Co-design of output-based security control and dynamic event-triggered mechanism for NCSs under hybrid cyber attacks

This paper investigates output-based dynamic event-triggered control for networked control systems (NCSs), in which hybrid cyber attacks randomly occur in communication network. First, a gain adjustable dynamic output feedback (DOF) controller is designed for NCSs and relaxes state-available constraint in presence of three types of attacks, including stochastic deception attacks, replay attacks and aperiodic denial-of-service (DoS) attacks. Second, a output-based dynamic event-triggered mechanism (DETM) is designed to optimize limited network resources under the cyber attacks. Third, a new switched system is established to describe the effect of hybrid cyber attacks, the DOF controller and the DETM simultaneously. Then, criteria for guaranteeing asymptotically stability of the switched system are obtained. Furthermore, the co-design method of DETM and DOF controller is provided to maintain the NCSs stability. Finally, an example is presented to show the effectiveness of the proposed methods in this paper.     

Proportional-integral control for synchronization of complex dynamical networks under dynamic event-triggered mechanism

In this paper, the exponential synchronization problem is investigated for a class of continuous-time complex dynamical networks (CDNs) with proportional-integral control strategy and dynamic event-triggered mechanism (DETM). To reduce communication overhead, a novel DETM is proposed to decide whether a certain control signal generated by proportional-integral controller should be transmitted or not. The dynamics of each network node is analyzed in conjunction with the proposed proportional-integral strategy under the DETM, and then a sufficient condition for achieving exponential synchronization of CDNs is provided. The validity of the DETM is further verified by the exclusion of the Zeno behavior. The gain matrices of the controller and the parameters of the DETM are jointly designed. The effectiveness of the proportional-integral control strategy under the DETM is demonstrated by a numerical example.     

Zonotopic fault detection for discrete-time systems with limited communication capability and sensor nonlinearity

In this paper, the fault detection filter (FDF) design problem based on a dynamic event-triggered mechanism (DETM) is investigated for discrete-time systems with signal quantization and sensor nonlinearity. In order to conserve the limited network resources, a newly event-triggered mechanism with dynamic threshold is adopted to reduce the number of transmitted data through network more effectively. With the consideration of DETM, signal quantization and sensor nonlinearity, a fault detection filter is constructed to achieve the robustly asymptotic stability of established model with expected fault detection objective. In addition, by influence of DETM, external interference and quantization errors, a zonotopic residual evaluation mechanism is constructed to detect the occurring fault of plant. Finally, a practical example is provided to illustrate the effectiveness of proposed design approach.     

Event-triggered control for uncertain stochastic systems under triple network attacks

This paper studies the control problem of uncertain stochastic systems, which takes into account the impact of network attacks. The types of network attacks considered are denial-of-service (DoS) attacks, deception attacks and replay attacks. In order to save network resources and improve communication utilization, the static event-triggered mechanism and adaptive event-triggered mechanism are cited respectively. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing improved Wirtinger-based integral inequality and Jensens inequality, the criteria on stochastic stability in the mean square for uncertain stochastic systems are proposed. Secondly, the design methods of static event-triggered controller and adaptive event-triggered controller are given respectively. Finally, a practical example is given to manifest the effectiveness of the theoretical results.     

Dynamic event-triggered leader-following consensus control of a class of linear multi-agent systems

We address the leader-following tracking consensus issue for a class of linear multi-agent systems (MASs) via dynamic event-triggered (DET) approaches in this paper. The DET communication mechanism is introduced by an additional internal dynamic variable, and is developed to schedule agents’ data transmission. State observers are also employed to tackle the scenario wherein inner information of follower agents are not available for measurement. And then, state-based and observer-based distributed control proposals are proposed on the basis of dynamic event-triggered mechanism (DETM), respectively. To avoid continuous measurement information monitor, we present a technical approach for generation of the combinational information from their own neighboring agents only at event instants. The stabilities of the resulting closed-loop systems, both state-feedback one and output-feedback one, are rigorously analyzed in theory, and it is proven that all signals in the closed-loop system are bounded and Zeno behavior is also excluded. Simulation examples are presented to illustrate the theoretical claims.     

Event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems

This paper is concerned with event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems. The approach of fuzzy logic systems (FLSs) approximation is extended to high-order stochastic nonlinear systems to deal with the unknown nonlinear uncertainties. A novel high-order adaptive fuzzy tracking controller is firstly presented via a backstepping approach and event-triggering mechanism which can mitigate the unnecessary waste of computation and communication resources. Based on the above techniques, frequently-used growth assumptions imposed on unknown system nonlinearities are removed and the influence for the high order is handled. The proposed high-order adaptive fuzzy tracking control method not only deals with the influence of high order, but also ensures that the tracking error converges to a small neighborhood of the origin in probability. Finally, the effectiveness of the proposed control method is illustrated by a numerical example.     

Event-triggered finite-time fault detection for delayed networked systems with conic-type nonlinearity and deception attacks

The paper is concerned with the finite-time fault detection (FTFD) problem for a class of delayed networked systems subject to conic-type nonlinearity and randomly occurring deception attacks (RODAs) via dynamic event-triggered mechanism (DETM). The nonlinear function with the conic-type constraint is limited to a known hypersphere with uncertain center. Moreover, a variable governed by Bernoulli distribution is introduced to characterize the RODAs phenomenon. In order to reduce unnecessary communication transmissions, a DETM is considered in the design of finite-time fault detection filter (FTFDF) for the addressed networked systems with time-delays. This paper focuses on the design of an FTFDF via the DETM to ensure the finite-time stochastic stability of error dynamics system with satisfactory the prescribed $H_{\infty }$ performance. Moreover, the desired FTFDF parameter matrices are obtained by solving linear matrix inequalities. In the end, a simulation example is employed to illustrate the validity of the proposed FTFD method.     

Reduced-order K-filters-based event-triggered adaptive command filtered tracking control for stochastic constrained nonlinear systems

To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method.     

Fuzzy adaptive event-triggered control for uncertain nonlinear system with prescribed performance: A combinational measurement approach

This paper addresses the adaptive fuzzy event-triggered control (ETC) problem for a class of nonlinear uncertain systems with unknown nonlinear functions. A novel ETC approach that exhibits a combinational triggering (CT) behavior is proposed to update the controller and fuzzy weight vectors, achieving the non-periodic control input signals for nonlinear systems. A CT-based fuzzy adaptive observer is firstly constructed to estimate the unmeasurable states. Based on this, an output feedback ETC is proposed following the backstepping and error transformation methods, which ensures the prescribed dynamic tracking (PDT) performance. The PDT performance indicates that the transient bounds, over-shooting and ultimate values of tracking errors are fully determined by the control parameters and functions chosen by users. The closed-loop stability is guaranteed under the framework of impulsive dynamic system. Besides, the Zeno phenomenon is circumvented. The theoretical analysis indicates that the proposed scheme guarantees control performance while considerably reducing the communication resource utilization and controller updating frequency. Finally, the numerical simulations are conducted to verify the theoretical findings.     

An improved design strategy for approximation-based adaptive event-triggered tracking of a class of uncertain nonlinear systems

This paper presents an improved adaptive design strategy for neural-network-based event-triggered tracking of uncertain strict-feedback nonlinear systems. An adaptive tracking scheme based on state variables transmitted from the sensor-to-controller channel is designed via only single neural network function approximator, regardless of unknown nonlinearities unmatched in the control input. Contrary to the existing multiple-function-approximators-based event-triggered backstepping control results with multiple triggering conditions dependent on all error surfaces, the proposed scheme only requires one triggering condition using a tracking error and thus can overcome the problem of the existing results that all virtual controllers with multiple function approximators should be computed in the sensor part. This leads to achieve the structural simplicity of the proposed event-triggered tracker in the presence of unmatched and unknown nonlinearities. Using the impulsive system approach and the error transformation technique, it is shown that all the signals of the closed-loop system are bounded and the tracking error is bounded within pre-designable time-varying bounds in the Lyapunov sense.     

Decentralized event-triggered finite-time attitude consensus control of multiple spacecraft under directed graph

This article investigates the finite-time consensus problem for the attitude system of multiple spacecraft under directed graph, where the communication bandwidth constraint, inertia matrix uncertainties and external disturbances are considered. An event-triggered communication mechanism is developed to address the problem of communication bandwidth constraint. In this event-triggered mechanism, spacecraft sends their attitude information to their neighbors only when the given event is triggered. Furthermore, an adaptive law is designed to counteract the effect of inertia matrix uncertainties and external disturbances. Then, a finite-time attitude consensus tracking control scheme is proposed based on the event-triggered communication mechanism and adaptive law. The proposed control scheme can guarantee the finite-time stability and convergence of the multiple spacecraft systems and exclude the Zeno phenomenon. Finally, simulation results validate the effectiveness of the proposed control scheme.     

Global adaptive event-triggered output feedback controller design for high-order nonlinear systems

This article focuses on the adaptive event-triggered output feedback stabilization problem for a class of high-order systems with uncertain output function. Firstly, an adaptive event-triggered mechanism with a dynamic gain is designed for the nominal system. Then the gain is employed into the observer and event-triggered controller to dominate the nonlinearities. Thirdly, it is proved that all system states converge to zero and the Zeno-behavior is excluded. Finally, a numerical example reveals the effectiveness of the proposed event-triggered control strategy.     

Event-triggered adaptive target tracking control for an underactuated autonomous underwater vehicle with actuator faults

In this paper, the target tracking control problem is investigated for an underactuated autonomous underwater vehicle (AUV) in the presence of actuator faults and external disturbances based on event-triggered mechanism. Firstly, the five degrees-of-freedom kinematic and dynamic models are constructed for an underactuated AUV, where the backstepping method is introduced as the major control framework. Then, radial basis function neural network (RBFNN) and adaptive control method are made full use of estimating and compensating the influences of uncertain information and actuator faults. Besides, the relative threshold event-triggered strategy is integrated into the tracking control to further reduce communication burden from the controller to the actuator. Moreover, through Lyapunov analysis, it is proved that the designed controllers guarantee that the tracking error variables of the underactuated AUV are uniformly ultimately bounded and can converge to a small neighborhood of the origin. Finally, the effectiveness and reasonableness of the designed tracking controllers are illustrated by comparative simulations.     

Dual-Condition event-Triggered distributed adaptive neural control for multi-Agent systems with nonlinear fault

This paper studies the cooperative adaptive dual-condition event-triggered tracking control problem for the uncertain nonlinear nonstrict feedback multi-agent systems with nonlinear faults and unknown disturbances. Under the framework of backstepping technology, a new threshold update method is designed for the state event-triggered mechanism. At the same time, we develop a novel distributed dual-condition event-triggered strategy that combined the fixed threshold triggered mechanism acted on the controller with the new event-triggered mechanism, which can better reduce the waste of communication bandwidth. To deal with the algebraic loop problem caused by the non-affine nonlinear fault, the Butterworth low-pass filter is introduced. At the same time, the unknown function problems are solved by the neural network technology. All signals of the system are semiglobally uniformly ultimately bounded and the tracking performance is achieved, which proved by the Lyapunov stability theorem. Finally, the results of the simulation test the efficiency of the proposed control scheme.     

Adaptive fault compensation control for nonlinear uncertain fractional-order systems: Static and dynamic event generator approaches

The tracking problem of the fractional-order nonlinear systems is assessed by extending new event-triggered control designs. The considered dynamics are accompanied by the uncertain strict-feedback form, unknown actuator faults and unknown disturbances. By using the neural networks and the fault compensation method, two adaptive fault compensation event-triggered schemes are designed. Unlike the available control designs, two static and dynamic event-triggered strategies are proposed for the nonlinear fractional-order systems, in a sense that the minimum/average time-interval between two successive events can be prolonged in the dynamic event-triggered approach. Besides, it is proven that the Zeno phenomenon is strictly avoided. Finally, the simulation results prove the effectiveness of the presented control methods.     

Adaptive optimal tracking controls of unknown multi-input systems based on nonzero-sum game theory

This paper focuses on the optimal tracking control problem (OTCP) for the unknown multi-input system by using a reinforcement learning (RL) scheme and nonzero-sum (NZS) game theory. First, a generic method for the OTCP of multi-input systems is formulated with steady-state controls and optimal feedback controls based on the NZS game theory. Then a three-layer neural network (NN) identifier is introduced to approximate the unknown system, and the input dynamics are obtained by using the derivative of the identifier. To transform the OTCP into a regulation optimal problem, an augmentation of the multi-input system is constructed by using the tracking error and the commanded trajectory. Moreover, we use an NN-based RL method to online learn the optimal value functions of all the inputs, which are then directly used to calculate the optimal tracking controls. All the NN weights are tuned synchronously online with a newly introduced adaptation based on the estimation error. The convergence of the NN weights and the stability of the closed-loop system are analyzed. Finally, a two-motor driven servo system and another nonlinear system are presented to illustrate the feasibility of the algorithm for both linear and nonlinear multi-input systems.     

Dynamic event-triggering sliding mode resilient control for multi-agent systems

The consensus problem for a multi-agent system (MAS) is investigated in this paper via a sliding mode control mechanism subject to stochastic DoS attack, which may occur on each transmission channel independently and randomly according to the Bernoulli distribution. A distributed dynamic event-triggered strategy is implemented on the communication path among agents, where dynamic parameters are introduced to adjust the threshold of event-triggered condition. After that, a distributed sliding mode controller is proposed for ensuring the stochastic consensus of the MAS. Meantime, a minimization problem is solved to obtain the correct controller gain matrix. At last, a numerical example is shown to demonstrate the presented results.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.     

Dynamic Event-Triggered Sliding Mode Resilient Control for Multi-Agent Systems

The consensus problem for a multi-agent system (MAS) is investigated in this paper via a sliding mode control mechanism subject to stochastic DoS attack, which may occur on each transmission channel independently and randomly according to the Bernoulli distribution. A distributed dynamic event-triggered strategy is implemented on the communication path among agents, where dynamic parameters are introduced to adjust the threshold of event-triggered condition. After that, a distributed sliding mode controller is proposed for ensuring the stochastic consensus of the MAS. Meantime, a minimization problem is solved to obtain the correct controller gain matrix. At last, a numerical example is shown to demonstrate the presented results.     

Leader-following consensus for multi-agent systems with actuator faults via adaptive event-triggered control

In this paper, the leader-following consensus problem is investigated by event-triggered control for multi-agent systems subject to time-varying actuator faults. Firstly, for a case of the leader without control input, a distributed event-triggered fault-tolerant protocol is proposed with the help of adaptive gains. Secondly, the proposed protocol is developed by an auxiliary nonlinear function to compensate the effect of the leader’s unknown bounded input. It is shown that under the both obtained protocols the tracking errors converge to an adjustable neighborhood around the origin, meanwhile the Zeno behavior is avoided. Moreover, the protocols are fully distributed in sense that any global information associated with the network is no longer utilized. Finally, numerical examples are presented to show the validity of the obtained protocols.