Observer-based Event-triggered Control Research Articles

Resilient observer-based event-triggered control for cyber-physical systems under asynchronous denial-of-service attacks

Resilient observer-based event-triggered control for cyber-physical systems under asynchronous denial-of-service attacks

Observer-Based Event-Triggered Formation Control of Multi-Agent Systems With Switching Directed Topologies

This paper investigates the formation control problem for linear multi-agent systems under switching directed topologies. Based on absolute or relative outputs, we propose two distributed observer-based event-triggered control schemes. Both schemes can guarantee the boundedness of formation errors under sufficient conditions. The schemes can also avoid Zeno behaviors by giving an estimation for the lower bound of sampling intervals. Finally, simulations and experiments validate the proposed approaches.

Event-Triggered Observer-Based $\mathcal {H}_\infty$ Consensus Control and Fault Detection of Multiagent Systems Under Stochastic False Data Injection Attacks

This paper investigates the event-triggered observer-based security consensus and fault detection problem for nonlinear multi-agent systems (MASs) under external disturbances and stochastic false data injection attacks (FDIAs) over a directed communication network. The randomly occurring FDIAs are modeled by random variables that follow the Bernoulli distribution. An observer-based event-triggered control strategy using only local measurements and information from neighboring agents is developed, where the Zeno behavior of event-triggered mechanism (ETM) is excluded. Interestingly, the observer errors are first regarded as disturbance and then attenuated by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> norm bounds, together with the external disturbances. Meanwhile, it is worth highlighting here that the same information used by the state observers is also adopted to construct residuals with adaptive thresholds, whose aim is to detect faults occurring in any agents. In addition, the accuracy of the observer and the performance of the fault detection mechanism are improved by introducing the disturbance compensation mechanism. Finally, simulation results are provided to illustrate the effectiveness and advantages of the proposed strategy.

Improved Observer-based Event-Triggered Control for Switched Delay Systems with Input Quantization

Improved Observer-based Event-Triggered Control for Switched Delay Systems with Input Quantization

Observer-based event-triggered control of linear system with two-time scales

In this paper, the stabilization of singularly perturbed systems by means of observer-based event-triggered control is studied. To obtain the ultimately bounded stability of the closed-loop system, two event-triggering conditions are designed, respectively, for the slow and the fast subsystems of the singularly perturbed systems based on the state errors between the observer and models. In each event-triggering condition, there are two different stages to be designed. In the first stage, the event-triggering conditions are given based on the observer error dynamics. While in the second stage, the absolute type event-triggering conditions are used. Under the designed event-triggering conditions, Zeno behavior can be eliminated from the closed-loop systems. Finally, numerical examples are provided to illustrate the efficiency and feasibility of the theoretical results.

Observer-based event-triggered adaptive containment control for multiagent systems with prescribed performance

This paper focuses on the problem of the event-triggered adaptive containment control for a class of nonlinear multiagent systems (MASs) with prescribed performance and immeasurable states. First, the radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain smooth nonlinear function, and the neural network-based state observer is designed to estimate the unmeasurable state. Besides, to reduce the control resource consumption and get a better balance between the system performance and network constraints, the switching threshold-based event-triggered control strategy is introduced. Based on this, the novel distributed containment controller is designed by utilizing the adaptive backstepping technique and the dynamic surface control (DSC) technique to guarantee that the output of each follower converges to the convex hull formed by multileader. Moreover, the containment errors can be converged to the prescribed boundary and all signals in closed-loop system are semi-global uniformly ultimately bounded (SGUUB) as well. Finally, the simulation examples are carried out to illustrate the efficiency of the proposed controller.

Non-fragile exponential [formula omitted] observer-based event-triggered control of uncertain systems with disturbance input: Theoretical studies and application investigations

This paper is concerned with the problem of exponential H∞ event-triggered controller design for uncertain systems with disturbance input. The proposed controller is based on a non-fragile observer which is resilient to gain variations. A new event-triggering condition is introduced deciding on the transmission of the current signal. An event-driven state-feedback controller updates the control signals according to the transmitted data. Utilizing the Lyapunov stability theorem, the sufficient conditions for exponential stability of the estimated states and the error system are proposed. It is proven that the state estimates and the error vector converge to a limited region with a pre-specified exponential rate. The stability conditions are given in the form of linear matrix inequalities (LMIs), by solving which, the controller and the observer gains are attained. It is also shown that a positive scalar limits the inter-execution intervals, by analyzing the Zeno behavior. The design procedure has been stated in a step-by-step manner which makes the design very convenient and straightforward. Eventually, the proposed approach is applied to the level control of a four-tank system. The simulation results illustrate the applicability and effectiveness of the method.

Sampled-data and event-triggered boundary control of a class of reaction–diffusion PDEs with collocated sensing and actuation

This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction–diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the underlying control approach. It is shown that the continuous-time output feedback boundary control applied in a sample-and-hold fashion ensures global closed-loop exponential stability, provided that the sampling period is sufficiently small. Further, robustness to perturbations of the sampling schedule is guaranteed. For the event-triggered implementation of the continuous-time controller, a dynamic triggering condition is utilized. The triggering condition determines the time instants at which the control input needs to be updated. Under the observer-based event-triggered boundary control, it is shown that there is a minimal dwell-time between two triggering instants independent of initial conditions. Further, the global exponential convergence of the closed-loop system to the equilibrium point is established. A simulation example is provided to validate the theoretical results.

Observer-based event-triggered control for linear MASs under a directed graph and DoS attacks

In this paper, we investigate the observer-based event-triggered consensus problem for linear multi-agent systems (MASs) under a directed graph and denial-of-service (DoS) attacks. A type of DoS attacks launched by malicious attackers at irregular intervals is considered, which can cause communication channel disruption. A novel event-triggered secure control scheme based on a closed-loop observer is proposed to determine the scheduling of the controller update, and a separation method with less conservativeness is employed to design the controller and observer gains. Then, the frequency and duration of DoS attacks that can be tolerated are analysed for the observer-based secure consensus problem. In addition, a strictly positive minimal event-triggered time interval for each agent is designed with the help of the proposed event-triggered condition to eliminate the Zeno behaviour. Finally, a numerical simulation is given to verify the theoretical analysis.

Observer-based event-triggered control and application in active suspension vehicle systems

This paper focuses on event-trigger control of automotive suspension systems. Firstly, fuzzy T-S systems which suitable for automobile suspension systems are studied. Parameter uncertainties and disturbances are included in the fuzzy T-S systems. Secondly, based on linear matrix inequalities (LMIs) and Lyapunov function, the conditions for the stability of fuzzy T-S systems are given. In the meantime, the controller and observer of the fuzzy T-S systems are designed. Finally, the theory is applied to the automotive suspension systems in the simulation.

Hybrid state observer‐based event‐triggered control for switched linear systems with quantized input

The paper investigates the design of hybrid state observer-based event-triggered controller for switched linear systems subject to quantized input and unknown but bounded additional disturbance and measurement noise. Firstly, by introducing a hybrid state observer and constructing a mode-dependent event-triggered mechanism, we design event-triggered controller for the considered switched linear systems. Then, by modeling the closed-loop system as an augmented asynchronous switched time-delay system, we deal with the asynchronous control problem caused by the switching between two consecutive trigger instants for the switched linear system. Thirdly, based on merging signal technique and multiple Lyapunov functional method, we obtain the sufficient criteria to guarantee the stability of the switched system when the switching signal meets an average dwell time condition, and further establish the hybrid observer-based event-triggered controller gains. Finally, a simulation example illustrates the validity of the results.

Observer-based event-triggered control for zero-sum games of input constrained multi-player nonlinear systems

In this paper, an event-triggered control (ETC) method is investigated to solve zero-sum game (ZSG) problems of unknown multi-player continuous-time nonlinear systems with input constraints by using adaptive dynamic programming (ADP). To relax the requirement of system dynamics, a neural network (NN) observer is constructed to identify the dynamics of multi-player system via the input and output data. Then, the event-triggered Hamilton–Jacobi–Isaacs (HJI) equation of the ZSG can be solved by constructing a critic NN, and the approximated optimal control law and the worst disturbance law can be obtained directly. A triggering scheme which determines the updating time instants of the control law and the disturbance law is developed. Thus, the proposed ADP-based ETC method cannot only reduce the computational burden, but also save communication resource and bandwidths. Furthermore, we prove that the signals of the closed-loop system and the approximate errors of the critic NN weights are uniformly ultimately bounded by using Lyapunov’s direct method, and the Zeno behavior is excluded. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed ETC scheme.

Observer-based event-triggered tracking control for large-scale high order nonlinear uncertain systems

Observer-based event-triggered tracking control for large-scale high order nonlinear uncertain systems

On the use of generalized holding devices in event-triggered observer-based controllers

This paper deals with the design of output feedback event-triggered controllers equipped with generalized holding devices. Both emulation and co-design settings are explored. Specifically, a robust observer-based event-triggered controller with a dwell time logic is proposed to achieve closed-loop stability. The closed-loop system is modeled as a hybrid system and analyzed via Lyapunov theory for hybrid systems. Sufficient conditions in the form of matrix inequalities are given to ensure global exponential stability and input-to-state stability with respect to measurement disturbances for the closed-loop system. The proposed conditions enable the design of the controller gains, event-triggering mechanism, and of general holding devices, thereby including classical zero-order-holder devices. Convex optimization schemes address the implicit objective consisting of reducing the number of updates of the control input. The effectiveness of the conditions are illustrated through an illustrative example borrowed from the literature.

Global Event-Triggered Output Feedback Stabilization of a Class of Nonlinear Systems

This article investigates the problem of global output feedback stabilization by using aperiodic-sampled-data control, i.e., event-triggered control, for a class of uncertain nonlinear systems under certain assumptions. By employing the technique of output feedback domination, an observer-based event-triggered output feedback control law is explicitly constructed to guarantee the globally asymptotic stabilization. To avoid the Zeno behavior, a combining mechanism with event-triggered and time-triggered is proposed to ensure that the two consecutive updated time for the sampled-data controller is larger than one positive constant. Finally, it is shown that the problem of global output feedback stabilization for a class of uncertain nonlinear systems is solved via the proposed event-triggered control law. Finally, some comparative simulation examples are given to show the efficiency of the introduced method.

Adaptive disturbance observer-based event-triggered fuzzy control for nonlinear system

This paper investigates the issue of tracking control of nonlinear system with external disturbance, an event-triggered fuzzy backstepping sliding-mode control strategy is proposed. Firstly, a fuzzy state estimator is designed to estimate the unmeasurable state, and a sliding-mode disturbance observer is presented on the estimation error. In which, consider the conservativeness of the observer parameter, a parameter adaptation law with a double nested structure is proposed to mitigate chattering problems caused by parameter conservativeness. Then an event-triggered mechanism along with backstepping control and sliding-mode strategy is designed to achieve tracking control and save the network resources, and the Zeno phenomenon can be avoided. Furthermore, the backstepping law combines with Lyapunov theory is used to prove that the tracking error can converge to a small bounded set and all the signals of closed-loop plant are bounded. Finally, simulation results are carried out to illustrate the potential of designed approaches.

Observer-based event-triggered type-2 fuzzy control for uncertain steer-by-wire systems

This paper addresses the tracking control problem for the uncertain steer-by-wire (SbW) system with the controller area network (CAN) communication and unavailable variables. First, an adaptive interval type-2 fuzzy logic system (IT2 FLS) and sliding mode observer are constructed to estimate the uncertain nonlinearity and unavailable variables of SbW control systems. Further, an event-triggered sliding mode control (ET-SMC) is presented to achieve the transient steering performance of SbW systems while saving CAN communication resources. Much importantly, the dynamic gain and nested technologies are incorporated in this scheme to deal with estimation error and the chattering phenomenon of the sliding mode control system. It is shown that the practical fixed-time stability of the closed-loop system can be guaranteed without the initial condition of tracking errors. Finally, simulations and vehicle experiments are presented to verify the designed scheme.

Observer-based event-triggered control of steer-by-wire systems with prespecified tracking accuracy

This paper addresses the event-triggered tracking control problem of the SbW system subject to unavailable steering angular velocity of front-wheels, time-varying external disturbance, and uncertain dynamics, including friction torque and self-aligning torque. First, an adaptive state observer is proposed to estimate the unavailable steering angular velocity of front-wheels. The uncertain nonlinearity and time-varying disturbance can be estimated by the adaptive interval type-2 fuzzy logic system (IT2 FLS) and the disturbance observer, respectively. An event-triggered control is proposed for SbW systems to guarantee the prespecified control performance and save communication resources in the controller-to-actuator channel. Much importantly, the nested robust terms are incorporated in the control scheme to counteract the observation error and overcome the negative influence of the event-triggering error. Theoretical analysis shows that the prespecified arbitrary tracking accuracy can be guaranteed within finite time, and the Zeno-behavior can be strictly avoided while saving communication resources in the controller-to-actuator channel. Finally, simulation and vehicle experiment results and some comparisons are given to evaluate the effectiveness of the proposed method.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Unmeasured Stochastic Nonlinear Systems With Unknown Control Directions.

The issue of adaptive output-feedback stabilization is investigated for a category of stochastic nonstrict-feedback nonlinear systems subject to unmeasured state and unknown control directions. By combining the event-triggered mechanism and backstepping technology, an adaptive fuzzy output-feedback controller is devised. In order to make the controller design feasible, a linear state transformation is introduced into the initial system. At the same time, the Nussbaum function technology is used to overcome the difficulties caused by unknown control directions, and the state observer solves the problem of the unmeasured state. Based on the fuzzy-logic system and its structural characteristics, the issue of unknown nonlinear function with nonstrict-feedback structure in the system is tackled. The designed controller could not only guarantee all signals of closed-loop systems are bounded in probability but also save communication resources effectively. Finally, numerical simulation and ship dynamics example are given to confirm the effectiveness of the proposed method.

Event-triggered observer-based H ∞ control of switched linear systems with time-varying delay

This paper is devoted to study the issue of event-triggered observer-based control of switched linear systems subject to time-varying state delay and exogenous disturbance. Firstly, an observer-based event-triggered controller is provided under the proposed event-triggered mechanism. Then, based on the average dwell time scheme and Jensen's Inequality technique, delay-dependent less conservative sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are obtained to guarantee the resulting augmented switched systems is exponential stabilisation and satisfies a prescribed control performance. Furthermore, observer-based event-triggered controller is designed, and it is shown that there exists a positive lower bound of inter-event intervals. Finally, numerical example and comparison results are provided to illustrate the effectiveness and advantages of the proposed method.