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.     

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.     

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.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

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.     

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.     

Stabilization of linear systems with time‐varying input delay by event‐triggered delay independent truncated predictor feedback

This article deals with the problem of stabilization of linear systems with time‐varying input delay by an event‐triggered delay independent truncated predictor feedback law, either of the state feedback type or the output feedback type. Only the information of a delay bound rather than the delay itself is required in the design of both control laws and event‐triggering strategies. For both the state feedback case and the output feedback case, an admissible delay bound that guarantees the stabilizability of a general linear system is established, and the Zeno behavior is shown to be excluded. For linear systems with all open‐loop poles at the origin or in the open left‐half plane, stabilization can be achieved for a delay under an arbitrarily large bound.     

Event‐triggered output synchronization of heterogeneous multi‐agent systems

This paper proposes a control architecture that employs event‐triggered control techniques to achieve output synchronization of a group of heterogeneous linear time‐invariant agents. We associate with each agent an event‐triggered output regulation controller and an event‐triggered reference generator. The event‐triggered output regulation controller is designed such that the regulated output of the agent approximately tracks a reference signal provided by the reference generator in the presence of unknown disturbances. The event‐triggered reference generator is responsible for synchronizing its internal state across all agents by exchanging information through a communication network linking the agents. We first address the output regulation problem for a single agent where we analyze two event‐triggered scenarios. In the first one, the output and input event detectors operate synchronously, meaning that resets are made at the same time instants, while in the second one, they operate asynchronously and independently of each other. It is shown that the tracking error is globally bounded for all bounded reference trajectories and all bounded disturbances. We then merge the results on event‐triggered output regulation with previous results on event‐triggered communication protocols for synchronization of the reference generators to demonstrate that the regulated output of each agent converges to and remains in a neighborhood of the desired reference trajectory and that the closed‐loop system does not exhibit Zeno solutions. Several examples are provided to illustrate the advantages and issues of every component of the proposed control architecture. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered control design for nonlinear systems with actuator failures and uncertain disturbances

Traditional adaptive event‐triggered design methods compensated for the event‐triggered error are not direct, and the stability analysis of resulting close‐loop systems is rather complicated. To alleviate the above restrictions, we propose a direct and simple event‐triggered co‐design method to solve the tracking control problem for parameter strict‐feedback systems with actuator faults and uncertain disturbances. By introducing a compensating terms in a smooth function form of a conventional control law and certain positive integrable functions, the effects of actuator faults and event‐triggered error can be compensated completely. Such a direct design method has the following features: (i) a direct compensation of the event‐triggered error is achieved without introducing any extra design parameters; (ii) it is not necessary to know any bound information on the parameters of event‐triggered threshold, and global asymptotic tracking control of the overall closed‐loop system is achieved; and (iii) the resulting stability criteria of the proposed event‐triggered control design are much simpler and easier to fulfill by virtue of the introduced co‐design method. Simulations are then carried out to validate the proposed schemes.     

Model Based Robust Control Law for Linear Event‐Triggered System

This paper proposes a framework to design an event‐triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event‐triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and mismatched system uncertainties. Derivation of event‐triggering rule with a non‐zero positive inter‐event time and corresponding stability criteria for uncertain event‐triggered system are the key contributions of this paper. The efficacy of proposed algorithm is carried out through a comparative study of simulation results.     

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.     

A novel event‐triggered extended state observer for networked control systems subjected to external disturbances

In this paper, the event‐triggered‐based state estimation problem is investigated for a class of nonlinear networked control systems subjected to external disturbances. A novel event‐triggered extended state observer (ESO) is utilized to estimate the so‐called total disturbance, and an output predictor is adopted for the proposed ESO between two consecutive transmission instants. It is also worth pointing out that, in the newly proposed ESO, an event‐triggered mechanism is adopted to update the measurement signal so as to save the communication resource. The sufficient conditions are provided such that the estimation error dynamics is exponentially ultimately bounded. Furthermore, it is proven that the Zeno behavior does not exist for the event‐triggering rules. A number of numerical simulations are conducted to verify the validity of the theoretical results.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Event‐triggered cascade high‐gain observer and its application

In this article, we consider the event‐triggered cascade high‐gain observer (ETCHGO) for a class of nonlinear systems. By cascading lower dimensional observers, we design a cascade high‐gain observer together with a Zeno‐free event‐triggered mechanism to estimate the state of the plant. We show that the ETCHGO has the same steady‐state performance as the continuous‐time cascade high‐gain observer, that is, there is a finite time after which the estimation error will not exceed the given threshold, and moreover, the finite time and the threshold can be made sufficiently small by adjusting some design parameters. We also investigate an ETCHGO with saturation, which will reduce the peaking value while maintaining the steady‐state estimation performance. Furthermore, we use the ETCHGO with saturation to solve the output feedback stabilization problem for a class of nonlinear systems. An example is given to illustrate our results.     

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme.     

Event‐Triggered Iterative Learning Control for Multi‐Agent Systems with Quantization

The emergence of networked control systems urges the digital control design to integrate communication constraints efficiently. In order to accommodate this requirement, this paper investigates the joint design of tracking problem for multi‐agent system (MAS) in the presence of resource‐limited communication channel and quantization. An event‐triggered robust learning control with quantization is firstly proposed and employed for MAS in this paper. The new event‐triggered distributed robust learning control system with the introduction of logarithmic quantization guarantees the asymptotic tracking property on the finite interval. Convergence analysis is given based on the Lyapunov direct method. Finally, numerical simulations are given to illustrate the efficacy of the event‐triggered approach compared with time‐triggered controllers.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

In this paper, a robust stabilization problem for a class of linear time‐varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time‐varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

An adaptive critic approach to event‐triggered robust control of nonlinear systems with unmatched uncertainties

In this paper, we develop a novel event‐triggered robust control strategy for continuous‐time nonlinear systems with unmatched uncertainties. First, we build a relationship to show that the event‐triggered robust control can be obtained by solving an event‐triggered nonlinear optimal control problem of the auxiliary system. Then, within the framework of reinforcement learning, we propose an adaptive critic approach to solve the event‐triggered nonlinear optimal control problem. Unlike typical actor‐critic dual approximators used in reinforcement learning, we employ a unique critic approximator to derive the solution of the event‐triggered Hamilton‐Jacobi‐Bellman equation arising in the nonlinear optimal control problem. The critic approximator is updated via the gradient descent method, and the persistence of excitation condition is necessary. Meanwhile, under a newly proposed event‐triggering condition, we prove that the developed critic approximator update rule guarantees all signals in the auxiliary closed‐loop system to be uniformly ultimately bounded. Moreover, we demonstrate that the obtained event‐triggered optimal control can ensure the original system to be stable in the sense of uniform ultimate boundedness. Finally, a F‐16 aircraft plant and a nonlinear system are provided to validate the present event‐triggered robust control scheme.