Dynamic Output Feedback Control for Systems Subject to Actuator Saturation via Event‐Triggered Scheme

In this paper, the event‐triggered dynamic output feedback control problem for linear systems with actuator saturation is investigated. Event‐triggered scheme only transmits the corresponding signal when the event‐triggered condition is violated. Due to its advantage of saving communication resources, it is utilized to design the dynamic output feedback controller. A criterion is established to guarantee the stability of the closed‐loop system by introducing an exponential term for the Lyapunov function, which corresponds to the exponential term in the event‐triggered condition. The explicit design of the coefficient matrices of the controller is presented. Furthermore, a lower bound of the inter‐event time is calculated to avoid Zeno behavior. An optimization algorithm is then formulated to maximize the estimation of the domain of attraction. Finally, a numerical example is given to illustrate the effectiveness of our methods and to show the trade‐off between the size of the domain of attraction and communication resources saving.     

Event‐triggered practical finite‐time output feedback stabilization of a class of uncertain nonlinear systems

This paper studies the event‐triggered practical finite‐time output feedback stabilization problem for a class of uncertain nonlinear systems with unknown control gains. First, a reduced‐dimensional observer is employed to implement the reconstruction of the unavailable states. Furthermore, a novel event‐triggered output feedback control strategy is proposed based on the idea of backstepping design and sign function techniques. It is shown that the practical finite‐time stability of the closed‐loop systems is ensured by Lyapunov analysis and related stability criterion. Compared with the existing methods, the main advantage of this strategy is that the observer errors and event‐trigger errors can be processed simultaneously to achieve the practical finite‐time stability. Finally, an example is adopted to demonstrate the validity of the proposed scheme.     

Robust practical output regulation for a class of uncertain linear minimum‐phase systems by output‐based event‐triggered control

In this paper, we consider the robust practical output regulation problem for a class of SISO uncertain linear minimum‐phase systems subject to external disturbances by an output‐based event‐triggered control law, where the reference inputs and the external disturbances are both generated by a so‐called exosystem with known dynamics. Our approach consists of two steps. First, on the basis of the internal model principle, we convert the problem into the robust practical stabilization problem of a well‐defined augmented system. Second, we design an output‐based event‐triggered mechanism and an output‐based event‐triggered control law to solve the stabilization problem, which in turn leads to the solvability of the original problem. What is more, we show that the event‐triggered mechanism prevents the Zeno behavior from happening. A numerical example is given to illustrate the design. Copyright © 2017 John Wiley & Sons, Ltd.     

On the stability issues of switched singular time‐delay systems with slow switching based on average dwell‐time

The issue of exponential stability analysis of continuous‐time switched singular systems consisting of a family of stable and unstable subsystems with time‐varying delay is investigated in this paper. It is very difficult to analyze the stability of such systems because of the existence of time‐delay and unstable subsystems. In this regard, on the basis of the free‐weighting matrix approach, by constructing the new Lyapunov‐like Krasovskii functional, and using the average dwell‐time approach, delay‐dependent sufficient conditions are derived and formulated in terms of LMIs to check the exponential stability of such systems. This paper also highlights the relationship between the average dwell‐time of the switched singular time‐delay system, its stability, exponential convergence rate of differential states, and algebraic states. Finally, a numerical example is given to confirm the analytical results and illustrate the effectiveness of the proposed strategy. Copyright © 2012 John Wiley & Sons, Ltd.     

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

In this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

Event‐triggered Guaranteed Cost Consensus of Networked Singular Multi‐agent Systems

The problem of event‐triggered guaranteed cost consensus of discrete‐time singular multi‐agent systems with switching topologies is investigated in this paper. To save the limited network communication bandwidth of multi‐agent systems, a novel event‐triggered networked consensus mechanism is proposed. Based on the graph theory and singular system theory, sufficient conditions of guaranteed‐cost consensus of discrete‐time singular multi‐agent systems are derived and given in the form of the linear matrix inequalities, respectively. A co‐design approach of the multi‐agent consensus gain matrix and the event‐triggered parameters is presented. Furthermore, based on the approach of second class equivalent transformation for singular systems, the cost function is determined, and an explicit expression of consensus functions is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

A new event‐driven output‐based discrete‐time control for the sporadic MIMO tracking problem

This paper presents a new sporadic control approach to the tracking problem for MIMO closed‐loop systems. An LTI sampled data plant with unmeasurable state affected by external unknown disturbances is considered. The plant is interconnected to an event‐based digital dynamic output‐feedback controller via a network. Both the external reference and the unknown disturbance are assumed to be generated as the free output response of unstable LTI systems. The main feature of the new event‐driven communication logic (CL) is that it works without the strict requirement of a state vector available for measurement. The purpose of the CL is to reduce as much as possible the number of triggered messages along the feedback and feedforward paths with respect to periodic sampling, still preserving internal stability and without appreciably degrading the control system tracking capability. The proposed event‐driven CL is composed of a sensor CL (SCL) and of a controller CL (CCL). The SCL is based on the computation of a quadratic functional of the tracking error and of a corresponding suitably computed time‐varying threshold: a network message from the sensor to the controller is triggered only if the functional equals or exceeds the current value of the threshold. The CCL is directly driven by the SCL: the dynamic output controller sends a feedforward message to the plant only if it has received a message from the sensor at the previous sampled instant. Formulation of the controller in discrete‐time form facilitates its implementation and provides a minimum inter‐event time given by the sampling period. An example taken from the related literature shows the effectiveness of the new approach. The focus of this paper is on the stability and performance loss problems relative to the sporadic nature of the control law. Other topics such as network delay or packets dropout are not considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Delay‐Dependent Exponential Stability for Discrete‐Time Singular Switched Systems with Time‐Varying Delay

In this paper, the exponential stability problem is investigated for a class of discrete‐time singular switched systems with time‐varying delay. By using a new Lyapunov functional and average dwell time scheme, a delay‐dependent sufficient condition is established in terms of linear matrix inequalities for the considered system to be regular, causal, and exponentially stable. Different from the existing results, in the considered systems the corresponding singular matrices do not need to have the same rank. A numerical example is given to demonstrate the effectiveness of the proposed result.     

Controlling the multi‐plant networked system with external perturbations via adaptive model‐based event‐triggered strategy

This paper concerns the multi‐plant networked control system with external perturbations by applying the adaptive model‐based event‐triggered control strategy. Compared with existing works, we introduce multiple plants topology in order to smooth the information exchanges among different plants. Gained insight into the adaptive model features in the view of event‐triggered thought, the event‐triggered rules, determining when the control inputs update, are obtained using the Lyapunov technique to reduce the communication cost. By designing some adaptive updating laws combined with the concept of event‐triggered, the unknown parameters in uncertain multi‐plant networked control systems are real‐time online estimated and adjusted with respect to the relevant nominal systems at event‐triggered instants. To avoid Zeno phenomena, a lower bound of event‐triggered execution interval is discussed. Furthermore, given the external perturbations, gain stability theory is introduced to analyze the stability of multi‐plant networked control systems with bounded perturbations, and then the sufficient conditions related to the multiple plants topology structure are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of our theoretic results.     

Robust feedback stabilization using high‐gain observer via event triggering

In this article, the problem of robust output feedback stabilization of single‐input single‐output nonlinear systems is studied in the event‐triggering framework. In this work, an event‐triggered output feedback law based on a high‐gain observer is constructed, which guarantees the stability of closed‐loop system. First, the high‐gain observer with a triggering scheme is designed to estimate the plant state in the presence of external disturbances subject to any satisfactory accuracy of the estimation error. The observer‐based triggering mechanism decides the transmission of plant output to the observer by observing a certain event condition. Similarly, another triggering mechanism is designed using the estimated state of observer that triggers the control signal to be updated only when it is satisfied. Under this proposed event‐triggering framework, the stability of closed‐loop system is then analyzed. Here, we provide the simplified design technique, in which the high‐gain parameter and the triggering thresholds can be selected independently to achieve any desired bound for the plant trajectory. The results are finally demonstrated through simulation of a numerical example.     

Dynamic self‐triggered output‐feedback control for nonlinear stochastic systems with time delays

In this paper, the dynamic self‐triggered output‐feedback control problem is investigated for a class of nonlinear stochastic systems with time delays. To reduce the network resource consumption, the dynamic event‐triggered mechanism is implemented in the sensor‐to‐controller channel. Criteria are first established for the closed‐loop system to be stochastically input‐to‐state stable under the event‐triggered mechanism. Furthermore, sufficient conditions are given under which the closed‐loop system with dynamic event‐triggered mechanism is almost surely stable, and the output‐feedback controller as well as the dynamic event‐triggered mechanism are co‐designed. Moreover, a dynamic self‐triggered mechanism is proposed such that the nonlinear stochastic system with the designed output‐feedback controller is stochastically input‐to‐state stable and the Zeno phenomenon is excluded. Finally, a numerical example is provided to illustrate the effectiveness of proposed dynamic self‐triggered output‐feedback control scheme.     

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.     

On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

In this paper, two suboptimal event‐triggered control techniques are proposed for both the regulation and the tracking problems in a broad class of nonlinear networked control systems. The proposed techniques are based on the state‐dependent Riccati equation (SDRE) methodology. In the case of the regulation problem, the asymptotic stability of the origin of the closed‐loop system under the proposed event‐triggered control law is investigated. In addition, for the tracking problem, it is proved that the tracking error between the system output and its desired trajectory converges asymptotically to zero under some mild conditions. It is shown that the proposed methods can considerably reduce the information exchange between the controller and the actuator. Due to the implementation procedures of the proposed techniques, no Zeno behavior is occurred. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed event‐triggered control techniques.     

Analysis and design of event‐triggered control algorithms using hybrid systems tools

This article proposes a general framework for analyzing continuous‐time systems controlled by event‐triggered algorithms. Closed‐loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event‐triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions. Using recently developed tools for robust stability, properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated by several event‐triggered strategies available in the literature, and observations about their key dynamical properties are made.     

Event‐triggered fault detection for switched systems with time‐varying sojourn probabilities

In this paper, a codesign strategy of an event‐triggered scheme and a fault detection filter (FDF) is developed for the networked switched systems with delayed measurements. A novel switching rule is proposed to better describe the switching behavior in a real system, under which the probability staying in each subsystem is time varying and results in a piecewise continuous system dynamics. An event‐triggered strategy based on the relative error with respect to the delayed measurement signal is established to reduce the communication burden. Our attention is concentrated on the construction of an event‐triggered fault detection technique for the proposed switched system with delayed measurements. Combining the stochastic analysis techniques and the average dwell time (ADT) method, a sufficient condition is obtained to guarantee the finite‐time boundedness of the generated residual system, the sensitivity of the residual signal to faults, and the disturbance attenuation of the switched system to external disturbances. Based on the established condition, a codesign strategy is developed to get the event‐triggered threshold and the FDF gain. Finally, two simulation results verify the effectiveness of the proposed design method.     

Observer‐based leaderless and leader‐following consensus for multiagent systems: A modified integral‐type event‐triggered design

This article aims to solve leaderless and leader‐following consensus problems for general linear systems by integral‐type event‐triggered control method. Different from the existing integral‐type event‐triggered controllers for multiagent systems (MASs), a modified distributed integral‐type event‐triggered scheme is designed via defining a measurement error without continuous communication. Then, distributed event‐triggered protocols are proposed for MASs to achieve the leaderless and leader‐following consensus. Moreover, for the case that all the agents' states are not available, distributed observers are given to estimate the full states. Meanwhile, leaderless and leader‐following consensus problems are investigated based on the observer‐based event‐triggered schemes. In addition, no agent will exhibit Zeno behavior. Finally, simulations are given to verify the effectiveness of our results.     

Distributed event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.