Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

Event‐triggered PCS Based Trajectory Tracking Control of Systems with Perturbation

This paper is aimed at reducing network load for saving bandwidth by designing appropriate trigger signals that decide when the transmission should be done. An event‐triggered piecewise continuous systems (PCS) based control for time‐varying trajectory tracking is proposed. By designing the sensor system and controller system, the communication between them is reduced while still retaining a satisfactory closed‐loop behavior of the whole system. The major idea behind a designed sensor system is the use of a Luenberger observer and planning of event‐triggered mechanism (ETM). The main principle behind the designed controller system is the proposal of a new event‐triggered PCS based controller. The development is motivated by consideration of variable network induced time delays. Tracking error is proved to be norm‐bounded in both the original and developed case. Finally, to show the proposed method's performance, we present the simulation results for a mobile cart.     

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.     

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.     

Sampled‐data H∞ control for networked systems with random packet dropouts

This paper is concerned with the H_∞ control problem for networked control systems (NCSs) with random packet dropouts. The NCS is modeled as a sampled‐data system which involves a continuous plant, a digital controller, an event‐driven holder and network channels. In this model, two types of packet dropouts in the sensor‐to‐controller (S/C) side and controller‐to‐actuator (C/A) side are both considered, and are described by two mutually independent stochastic variables satisfying the Bernoulli binary distribution. By applying an input/output delay approach, the sampled‐data NCS is transformed into a continuous time‐delay system with stochastic parameters. An observer‐based control scheme is designed such that the closed‐loop NCS is stochastically exponentially mean‐square stable and the prescribed H_∞ disturbance attenuation level is also achieved. The controller design problem is transformed into a feasibility problem for a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Event‐triggered fault‐tolerant control and scheduling codesign for nonlinear networked control systems with medium‐access constraint and packet disordering

This paper studies an event‐triggered communication, scheduling, and fault‐tolerant control codesign method for nonlinear networked control systems with medium‐access constraint, delay, and packet disordering using an adaptive approximation method and adaptive technique. By considering nonlinear dynamics and controller reconfiguration, a novel event‐triggering scheme with an adjustable triggering condition and adaptive triggering thresholds is proposed. The stochastic event‐driven actuator scheduling is investigated without the assumption that the controller can access the current modes of the actuators. By considering the Markovian delay and focusing on the transmitter node, a new packet reordering approach is used to cope with packet disordering. This paper proposes an active fault‐tolerant control method, in which the nominal controller is redesigned for the postfault plant by using the fault information provided by an estimator. It is proven that the estimation error of the estimator is uniformly bounded, the reconfigurable controller and event‐trigger ensure the boundedness in probability of the state tracking error before and after the fault occurrence in the presence of medium‐access constraint, delay, and packet disordering while reducing communication load. The effectiveness of the proposed method is demonstrated in the numerical example.     

Mixed Event/Time‐Triggered Static Output Feedback L2‐Gain Control for Networked Control Systems

This paper considers the design of mixed event/time‐triggered controllers for networked control systems (NCSs) under transmission delay and possible packet dropout. Assuming that a conventional delayed static output feedback L₂‐gain controller exists, we propose an output‐based mixed event/time‐triggered communication scheme for reducing the network traffic in a NCS. Moreover, we show that a conventional delayed static output feedback L₂‐gain controller can be obtained by solving a linear matrix inequality with a matrix equality constraint. A numerical example is proposed for demonstrating the theoretical results.     

Robust event‐triggered control of second‐order disturbed leader‐follower MASs: A nonsingular finite‐time consensus approach

This paper addresses the finite‐time and the prescribed finite‐time event‐triggered consensus tracking problems for second‐order multi‐agent systems (MASs) with uncertain disturbances. The prescribed finite‐time event‐triggered consensus of the second‐order disturbed MASs was obtained for the first time and the controller is nonsingular. Furthermore, a new self‐triggered control scheme is presented for the finite‐time consensus tracking, and the continuous communication can be avoided in the triggering condition monitoring. Hence, the finite‐time consensus tracking can be achieved with intermittent communication. Moreover, Zeno behavior is excluded for each follower. The efficiency of the proposed algorithms is verified by numerical simulations.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Tracking control for sampled‐data systems with uncertain time‐varying sampling intervals and delays

In this paper, a solution to the approximate tracking problem of sampled‐data systems with uncertain, time‐varying sampling intervals and delays is presented. Such time‐varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time‐varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input‐to‐state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete‐time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady‐state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Nonlinear bilateral teleoperators under event‐driven communication with constant time delays

Bilateral teleoperation systems provide a platform for human operators to remotely manipulate slave robots in engaging various tasks in remote environments. Most of the previous studies in bilateral teleoperation were developed under continuous transmission or periodic communication with fixed data exchanging rates. This paper presents control schemes for bilateral teleoperation systems using nonperiodic event‐driven communication. By using P‐like and PD‐like controllers, this study proposes triggering conditions for teleoperators to reduce network access frequency so that robots only transmit output signals when necessary. Stability and position tracking of the control system are studied, and nonzero minimum interevent time is guaranteed. The proposed event‐driven teleoperation is studied with a velocity estimator to avoid the requirement of velocity information in the controller and triggering condition. Without velocity measurements, the boundedness of tracking errors and stability are ensured for teleoperation systems under event‐driven communication. Simulations and experiments are illustrated to validate the performance of the proposed event‐driven teleoperation systems.     

Observer‐based H ∞ output tracking control for networked control systems

This paper is concerned with observer‐based H _∞ output tracking control for networked control systems. An observer‐based controller is implemented through a communication network to drive the output of a controlled plant to track the output of a reference model. The inputs of the controlled plant and the observer‐based tracking controller are updated in an asynchronous way because of the effects of network‐induced delays and packet dropouts in the controller‐to‐actuator channel. Taking the asynchronous characteristic into consideration, the resulting closed‐loop system is modeled as a system with two interval time‐varying delays. A Lyapunov–Krasovskii functional, which makes use of information about the lower and upper bounds of the interval time‐varying delays, is constructed to derive a delay‐dependent criterion such that the closed‐loop system has a desired H _∞ tracking performance. Notice that a separation principle cannot be used to design an observer gain and a control gain due to the asynchronous inputs of the plant and the controller. Instead, a novel design algorithm is proposed by applying a particle swarm optimization technique with the feasibility of the stability criterion to search for the minimum H _∞ tracking performance and the corresponding gains. The effectiveness of the proposed method is illustrated by an example. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential stability of output‐based event‐triggered control for switched singular systems

This paper presents the exponential stability of output‐based event‐triggered control for switched singular systems. An event‐triggered mechanism is introduced based on measure output, by employing the Lyapunov functional method and average dwell time approach, some sufficient conditions for exponential stability of the switched singular closed‐loop systems are derived. Furthermore, dynamic output feedback controller parameters are obtained. Lastly, a numerical example is given to illustrate the validity of the proposed solutions.     

Event‐triggered optimal tracking control of nonlinear systems

We propose a novel event‐triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event‐triggered controller. Because the actor network updates only when an event occurs, we shall use a zero‐order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed‐loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one‐link rigid robot under gravitation field, and a controlled Van‐der‐Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Development Of Cvt Control System And Its Use For Fuel‐Efficient Operation Of Engine

Continuously variable transmission (CVT) provides an automobile with the ability to change the gear ratio continuously, which can then improve not only ride quality such as acceleration performance but also fuel‐efficiency. However, to take advantage of the ability, a control system that can precisely control the gear ratio is required. This paper proposes such a control system for a belt‐driven CVT system. For controller design, first the CVT system is modeled by analytical and experimental approaches. The resultant static and dynamic characteristics provide a nonlinear first‐order model with an uncertain time constant and time delay. The nonlinear steady‐state gain is adjusted to one by a gain‐scheduled pre‐compensator. Thereby the plant model becomes a linear first‐order lag system with a dead time. The next step is controller design using the plant model. To guarantee stability and control performance against the parameter variation and time delay, the μ‐synthesis, a robust control method, is employed for feedback control. In addition, a feedforward controller is incorporated into the feedback control system to obtain better output response. The feedforward controller is given by a combination of the inverse system of the plant and a reference model that gives desired output response. As a result, the control system becomes a two‐degree‐of‐freedom control system. To evaluate the performance of the control system and its effectiveness on the fuel‐efficiency, computer simulation and driving tests were conducted. The simulation and experiment results prove that the proposed control system can make the gear ratio track a reference output quickly and precisely in the presence of the uncertainties. The results also show that the control system improves fuel‐efficiency by changing the gear ratio so that the engine torque and its revolution speed can satisfy optimum‐efficiency operating condition.     

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.     

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

This paper focuses on the distributed event‐triggered fixed‐time consensus control problem of leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances. Two distributed fixed‐time consensus protocols are proposed based on distributed event‐triggered strategies, which can substantially reduce energy consumption and the frequency of the controller updates. It is proved that under the proposed distributed event‐triggered consensus tracking control strategies, the Zeno behavior is avoided. Compared with the finite‐time consensus tracking, the fixed‐time consensus tracking can be achieved within a settling time regardless of the initial conditions. Finally, 2 examples are performed to validate the effectiveness of the distributed event‐triggered fixed‐time consensus tracking controllers.