Observer-based Event-triggered Control Research Articles

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.

Observer-Based Control for Cyber-Physical Systems Under Denial-of-Service With a Decentralized Event-Triggered Scheme.

This article concerns the problem of observer-based event-triggered control for cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. In contrast to the existing studies where DoS attacks on different channels are the same, the considered attacks compromise each channel independently. Correspondingly, a decentralized event-triggered scheme is adopted based on the tradeoff between the transmission efficiency and tolerable attack intensity with guarantees on the closed-loop stability. Inspired by the Lyapunov theory for switched systems, the proposed stabilization criteria reveals a link between the tolerable attack intensity and the event-triggering parameters. An example is finally provided to illustrate the effectiveness of the proposed approaches.

Observer-Based Event-Triggered Predictive Control for Networked Control Systems under DoS Attacks.

This paper studies the problem of DoS attack defense based on static observer-based event-triggered predictive control in networked control systems (NCSs). First, under the conditions of limited network bandwidth resources and the incomplete observability of the state of the system, we introduce the event-triggered function to provide a discrete event-triggered transmission scheme for the observer. Then, we analyze denial-of-service (DoS) attacks that occur on the network transmission channel. Using the above-mentioned event-triggered scheme, a novel class of predictive control algorithms is designed on the control node to proactively save network bandwidth and compensate for DoS attacks, which ensures the stability of NCSs. Meanwhile, a closed-loop system with an observer-based event-triggered predictive control scheme for analysis is created. Through linear matrix inequality (LMI) and the Lyapunov function method, the design of the controller, observer and event-triggered matrices is established, and the stability of the scheme is analyzed. The results show that the proposed solution can effectively compensate DoS attacks and save network bandwidth resources by combining event-triggered mechanisms. Finally, a smart grid simulation example is employed to verify the feasibility and effectiveness of the scheme’s defense against DoS attacks.

Optimal actuator switching synthesis of observer-based event-triggered state feedback control for distributed parameter systems

The study aims to explore the optimal actuator switching scheme of observer-based event-triggered state feedback control for distributed parameter systems. The performance of distributed parameter systems is improved through the observer-based event-triggered control, in which the state feedback is updated only when a triggered event happens. In such an event-triggered mechanism, the event-based closed-loop system and minimum time interval between consecutive events are bounded. Based on finite horizon linear quadratic regulator (LQR) optimal control, the optimal switching algorithm is proposed based on the event-triggered mechanism during an unfixed time interval. Finally, the proposed scheme is verified through a simulation case.

Self-Triggered and Event-Triggered Control for Linear Systems With Quantization

This paper considers the observer-based event-triggered output control problem with quantization. Both plant-to-controller (measured output) channel and controller-to-plant (control input) channel have their own dynamic uniform quantizers and samplings. Therefore, the whole system has four asynchronous clocks, two quantizer updating clocks, and two sampling updating clocks. The main contribution of this paper is the proposed self-triggered and event-triggered control method based on these four clocks. The whole system is stabilized by two steps, i.e., system and controller synchronization, and controller stabilization. In the synchronization process, novel event-triggered and self-triggered samplings are proposed in terms of dynamic quantizer parameters. While in the stabilization process, event-triggered sampling is designed based on controller states and quantizer parameters. Moreover, it is proved that the Zeno behavior would not occur. The practicality and efficiency of the proposed method are illustrated by a numerical example borrowed from recent literature.

Input-to-State Stabilization of a Class of Uncertain Nonlinear Systems via Observer-Based Event-Triggered Impulsive Control

This article concerns the problem of input-to-state stabilization for a group of uncertain nonlinear systems equipped with nonabsolutely available states and exogenous disturbances. To appropriately cope with these partially measurable state variables as well as dramatically minimize controller updating burden and communication costs, an event-triggered mechanism is skillfully devised and an observer-based impulsive controller with the combination of sample control is correspondingly presented. By resorting to the iterative method and Lyapunov technology, some sufficient criteria are established to guarantee the input-to-state stability of the newly uncertain controlled system under the employed controller, in which an innovative approximation condition as to the uncertain term is proposed and the linear matrix inequality technique is utilized for restraining sophisticated parameter uncertainties. Furthermore, the Zeno behavior in the proposed event-triggered strategy is excluded. The control gains and event-triggered mechanism parameters are conjointly designed by resolving some inequalities of linear matrix. Eventually, the availability and feasibility of the achieved theoretical works are elucidated by two simulation examples.

Observer-based event-triggered fixed-time control for nonlinear system with full-state constraints and input saturation

This paper investigates the continuous composite control scheme for the tracking of nonlinear system with mismatched disturbances, input saturation and full-state constraints. Based on the fixed-time stability theory, a novel fixed-time disturbance observer is proposed, which switches from a uniform second-order sliding mode observer with high-degree term to the classical continuous super-twisting observer. Then, a command filtered backstepping control scheme is designed to enforce the tracking error into a small neighbourhood of the origin in fixed time while the full-state constraint and input saturation constraint are satisfied. To further reduce the communication burden, an event-triggered communication strategy between the controller and the actuator input is also developed. Furthermore, all the signals in the closed-loop system are proven to be bounded. Finally, the effectiveness of the proposed control strategy is illustrated by numerical simulations.

Observer-based event-triggered control for uncertain fractional-order systems

In this paper, the observer-based event-triggered control problem for a class of uncertain fractional-order systems with order 0 < α < 1 is investigated. Owing to the difficulties of measuring system full-state in practice, a fractional-order observer is firstly designed to construct an event-triggered condition, which eventually decides whether the current signal should be transmitted. Then, by utilizing the observer-based feedback controller, a sufficient condition in the form of linear matrix inequalities (LMIs) is presented to guarantee the asymptotic stability of the augmented closed-loop system. After that, the corresponding design conditions for the observer gain and controller gain are provided. Furthermore, the Zeno behavior of the considered systems is discussed, and a positive lower bound of inter-execution intervals is estimated to solve infinite triggering and sampling issues. Finally, an illustrative example and simulations are provided to illustrate the effectiveness of the proposed approaches.

Event-Triggered Fuzzy Bipartite Tracking Control for Network Systems Based on Distributed Reduced-Order Observers

This article studies the distributed observer-based event-triggered bipartite tracking control problem for stochastic nonlinear multiagent systems with input saturation. First, different from conventional observers, we construct a novel distributed reduced-order observer to estimate unknown states for the stochastic nonlinear systems. Then, an event-triggered mechanism with relative threshold is introduced to reduce the burden of communication. In addition, the bipartite tracking controller is proposed for stochastic multiagent systems by using fuzzy logic systems and the backstepping approach. Meanwhile, it is proved that the designed method can guarantee that all the signals in the closed-loop systems are bounded in probability, and the distributed consensus tracking errors can converge to a small neighborhood of the origin via the Lyapunov stability theory. Finally, a simulation example is given to prove the effectiveness of the designed scheme.

Observer-Based Event-Triggered Circle Formation Control for First- and Second-Order Multiagent Systems

This paper proposes an observer-based event-triggered algorithm to solve circle formation control problems for both first- and second-order multiagent systems, where the communication topology is modeled by a spanning tree-based directed graph with limited resources. In particular, the observation-based event-triggering mechanism is used to reduce the update frequency of the controller, and the triggering time depends on the norm of the state function and the trigger threshold of measurement errors. The analysis shows that sufficient conditions are established for achieving the desired circle formation, while there exists at least one agent for which the next interevent interval is strictly positive. Numerical simulations of both first- and second-order multiagent systems are also given to demonstrate the effectiveness of the proposed control laws.

Interval observer-based event-triggered control for switched linear systems

This paper studies the interval observer-based event-triggered controller design for switched systems involving additive disturbance and measurement noise. We first extend the definition of asymptotic interval observers for general non-switched systems into switched ones. Then, by giving the bound of the disturbance and the measurement noise and adopting the multiple Lyapunov function method, some sufficient conditions are derived and applied to build the interval observer, which supply certain information at any instant: an upper bound and a lower bound are provided for each component of the states. Next, we propose an event-triggered sampling mechanism and design an interval observer-based state feedback controller for the considered switched systems. Finally, we afford two examples to illustrate the validity of the derived results.

Observer-based event-triggered boundary control of a linear 2 × 2 hyperbolic systems

This paper deals with an observer-based event-triggered boundary control for a coupled 2 × 2 linear hyperbolic system. The approach builds on an output feedback controller depending on estimated states along with a dynamic triggering condition which establishes the time instants at which the control value needs to be sampled/updated. This work combines some recent results on boundary stabilization via the backstepping approach with some event-triggered control strategies for this kind of PDE system. In this paper, it is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent on initial conditions) between two triggering times and furthermore the well-posedness and global exponential stability are guaranteed. A simulation example is presented to validate the theoretical results with further discussions on the advantages of the proposed scheme.

Distributed Adaptive Event-Triggered Fault-Tolerant Synchronization for Multiagent Systems

This article investigates the fully distributed observer-based adaptive fault-tolerant synchronization problem (SP) of multiagent systems with event-triggered control mechanisms. First, a nonlinear and discontinuous adaptive observer-based event-triggered fault-tolerant controller is proposed for each agent to overcome the occurrence of unknown faults and unmeasurable full states of the controlled system. Besides, an adaptive triggering function consisting of state-dependent and time-dependent threshold is developed to adjust the parameter of triggering threshold online. Then, a modified nonlinear and continuous observer-based controller with adaptive ETC strategy is developed to overcome the chattering phenomenon from the discontinuous controller. It is proved that under two controllers, the SP not only can be achieved in a fully distributed way without continuous communication for both the controller updates and the triggering condition detecting but also exclusion of “Zeno behavior” can be realized. Finally, the effective algorithms can be verified by giving numerical simulations related to mobile robots.

Distributed Functional Observer-based Event-triggered Containment Control of Multi-agent Systems

This paper studies the containment control problem of linear multi-agent systems (MASs) with a directed graph, where the states of the followers will asymptotically converge to the convex hull formed by those of the leaders. By introducing the functional observer, a novel distributed event-triggered control strategy is presented to schedule communications between agents, which depends on the relative input and output measurements with its neighbors. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results.

Observer-Based Event-Triggered Control of Time-Delay Systems Involved Actuator Failures: Switching Method

The problem of the observer-based event-triggered control for a more general class of time-delay systems with actuators failure is investigated. Firstly, due to the system state cannot be measured in practice, a state feedback observer is used to reconstruct the state of the system. Then, based on the switching method, a solution for controller is derived such that the resulting closed-loop system is exponentially stable. Moreover, an event-triggered scheme is presented, which is defined as some error signals exceeding a given threshold. Finally, an example is given to illustrate the effectiveness of the proposed method.

Observer-based event-triggered output feedback control for fractional-order cyber–physical systems subject to stochastic network attacks

This paper is engaged in investigating the observer-based event-triggered output feedback control issue for fractional-order cyber–physical systems with stochastic network attacks, where the order scale of the fractional derivative used is 0<α<1. An event-triggered scheme (ETS) with output-independent threshold is proposed to renew the observer input so as to reduce the redundant data communications. Considering the effects of the ETS and network attacks, a novel closed-loop fractional-order control system model is constructed. By making use of fractional-order Lyapunov indirect approach, sufficient conditions that can insure the global stochastic asymptotic stability of the established closed-loop control system are obtained. Moreover, according to the singular value decomposition (SVD) of matrix, the co-design of the gains of the desired observer and controller is addressed by finding the solution of the linear matrix inequalities (LMIs). Finally, a numerical example and a diesel engine control system are provided to validate the feasibility of the adopted observer-based control method.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Leader-Following Consensus of Nonlinear Strict-Feedback Systems.

In this article, the leader-following consensus problem via the event-triggered control technique is studied for the nonlinear strict-feedback systems with unmeasurable states. The follower's nonlinear dynamics is approximated using the fuzzy-logic systems, and the fuzzy weights are updated in a nonperiodic manner. By introducing a fuzzy state observer to reconstruct the system states, an observer-based event-triggered adaptive fuzzy control and a novel event-triggered condition are designed, simultaneously. In addition, the nonzero positive lower bound on interevent intervals is presented to avoid the Zeno behavior. It is proved via an extension of the Lyapunov approach that ultimately bounded control is achieved for the leader-following consensus of the considered multiagent systems. One remarkable advantage of the proposed control protocol is that the control law and fuzzy weights are updated only when the event-triggered condition is violated, which can greatly decrease the data transmission and communication resource. The simulation results are provided to show the effectiveness of the proposed control strategy and the theoretical analysis.

Observer-based event-triggered control for semilinear time-fractional diffusion systems with distributed feedback

This paper is concerned with the observer-based distributed event-triggered feedback control for semilinear time-fractional diffusion systems under the Robin boundary conditions. To this end, an extended Luenberger-type observer is presented to solve the limitations caused by the impossible availability of full-state information that is needed for feedback control in practical applications due to the difficulties of measuring. With this, we propose the distributed output feedback event-triggered controllers via backstepping technique under which the considered systems admit Mittag–Leffler stability. It is shown that the given event-triggered control strategy could significantly reduce the amount of transmitted control inputs while guaranteeing the desired system performance with the Zeno phenomenon being excluded. A numerical illustration is finally presented to illustrate our theoretical results.

Distributed Optimal Coordination for Heterogeneous Linear Multiagent Systems With Event-Triggered Mechanisms

This note considers the distributed optimal coordination (DOC) problem for heterogeneous linear multiagent systems. The local gradients are locally Lipschitz and the local convexity constants are unknown. A control law is proposed to drive the states of all agents to the optimal coordination that minimizes a global objective function. By exploring certain features of the invariant projection of the Laplacian matrix, the global asymptotic convergence is guaranteed utilizing only local interaction. The proposed control law is then extended with event-triggered communication schemes, which removes the requirement for continuous communications. Under the event-triggered control law, it is proved that no Zeno behavior is exhibited and the global asymptotic convergence is preserved. The proposed control laws are fully distributed, in the sense that the control design only uses the information in the connected neighborhood. Furthermore, to achieve the DOC for linear multiagent systems with unmeasurable states, an observer-based event-triggered control law is proposed. A simulation example is given to validate the proposed control laws.