Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The controller updates considered here are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation is considered first and then its distributed counterpart, in which agents require knowledge only of their neighbors' states for the controller implementation. The results are then extended to a self-triggered setup, where each agent computes its next update time at the previous one, without having to keep track of the state error that triggers the actuation between two consecutive update instants. The results are illustrated through simulation examples.

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Distributed Event-Triggered Control for Multi-Agent Systems

Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event- and self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event- and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well.

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An introduction to event-triggered and self-triggered control

This note is concerned with event-triggered H∞ controller design for networked control systems. A novel event-triggering scheme is proposed, which has some advantages over some existing schemes. A delay system model for the analysis is firstly constructed by investigating the effect of the network transmission delay. Then, based on this model, criteria for stability with an H∞ norm bound and criteria for co-designing both the feedback gain and the trigger parameters are derived. These criteria are formulated in terms of linear matrix inequalities. Simulation results have shown that the proposed event-triggering scheme is superior to some existing event-triggering schemes in the literature.

A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems

Event-triggered control (ETC) is a control strategy that is especially suited for applications where communication resources are scarce. By updating and communicating sensor and actuator data only when needed for stability or performance purposes, ETC is capable of reducing the amount of communications, while still retaining a satisfactory closed-loop performance. In this paper, an ETC strategy is proposed by striking a balance between conventional periodic sampled-data control and ETC, leading to so-called periodic event-triggered control (PETC). In PETC, the event-triggering condition is verified periodically and at every sampling time it is decided whether or not to compute and to transmit new measurements and new control signals. The periodic character of the triggering conditions leads to various implementation benefits, including a minimum inter-event time of (at least) the sampling interval of the event-triggering condition. The PETC strategies developed in this paper apply to both static state-feedback and dynamical output-based controllers, as well as to both centralized and decentralized (periodic) event-triggering conditions. To analyze the stability and the L2-gain properties of the resulting PETC systems, three different approaches will be presented based on 1) impulsive systems, 2) piecewise linear systems, and 3) perturbed linear systems. Moreover, the advantages and disadvantages of each of the three approaches will be discussed and the developed theory will be illustrated using a numerical example.

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Periodic event-triggered control for nonlinear systems

Brief paper: A state-feedback approach to event-based control

Event-based control is a control methodology that is currently being developed as a means to reduce the communication between the sensors, the controller and the actuators in a control loop. The sampling instants are not determined periodically by a clock, but by an event generator, which adapts the information flow in the feedback loop to the current behavior of the closed-loop system. A communication among the components is invoked only after an event has indicated that the control error exceeds a tolerable bound.

Event-Based Control

Event-based control aims at reducing the information exchange over the communication network in control systems. This paper extends an event-based state-feedback approach published recently towards event-based output feedback. The measurable output is affected by measurement noise. The analysis shows that by incorporating a state observer in the event generator, a stable behavior of the event-based control loop can be guaranteed. Moreover, it will be shown that the maximum communication frequency within the control loop is bounded.

Event-based output-feedback control

This paper presents an approach to event-triggered model predictive control for discrete-time linear systems subject to input and state constraints as well as exogenous disturbances. Stability properties are derived by evaluating the difference between the event-triggered implementation and the conventional time-triggered scheme. It is shown that the event-triggered implementation, in stationarity, is able to keep the state in an explicitly computable set given by the disturbance bound and the event threshold. Simulation results underline the effectiveness of the proposed scheme in terms of reducing the communication and computational effort while guaranteeing a desired performance.

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Daniel Lehmann

Papers

Brief paper: A state-feedback approach to event-based control

Event-Based Control

Event-based output-feedback control

Event-triggered model predictive control of discrete-time linear systems subject to disturbances

Extension and experimental evaluation of an event-based state-feedback approach