Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

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.     

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 Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.     

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.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Event‐triggered Control of Linear Systems with Saturated Inputs

This paper investigates the event‐triggered control of linear systems with saturated state feedback and saturated observer‐based feedback, respectively. The problem of simultaneously deriving stabilizing event‐triggered controllers and tackling saturation nonlinearity is cast into a standard linear matrix inequalities problem. Key topics are studied, such as event‐triggered observer design and event‐triggered saturated observer‐based feedback synthesis. Important issues are touched on, including the existence of the positive lower bound for inter‐event times, and self‐triggered algorithms.     

Prescribed performance control of strict‐feedback systems under actuation saturation and output constraint via event‐triggered approach

In this work, we study the performance‐guaranteed event‐triggered control for a class of uncertain nonlinear systems in strict‐feedback form subject to input saturation and output constraint. The prescribed performance (ie, convergence rate, tracking error accuracy) and output constraint are firstly taken into account for nonlinear systems with event‐triggered input. By blending a speed transformation into the barrier Lyapunov function and introducing an intermediate variable to the system, two different event‐triggered control schemes are proposed for systems with and without saturation, respectively. Each scheme has two rules to determine triggering time sequences, one for control signal updating and the other for control signal transmission with the latter being a subsequence of the first. Meanwhile, it is proved that the tracking error converges to a preset compact set around zero at the prescribed decay rate and the output is maintained within a given bound at all times. Simulation verification also confirms the effectiveness of the proposed approach.     

Output‐feedback control strategies of lower‐triangular nonlinear nonholonomic systems in any prescribed finite time

In this paper, output‐feedback control strategies are proposed for lower‐triangular nonlinear nonholonomic systems in any prescribed finite time. Specifically, by employing the input‐state–scaling technique, the controlled systems are firstly converted into lower‐triangular nonlinear systems, which makes it possible to study such systems using the high‐gain technique. Then, by introducing a scaling of the state by a function that grows unbounded toward the terminal time and proposing a high‐gain observer–prescribed finite time recovering the system states, the output‐feedback regulation control problem in any prescribed finite time is firstly achieved for nonlinear nonholonomic systems with unknown constant incremental rate. Moreover, by designing another time‐varying high gain, the output‐feedback stabilization control problem in any prescribed finite time is then achieved for nonlinear nonholonomic systems with a time‐varying incremental rate. Finally, a numerical example is introduced to show the effectiveness of proposed control strategies.     

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.     

Output feedback stabilization using super‐twisting control and high‐gain observer

An output feedback controller is designed for a class of uncertain nonlinear systems with relative degree higher than one. A super‐twisting sliding mode state feedback controller is designed and implemented using a high‐gain observer. It is proved that the controller achieves practical stabilization and the ultimate bound can be reduced by decreasing a design parameter. The performance of the controller is illustrated by simulation.     

Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete‐time nonlinear sliding mode observer for state and unknown input estimations of a class of single‐input/single‐output nonlinear uncertain systems. The uncertainties are characterized by a state‐dependent vector and a scalar disturbance/unknown input. The discrete‐time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete‐time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive tracking for MIMO nonlinear systems with Unknown fast time‐varying parameters

In this paper, we consider a class of MIMO nonlinear systems with fast time‐varying parametric uncertainties. First, the tracking problem of general nonlinearly time‐varyingly parameterized systems is solved. Then, a Lyapunov‐based singularity free adaptive controller is proposed for the considered system. Specifically, an estimation approach with a proportional plus integral adaptation scheme is utilized to update the estimations of the unknown parameters under a mild assumption that the signs of the leading minors of the input gain matrix are known. The asymptotic stability is achieved with full state feedback. Furthermore, we design an output feedback controller by utilizing a standard high‐gain observer and achieve uniformly ultimately bounded convergence. Simulation examples illustrate the effectiveness of the proposed methods.     

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.     

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.     

Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers

In this paper, we investigate the observation and stabilization problems for a class of nonlinear Lipschitz systems, subject to network constraints, and partial state knowledge. In order to address these problems, an impulsive observer is designed, making use of the event‐triggered technique in order to diminish the network communications. Sufficient conditions are given to ensure a milder version of the separation principle for these systems, controlled via an event‐triggered controller. The proposed observer ensures practical state estimation, while the corresponding dynamic controller ensures practical stabilization. The sampling and the data transmission are carried out asynchronously. The dynamic controller is tested in simulation on a flexible joint. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems

This article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.     

Output feedback regulation control for a class of cascade nonlinear systems by time‐varying Kalman observer

The global output feedback regulation problem is studied for a class of cascade nonlinear systems. The considered system represents more general classes of nonlinear uncertain systems, including the integral input‐to‐state stable (iISS) unmodeled dynamics, the unknown control direction, the parameter uncertainty, and the external disturbance additively in the input channel. Technically, we explore the changing supply rate technique for the iISS system to deal the iISS unmodeled dynamics and apply the Nussbaum‐type gain into the control design to overcome the unknown control direction. Additionally, a dynamic extended state observer in the form of a time‐varying Kalman observer is novelly constructed to overcome the unmeasured state components in the nonlinear uncertainties. It is shown that the global regulation problem is well addressed by the proposed method, and its efficacy is demonstrated by a fan speed control system.     

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.     

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

This paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and the one‐sided Lipschitz condition. By constructing the novel Lyapunov–Krasovskii functional while utilizing the free‐weighting matrices approach, the one‐sided Lipschitz condition and the quadratic inner‐bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time‐varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.