Distributed event-triggered control for networked control systems with stochastic cyber-attacks

This paper is concerned with the problem of distributed event-triggered controller design for networked control systems (NCSs) with stochastic cyber-attacks. A decentralized event-triggered scheme is introduced to save the energy consumption and alleviate the transmission load of the network. Each sensor can make its own decision to determine whether the sampled data is delivered to the network or not. By taking two kinds of random cyber-attacks into consideration, a novel mathematical model is constructed for distributed event-triggered NCSs. Sufficient conditions which can guarantee the stability of the control system are obtained by applying Lyapunov stability theory, and the design method of the controller gain is presented in an exact expression. Finally, an example is given to demonstrate the effectiveness of the proposed method.     

State estimation for networked systems with Markovian communication constraints and multiple packet dropouts

In this paper, the state estimation problem for discrete-time networked systems with communication constraints and random packet dropouts is considered. The communication constraint is that, at each sampling instant, there is at most one of the various transmission nodes in the networked systems is allowed to access a shared communication channel, and then the received data are transmitted to a remote estimator to perform the estimation task. The channel accessing process of those transmission nodes is determined by a finite-state discrete-time Markov chain, and random packet dropouts in remote data transmission are modeled by a Bernoulli distributed white sequence. Using Bayes’ rule and some results developed in this study, two state estimation algorithms are proposed in the sense of minimum mean-square error. The first algorithm is optimal, which can exactly compute the minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm obtained under a lot of Gaussian hypotheses. The proposed suboptimal algorithm is recursive and has time-independent complexity. Computer simulations are carried out to illustrate the performance of the proposed algorithms.     

Fuzzy event-triggered control for nonlinear networked control systems

This paper is focus on an event-triggered control design problem for nonlinear networked control systems with missing data and transmission delay in the interval type-2 (IT2) fuzzy form. An event-triggered controller is presented under a sampled-state-error mechanism. By dividing the event-triggered interval into some subsets, stability analysis is carried out based on Lyapunov-Krasovskii functional (LKF), and the stability of the closed-loop system is ensured. The proposed design is applied to the continuous stirred tank reactor system (CSTR) and the manipulator system. The control strategy is effective, and the merit of the event-triggered mechanism is indicated.     

An improved memory-event-triggered control for networked control systems

In this paper, the H_∞ control problem is investigated for a class of networked control systems with network-induced delay. A memory event-triggered scheme (METS) is proposed to reduce the redundant packet transmission in the network channel. Different from the normal event-triggered scheme (ETS), some recent released packets are stored at the event generator and controller sides, which are utilized for the first time to generate the triggered events and design the memory-based controller. The proposed METS has the following two merits. (1) The information of certain recent released signals are first utilized, which helps to improve the triggering instants at the crest or trough of the responses. (2) A state-dependent time-varying threshold parameter is designed, which can adjust the packet transmission rate according to the information of the state. Based on the proposed METS, a memory event-triggered controller is designed, the controller feedback gains and triggering parameters can be co-designed by solving a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Optimal tracking performance for networked control systems with quantization

This paper investigates the optimal tracking performance of the multiple-input multiple-output (MIMO) discrete-time networked control systems (NCSs) considering the quantization of communication channel. The tracking performance is adopted for the H₂ square error criterion. The optimal tracking performance expression is obtained by using the co-prime factorization, the partial factorization, the inner–outer factorization and the spectral decomposition methods. Moreover, the paper also includes the exploration of the optimal tracking performance with input power constraint. The obtained results have demonstrated that the optimal tracking performance is influenced by the non-minimum phase zeros, unstable poles and their directions, the reference signal and the quantization interval. Moreover the theoretical results have also been proven using a number of different examples.     

Reliable control for networked control systems with probabilistic actuator fault and random delays

In this paper, the reliable control design is considered for networked control systems (NCSs) against probabilistic actuator fault with different failure rates, measurements distortion, random network-induced delay and packet dropout. A new distribution-based fault model is proposed, which also contains the probability distribution information of the random delay and packet dropout. By using Lyapunov functional and new technique in dealing with time delay, stability and stabilization criteria are derived in terms of linear matrix inequalities. The provided numerical example and vertical takeoff and landing (VTOL) aircraft system illustrate that: firstly, using the distribution information of the delay, the maximum effective delay bound (MEDB) can be greatly improved, secondly, the proposed reliable controller can stabilize the NCSs with probabilistic actuator fault and measurements distortion, which may be unstable under the controller designed without considering the unreliable cases.     

Event-triggered fault estimation and fault-tolerant control for networked control systems

This paper is concerned with the event-triggered fault estimation and fault-tolerant control for continuous-time dynamic systems subject to system fault and external disturbance under network environment. Firstly, based on the event-triggered sampling, a fault diagnosis observer is constructed to estimate both the system state and the system fault simultaneously, and a multi-objective constraint is established to guarantee the estimation accuracy. Based on the estimated system state and fault signal, a fault-tolerant controller is proposed to compensate the influence of occurred faults and maintain the system performance. The event-triggered scheme and the fault-tolerant controller are co-designed to guarantee the required performance of faulty system and reduce the consumption of communication resources. Finally, simulation results of an F-404 aircraft engine system are provided to demonstrate the effectiveness of the proposed method.     

Cooperative surrounding control with collision avoidance for networked Lagrangian systems

This paper investigates the cooperative surrounding control problem for networked multi-agent systems with nonlinear Lagrangian dynamics. With the consideration of the target with constant and time-varying velocity, two cooperative surrounding control algorithms with collision avoidance are proposed, in which possible collision among agents is prevented so as to achieve a more reliable and safer performance. For the case when the target has a constant velocity, a velocity observer is designed firstly for each agent. Secondly, to handle the nonlinear dynamics and avoid collisions, the neural networks and potential functions are used for the controller design. Then, the cooperative surrounding control algorithm is proposed such that all the agents surround the target with the desired relative positions. For the case when the target has a time-varying velocity, the velocity observer is designed under the assumption that the target’s partial acceleration is known for each agent. Then, the cooperative surrounding control algorithm is proposed such that the surrounding error between the target and each agent is bounded. The main difference between these two algorithms is that the former can ensure the collision avoidance among target and agents, while the latter can do so only among agents because the target’s velocity is time-varying. The Lyapunov theory is used to prove the stability of the cooperative surrounding control algorithms. The simulation illustrates the effectiveness of the theoretical results.     

Modified tracking performance limitation of networked time-delay systems with two-channel constraints

This paper investigates the modified tracking performance limitation of the networked time-delay systems with two-channel constraints. We consider both the white Gaussian noise and packet dropout constraints in the communication channels. In the plant, the non-minimum phase, unstable poles and time-delay are considered. The modified tracking performance limitation expressions will be achieved using the co-prime factorization and the spectral decomposition technique, and the two-parameter controller is adopted. The results show that the modified tracking performance limitation is related to the intrinsic properties of the given plant, including the non-minimum phase zeroes, the unstable poles and the time-delay. Furthermore, the network communication parameters, e.g. the white Gaussian noise, the packet-dropouts probability and the modified factor affect the modified tracking performance limitation of the networked time-delay systems. Finally, some particular examples are provided to illustrate the efficiency of the proposed method.     

Event-based control for networked T-S fuzzy cascade control systems with quantization and cyber attacks

This paper investigates the event-based control for networked T-S fuzzy cascade control systems with quantization and cyber attacks. In order to solve the problem of limited communication resources, an event-triggered scheme and a quantization mechanism are adopted, which can effectively reduce the burden of communication and save the network resources of the system. By considering the influence of cyber attacks, a newly quantized T-S fuzzy model for networked cascade control systems (NCCSs) under the event-triggered scheme is established. By using the Lyapunov stability theory, sufficient conditions guaranteeing the asymptotical stability of networked T-S fuzzy cascade control systems are obtained. In addition, the controller gains are derived by solving a set of linear matrix inequalities. Finally, a numerical example is presented to verify the validity of the proposed method.     

Event-triggered sliding mode control for networked linear systems

This paper investigates the control-based event-triggered sliding mode control for a networked linear system whose feedback information is transmitted over a digital communication network. In this paper, a novel event-triggered mechanism based on control value is proposed. Different from traditional event-triggered mechanisms that are normally based on states, our mechanism pays more attention to the desired control input value of the system. When the deviation between the current control input and the control input being calculated on the basis of the previous system state exceeds a given threshold, an event is triggered. For the sake of reducing the information to be transmitted, a quantization policy is executed and only a few bits are needed to transmit the feedback symbol of each sample. The combination of the control-based event-triggered mechanism and the quantization policy can significantly reduce both the transmission frequency and the number of bits of each feedback packet. For the concerned system, sliding mode control is implemented. The reachability of the sliding mode surface and the robust stability of the system are analyzed by fully taking quantization effects into account. Moreover, the effects of transmission delay of feedback packets on the event-triggering mechanism are considered. Under the proposed mechanism, the lower bound of event intervals is proven to be non-zero, i.e., the Zeno behavior is excluded. Simulations of a mechanical system are done to further verify the superiority of the proposed mechanism.     

Distributed event-triggered control co-design for large-scale systems via static output feedback

This work investigates the problem of distributed control for large-scale systems, in which a communication network is available to exchange information. To avoid the unnecessary communication, an event-triggered control (ETC) mechanism is introduced, in which the transmission occurs only when a certain event is triggered. Under the assumption that only the output signal is available, the static output feedback (SOF) is considered in this work. The aim of the co-design is to design an SOF controller and an ETC condition simultaneously such that the overall closed-loop system is stabilized with a certain level of performance. To this end, an event-triggering scheme based on output signals is proposed to determine when the event is triggered. Then the closed-loop system is modeled as a linear perturbed system. The distributed control co-design is formulated as a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, a numerical example is presented to show the effectiveness of the proposed design method.     

Observer-based fault-tolerant control for a class of networked control systems with transfer delays

In this paper, an observer-based fault-tolerant control (FTC) method is proposed for a class of networked control systems (NCSs) with transfer delays. Markov chain is employed to characterize the transfer delays. Then, such kind of networked control systems are modelled as Markovian jump systems. An observer-based FTC scheme using the delayed state information and the estimated fault value is presented to guarantee the stability of the faulty systems. An inverted pendulum example is used to illustrate the efficiency of the proposed method.     

Fault-tolerant control for model-free networked control systems under DoS attacks

This paper studies the fault-tolerant model-free adaptive control (FT-MFAC) problem for a class of single-input single-output (SISO) nonlinear networked control systems (NCSs) under denial-of-service (DoS) attacks. A novel FT-MFAC framework is established with the consideration of DoS attacks and the sensor fault, in which DoS attacks obeying the Bernoulli distribution randomly happen in the sensor-to-controller channel and the sensor fault is approximated by the radial basis function neural network (RBFNN). Based on the proposed framework, an FT-MFAC algorithm that uses only input/output data is proposed to guarantee that the output tracking error is bounded in the sense of mean square. Finally, the effectiveness of the proposed algorithm is illustrated by a simulation.     

Input-output finite-time stability for networked control systems with memory event-triggered scheme

This paper has investigated the input-output finite time stability (IO-FTS) for a class of networked control systems (NCSs) with network-induced delay. To reduce the frequents of packets transmission, a novel memory event-triggered scheme (METS) has been proposed. Different from existing event-triggered schemes, the proposed METS can make use of certain released packets to generate new event. By this way, the event generator can do more precise decision and better control performance can be expected. By using a Lyapunov functional method, sufficient condition for the IO-FTS of NCSs has been derived. Then a co-design method is proposed to obtain the memory feedback gains and parameters of the METS. Finally, a simulation example is carried out and the effectiveness of the designed METS is validated. The IO-FTS of NCSs with solved memory feedback gains is also confirmed.     

Dynamic event-triggered control of networked control systems with uncertainty and transmission delay

This paper presents a method for designing dynamic event-triggered controller of networked control systems (NCSs) with uncertainty and time delays. Under the condition that the Lyapunov function of the system is allowed to increase at each jump point, the globally exponentially stable (GES) of the system can be achieved by using the Riccati differential equation and the principle of average dwell time (ADT). The minimum allowable inter-event interval is obtained by limiting the increment of the Lyapunov function within the transmission interval. Both the static event triggering and no transmission delay are included in the designed dynamic event triggering mechanism as special cases. A numerical example is given to verify the correctness and validity of the proposed method.     

Quantized control of event-triggered networked systems with time-varying delays

The paper is a study of quantized control for stochastic Markov jump systems with interval time-varying delays and bounded system noise under event-triggered mechanism. A new scheme of Lyapunov–Krasovskii functional which contains the quadratic terms and integral terms is presented. Then quadratic convex technology, the theory of stochastic switching system, and logarithmic quantizer are applied to this paper. The design of quantized controller is obtained with those methodologies. Different from previous results, our derivation applies the idea of second-order convex combination. The conservatism of stability criteria for systems is reduced by using this method. A numerical example under different conditions is given to demonstrate the effectiveness and validity of the new design techniques.     

A novel controller design and evaluation for networked control systems with time-variant delays

A new delayed state-variable model for networked control systems is presented, upon which a linear quadratic regulator (LQR) is designed. A method of delays-estimation online is also given. A fuzzy logic with LQR controller is addressed for the difficulty on implementation of LQR in networked control systems (NCSs) with time-variant delays. Simulation results prove that the novel controller can make the system stable and robustly preserve the performance in terms of time-variant delays.     

Stochastic fault tolerant control of networked control systems

A problem of stabilization about uncertain networked control systems (NCSs) with random but bounded delays is discussed in this paper. By using augmented state-space method, this class of problems can be modeled as discrete-time jump linear systems governed by finite-state Markov chains. A new switched model based on probability is proposed to research problems of reliable control when actuators become ageing or partially disabled. Using improved V-K iteration algorithm, a class of reliable controllers are designed to make systems asymptotically mean square stable under several stochastic disturbances such as random time-delay and stochastic actuator failure and the maximal redundancy degree is given through this method.