic form Lyapunov stability analysis. The risk of zeno behaviour is reduced by an event-triggered communication condition that is activated when a threshold is exceeded. The effectiveness of the centralized event-triggered system in improving stability and resilience in connected vehicle platooning scenarios is evaluated numerically through simulations.

A Note on Stability of Event-Triggered Control Systems With Time Delays

A Note on Stability of Event-Triggered Control Systems With Time Delays

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.

Sequential output information based predictive control for event-triggered networked control systems

In a Networked Control System (NCS), event-triggering is often used to reduce the number of network transmission instances and improve network usage. This paper considers transmitting output data rather than the estimated state for such event-triggered schemes. Output transmission facilitates efficient transmission by reducing the size of the packets sent over the network. However, since the state observer utilizes delayed information output transmission deteriorates system performance and requires improved observer-based prediction schemes for closed-loop control. The performance of a new scheme involving the transmission of sequential output information in a single packet to improve the state observer’s performance is demonstrated in this paper. A sequential observer is constructed that uses successive output information to better observe the states, and a prediction scheme is used to take care of the delays due to event-triggering, network delays, and dropouts. Further, event-triggering is employed in both the feedback and forward channels. The demonstrated efficacy of this sequential approach in the networked control of an inverted pendulum system and a DC motor system emphasizes its potential as a practical solution for improved control in NCSs, particularly in the face of network constraints and communication challenges.

A novel one-bit dynamic quantizer for event-triggered control systems

We investigate the problem of feedback stabilization of networked control linear systems with unknown initial state. In particular, the sampling and the quantization effects of network are considered and we propose a quantized event-triggered control technique to handle this case. To cope with unknown initial state, a novel exponential dynamic quantizer is synthesized, which enables to capture the state in a finite time. Moreover, the dynamic quantization policy only depends on the sign of the quantization error and allows for one-bit transmission rather than packet-based transmission, which is desirable in practice. Then, the quantized state measurements are transmitted to the controller using an event-triggering mechanism to reduce the amount of transmissions over the network. The approach ensures global asymptotic stability property for the closed-loop system and prevents the occurrence of Zeno behavior. The entire closed-loop system is represented as a hybrid dynamical system and the closed-loop stability is assessed using suitable Lyapunov functions. The effectiveness of the proposed approach is demonstrated through numerical simulations.

Stability Analysis for Model-Based Event-Triggered Nonlinear Control Systems Under DoS Attacks

In this paper, we study the stability of a novel nonlinear event-triggered control system under denial-of-service (DoS) attacks based on an ISS-Lyapunov function analysis. A new dual-mode model-based event-triggering strategy is proposed which works based on consistency between the approximate and exact discretization of the nonlinear plant. We combine an event-triggered module with a controller based on the state prediction, together with a packetized transmission at the controller-to-actuator channel to provide the desired stability properties under DoS attacks. We also provide proof of Zeno-free behavior for the event-based system. Our proposed method provides a maximum percentage of time that the system can tolerate attacks without performance degradation. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

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.

Robustifying event-triggered control to measurement noise

While many event-triggered control strategies are available in the literature, most of them are designed ignoring the presence of measurement noise. As measurement noise is omnipresent in practice and can have detrimental effects, for instance, by inducing Zeno behavior in the closed-loop system and with that the lack of a positive lower bound on the inter-event times, rendering the event-triggered control design practically useless, it is of great importance to address this gap in the literature. To do so, we present a general approach for set stabilization of (distributed) event-triggered control systems affected by additive measurement noise. It is shown that, under general conditions, Zeno-free static as well as dynamic triggering rules can be designed such that the closed-loop system satisfies an input-to-state practical set stability property. We ensure Zeno-freeness by proving the existence of a uniform strictly positive lower-bound on the minimum inter-event time. The general approach is applied to point stabilization and consensus problems as particular cases, where we show that, under similar assumptions as the original work, existing schemes can be redesigned to robustify them to measurement noise. Consequently, using this approach, noise-robust triggering conditions can be designed both from the ground up and by simple redesign of several important existing schemes. Simulation results are provided that illustrate the strengths of this novel approach.

A switching approach to event-triggered control systems under denial-of-service attacks

This paper addresses the resilient event-triggered control (ETC) of networked control systems under denial-of-service (DoS) attacks. The scenario in which the presence of DoS attacks limits the data rate is studied considering a deterministic DoS attack model that constrains the frequency and duration of the DoS attack sequence in an average sense. Based on a switching approach, constructive sufficient conditions are proposed to design the resilient ETC scheme in both emulation and co-design approaches. The conditions establish a limitation to the average DoS frequency and duration such that the exponential stability of the closed-loop equilibrium and the Zeno-freeness is guaranteed even in the presence of DoS attacks. Moreover, optimization problems subject to LMI constraints are formulated to solve the emulation and co-design problems by enlarging the resilience to the considered class of DoS attacks while the number of transmissions is reduced. This establishes a clear trade-off between resilience and resource awareness in networked control systems under DoS attacks. The effectiveness of the proposed conditions is illustrated in two numerical examples.

Abstracting the Traffic of Nonlinear Event-Triggered Control Systems

Scheduling communication traffic in networks of event-triggered control (ETC) systems is challenging, as their sampling times are unknown, hindering application of ETC in networks. In previous work, finite-state abstractions were created, capturing the sampling behaviour of LTI ETC systems with quadratic triggering functions. Offering an infinite-horizon look to all sampling patterns of an ETC system, such abstractions can be used for scheduling of ETC traffic. Here we significantly extend this framework, by abstracting perturbed uncertain nonlinear ETC systems with general triggering functions. To construct an ETC system's abstraction: a) the state space is partitioned into regions, b) for each region an interval is determined, containing all intersampling times of points in the region, and c) the abstraction's transitions are determined through reachability analysis. To determine intervals and transitions, we devise algorithms based on reachability analysis. For partitioning, we propose an approach based on isochronous manifolds, resulting into tighter intervals and providing control over them, thus containing the abstraction's non-determinism. Simulations showcase our developments.

Traffic models of periodic event-triggered quantized control systems

Periodic Event-Triggered Quantized Control (PETQC) is a type of event-triggered control (ETC) that takes into account the quantization effect introduced by network transmission and only requires to measure the plant output periodically instead of continuously. In this work, we present an abstract model for the traffic generated by the dynamics of PETQC implementations. Construction of the abstract models is done in two steps. Our first step is to divide the state space into finite regions. Each region is then analyzed with LMIs to examine the event-triggering behavior. The state transitions among different regions are resulted from reachability analysis.

A New Event-Triggered Control Scheme for Stochastic Systems

This article studies event-triggered control of stochastic linear discrete-time systems with discounted quadratic cost functions. A new dynamic event-triggering condition is proposed, which has simultaneously stochastic and deterministic features. The designed event-triggered control system ensures the control performance to be within a desirable level relative to that using periodic time-triggered control, while discarding the unnecessary transmissions. By adjusting the parameters, the proposed event-triggering condition can be reduced to some existing ones in the literature. It is shown that the three features (dynamic, stochastic, and deterministic) are all helpful to further increase the average interevent times. Then, the criteria in terms of the parameters are presented to ensure mean-square stability of the closed-loop systems. Moreover, an improved version of the proposed event-triggering condition is given to enlarge the minimum interevent times. Finally, numerical simulations are given to illustrate the efficiency and feasibility of the proposed results.

A machine-learning-based event-triggered model predictive control for building energy management

Model predictive control (MPC) for building energy management has exhibited a huge potential for largely cutting down energy use and improving human comfort. However, the high demand for computational power for solving the optimization is challenging the widespread deployment of MPC in real buildings. Typical MPC employs a time-triggered mechanism (TTM) that runs optimization recurrently at each time step without considering the necessity, which could cause excessive computation resource usage. This paper proposes an event-triggered mechanism (ETM) that only runs optimization when triggering events occur. Contrary to conventional ETMs that only considers the current information (e.g., room conditions), the ETM proposed is based on a cost function that covers the past, current, and future information. Based on the proposed ETM, a machine-learning-based event-triggered model predictive control (ETMPC) system that optimizes both building energy efficiency and thermal comfort is developed. The developed ETMPC system is then employed for air-conditioning control for performance evaluation through simulations. The control performance of the proposed ETMPC is compared to an MPC employing TTM and a common thermostat. Compared to the MPC employing TTM, the proposed ETMPC reduced the computational load in terms of the number of optimization runs by 77.6%–88.2%, meanwhile, achieving similar energy savings (more than 9.3% energy saving over the thermostat) as the MPC employing TTM does (9% energy saving over the thermostat). With the significant reduction of computational load, the ETMPC achieves similar thermal comfort performance as the MPC employing TTM does, and it is significantly better over the thermostat.

Event-Triggered Impulsive Control for Nonlinear Systems With Actuation Delays

This article studies impulsive stabilization of nonlinear systems. We propose two types of event-triggering algorithms to update the impulsive control signals with actuation delays. The first algorithm is based on continuous event detection, while the second type makes decision about updating the impulsive control inputs according to periodic event detection. Sufficient conditions are derived to ensure asymptotic stability of the impulsive control systems with the designed event-triggering algorithms. Lower bounds of the time period between two consecutive events are also obtained, so that the closed-loop impulsive systems are free of Zeno behavior. That is to say that the pulse phenomena are excluded from the event-triggered impulsive control systems, in the community of impulsive differential equations. An illustrative example demonstrates effectiveness of the proposed algorithms and our theoretical results.

Periodic Event-Triggered Networked Control Systems Subject to Large Transmission Delays

This article studies periodic event-triggered networked control for nonlinear systems, where the plants and controllers are connected by multiple independent communication channels. Several network-induced imperfections are considered simultaneously, including time-varying intersampling times, sensor node scheduling, and especially, large time-varying transmission delays, where the transmitted signal may arrive at the destination node after the next transmission occurs. A new hybrid system approach is provided to model the closed-loop system that contains all communication related behavior. Then, by constructing new storage functions on the system state and updating errors, the relationship between the maximum allowable sampling period and maximum allowable delay number in sampling is analyzed, where the latter denotes how many inter-sampling periods can be included in one transmission delay. Moreover, to efficiently reduce unnecessary transmissions, a new dynamic event-triggered control scheme is proposed, where the event-triggering conditions are detected only at aperiodic and asynchronous sampling instants. From emulation-based method, where the controllers are initially designed by ignoring all the network-induced imperfections, sufficient conditions on the dynamic event-triggered control are given to ensure closed-loop input-to-state stability with respect to external disturbances. Finally, two nonlinear examples are simulated to illustrate the feasibility and efficiency of the theoretical results.

Adaptive control for the nonlinear event-triggered networked control system: a decoupling method

In this paper, the adaptive control for a kind of nonlinear system over the event-driven sensors-controller communication network is addressed. Over this network, the existing strategy has been developed. However, the event-triggered mechanism and adaptive estimators are coupled together, which results in extra information delivery of the adaptive estimators over the network or extra computation equipment on the sensor side. To overcome this limitations, two kinds of adaptive control strategies are proposed in this paper. At first, the control strategy with the new event-triggered adaptive estimator is developed for the system without external disturbances where the event-triggered mechanism does not need the information of the adaptive estimators. It is proved that the closed-loop system is asymptotically stable and the Zeno behaviour is excluded. Furthermore, for the system with external disturbances, a robust control scheme with modified adaptive estimator and event-triggered mechanism is proposed and the practical stability of the closed-loop system is guaranteed. Also, the Zeno behaviour is excluded carefully. Comparing with the existing results, due to the decoupling structure of event-triggered mechanism and adaptive estimators, it is unnecessary to transfer the estimators’ information to the event-triggered mechanism on the sensor side, which saves the communication cost. What’s more, although the system state is sampled and event driven, the asymptotical stability is still guaranteed. Also, the developed strategy can handle with the external disturbances. Finally, two examples are performed to illustrate the effectiveness of the schemes and some comparisons are displayed to explain the advantages of the methods.

Event-based control of a damped linear wave equation

This paper aims at proposing a sufficient matrix inequality condition to carry out the global exponential stability of the wave equation under an event-triggering mechanism that updates a damping source term. The damping is distributed in the whole space but sampled in time. The well-posedness of the closed-loop event-triggered control system is shown. Furthermore, the avoidance of Zeno behavior is ensured provided that the initial data are more regular. The interest of the results is drawn through some numerical simulations.

Event-triggered stabilisation of sampled-data singular systems: a hybrid control approach

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.