Query: Event-triggered  control,

title: Observer Based Event Triggered Control for Networked Linear Systems Subject to Denial of Service Attacks
abstract: This paper is concerned with the observer based event triggered control for a continuous networked linear system subject to denial of service (DoS) attacks, where the attacks are launched periodically to block the data transmission in control channels. First, a new observer state based resilient event triggering scheme is developed in the presence of DoS attacks. Second, a novel event based switched system model is established by considering the effect of the event triggering scheme and DoS attacks simultaneously. By virtue of this new model combined with a piecewise Lyapunov Krasovskii functional method, the sufficient conditions are derived to guarantee exponential stability of the resulting switched system. It is shown that the proposed results can establish a quantitative relationship among the launching/sleeping periods of the attacks, the event triggering parameters, the sampling period, and the exponential decay rate. Third, criteria for designing a desired observer based event triggered controller are provided and expressed in terms of a set of linear matrix inequalities. Finally, an offshore structure model is presented to illustrate the efficiency of the developed control method.

title: Adaptive event triggered control for a class of nonlinear systems with periodic disturbances
abstract: This paper investigates the adaptive event triggered control problem for a class of nonlinear systems subject to periodic disturbances. To reduce the communication burden, a reliable relative threshold strategy is proposed. Fourier series expansion and radial basis function neural network are combined into a function approximator to model suitable time varying disturbed function of known periods in strict feedback systems. By combining the Lyapunov stability theory and the backstepping technique, the proposed adaptive control approach ensures that all the signals in the closed loop system are bounded, and the tracking error can be regulated to a compact set around zero in finite time. Finally, simulation results are presented to verify the effectiveness of the theoretical results.

title: Secure Cooperative Event Triggered Control of Linear Multiagent Systems Under DoS Attacks
abstract: This paper studies secure cooperative event triggered control of linear multiagent systems under denial of service (DoS) attacks. The DoS attacks refer to interruptions of communication channels carried out by an intelligent adversary. We consider a class of time sequence based DoS attacks allowed to occur aperiodically. Then, an explicit analysis of the frequency and duration of DoS attacks is investigated for both secure leaderless and leader following consensus problems. A resilient cooperative event triggered control scheme is developed and scheduling of controller updating times is determined in the presence of DoS attacks. It is shown that based on the proposed distributed algorithms, all the agents can achieve secure consensus exponentially. The effectiveness of the developed methods is illustrated through three case studies: 1) multiple robot coordination; 2) distributed voltage regulation of power networks; and 3) distributed cooperative control of unstable dynamic systems.

title: Consensus of multi agent systems via fully distributed event triggered control
abstract: This article studies consensus of linear multi agent systems (MASs) on undirected graphs. An adaptive event triggering protocol is constructed for consensus control by using relative information between agents. Sufficient conditions are established for consensus of linear MASs without and with external disturbances, respectively. Zeno behavior is proved to be excluded. Moreover, a self triggered realization based on sampled information is formulated for the protocol. Since the proposed protocol incorporates both adaptive control and event triggered control, it can be implemented in a fully distributed way and only makes use of the sampled relative information between neighboring agents. Two numerical examples are finally provided for demonstrating the effectiveness and advantages of the theoretical results.

title: Robust Event Triggered Control Invariance of Probabilistic Boolean Control Networks
abstract: In this brief, the robust control invariance problem of probabilistic Boolean control networks (PBCNs) is investigated by a class of event triggered control (ETC) which is an intermittent control scheme in essential. By resorting to the semi tensor product (STP) technique, a PBCN with ETC can be equivalently described in a form of an algebraic linear system. Based on which, a matrix testing condition is derived to judge whether the given set can be a robust ETC invariant set (RETCIS) Subsequently, a necessary and sufficient condition is developed for the existence of event triggered controllers. Meanwhile, all feasible event triggered controllers are designed for guaranteeing the given set to be an RETCIS. Finally, a biological example is employed to demonstrate the availability of theoretical results.

title: Switching Like Event Triggered Control for Networked Control Systems Under Malicious Denial of Service Attacks
abstract: This article investigates the switching like event triggered control for networked control systems (NCSs) under the malicious denial of service (DoS) attacks. First, by dividing the DoS attacks into S interval (DoS free case) and D interval (DoS case) a switching like event triggered communication scheme (SETC) is well designed to deal with intermittent DoS attacks to improve communication efficiency while keeping the desired control performance. Second, by considering the SETC and NCSs into a unified framework, the studied system is transferred into a time delay system. Then, under the constraint of the number of maximum allowable data dropouts induced by DoS attacks, a stability criterion and a stabilization criterion are derived, which can be used to estimate the event triggered communication parameters and obtain the security controller gain simultaneously. Moreover, the derived stabilization criterion can also provide a tradeoff to balance communication efficiency and $H_{\infty control performance. At last, a networked invert pendulum on a cart is conducted to show the effectiveness of the proposed method.

title: Adaptive Event Triggered Control of Nonlinear Systems With Controller and Parameter Estimator Triggering
abstract: In this note, the event triggered adaptive control for a class of uncertain nonlinear systems is considered. Unlike the traditional adaptive event triggered control, the controller and parameter estimator are event triggered simultaneously. Asymptotical convergence of stabilization error is guaranteed. To solve this problem, we design a set of event triggering conditions, which is updated for each triggering. At the same time, the input to state stable assumption is not needed. It is shown that the proposed control schemes guarantee that all the closed loop signals are globally bounded and the stabilization error converges to the origin asymptotically. Simulation results illustrate the effectiveness of our scheme.

title: Periodic Event Triggered Control for Nonlinear Networked Control Systems
abstract: Periodic event triggered control (PETC) is an appealing paradigm for the implementation of controllers on platforms with limited communication resources, a typical example being networked control systems. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario, where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the control inputs available locally, to decide whether a transmission is needed over the considered network. Following the emulation approach, we show how to design local triggering generators to ensure input to state stability and \mathcal {L}_p$ stability for the overall system based on a continuous time output feedback controller that robustly stabilizes the network free system. The method is applied to a class of Lipschitz nonlinear systems, for which we formulate the design conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.

title: Adaptive Neural Event Triggered Control for Discrete Time Strict Feedback Nonlinear Systems
abstract: This paper proposes a novel event triggered (ET) adaptive neural control scheme for a class of discrete time nonlinear systems in a strict feedback form. In the proposed scheme, the ideal control input is derived in a recursive design process, which relies on system states only and is unrelated to virtual control laws. In this case, the high order neural networks (NNs) are used to approximate the ideal control input (but not the virtual control laws) and then the corresponding adaptive neural controller is developed under the ET mechanism. A modified NN weight updating law, nonperiodically tuned at triggering instants, is designed to guarantee the uniformly ultimate boundedness (UUB) of NN weight estimates for all sampling times. In virtue of the bounded NN weight estimates and a dead zone operator, the ET condition together with an adaptive ET threshold coefficient is constructed to guarantee the UUB of the closed loop networked control system through the Lyapunov stability theory, thereby largely easing the network communication load. The proposed ET condition is easy to implement because of the avoidance of: 1) the use of the intermediate ET conditions in the backstepping procedure; 2) the computation of virtual control laws; and 3) the redundant triggering of events when the system states converge to a desired region. The validity of the presented scheme is demonstrated by simulation results.

title: A Distributed Dynamic Event Triggered Control Approach to Consensus of Linear Multiagent Systems With Directed Networks
abstract: In this paper, we study the consensus problem for a class of linear multiagent systems, where the communication networks are directed. First, a dynamic event triggering mechanism is introduced, including some existing static event triggering mechanisms as its special cases. Second, based on the dynamic event triggering mechanism, a distributed control protocol is developed, which ensures that all agents can reach consensus with an exponential convergence rate. Third, it is shown that, with the dynamic event triggering mechanism, the minimum interevent time between any two consecutive triggering instants can be prolonged and no agent exhibits Zeno behavior. Finally, an algorithm is provided to avoid continuous communication when the dynamic event triggering mechanism is implemented. The effectiveness of the results is confirmed through a numerical example.