Consensus of discrete-time multi-agent systems over packet dropouts channels

In this paper, we investigate the consensus problem for discrete linear multi-agent systems (MASs) with Markovian packet dropouts. Both identical and nonidentical packet dropouts are studied. For the discrete-time MASs under identical packet dropouts, we present the expectation of the total sojourn time of packet dropouts and successful message transmission, the switching number from packet dropouts to successful message transmission, and the awaken number of packet dropouts and successful message transmission. Based on these expectations, a linear consensus controller is designed through analyzing the transient properties of the Markov process such that the MASs can reach consensus almost surely for any initial distribution of packet dropouts. When it comes to the nonidentical packet dropouts where all the packets are independent and stochastic, a Markovian-lossy-channel based switching model (MLCBS model) is proposed. Based on the MLCBS model, we also propose an easy-to-implement linear consensus controller such that the MASs with nonidentical packet dropouts can achieve consensus almost surely. Finally, the theoretical results are illustrated by simulation examples.     

Security control of networked systems with deception attacks and packet dropouts: A discrete-time approach

This paper is concerned with the security control problem for a class of networked systems subject to deception attacks and packet dropouts. First, by taking into account the deception attacks and packet dropouts in an unified framework, a discrete-time stochastic system is presented. In virtue of matrix exponential computation, an equivalent discrete-time stochastic model is established. Based on this, the security analysis is given by the law of total expectation and some sufficient conditions are provided. Subsequently, a controller is designed. Finally, the effectiveness of the proposed method is illustrated by two examples including a practical power grid system.     

Optimal tracking performance and design of networked control systems with packet dropouts

The optimal tracking problem for single-input–single-output (SISO) networked control system over a communication channel with packet dropouts is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. It is shown that the optimal tracking performance is constrained by nonminimum phase zeros, unstable poles, the characteristics of the reference signal and packet dropout probability, and the optimal controller is obtained. It is also shown that when the communication constraint does not exist, the optimal tracking performance reduces to the existing normal tracking performance of the control system without a communication channel. The result shows how the packet dropouts probability of a communication channel may fundamentally constrain a control system's tracking ability. Some typical examples and simulations are given to illustrate the theoretical results.     

Modeling and stabilization of networked control systems with bounded packet dropouts and occasionally missing control inputs subject to multiple sampling periods

The paper is concerned with the modeling and stabilization problem of networked control systems under simultaneous consideration of bounded packet dropouts and occasionally missing control inputs. In particular, the focus of the paper is to capture the case where the packet dropouts and control inputs missing are subject to multiple sampling periods, and not periodic as in existing results. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original linear system is firstly transformed to a switched stochastic time-delay system. Meanwhile, the probability distribution values of stochastic delay taking values in m(m ≥ 2) given intervals can be explicitly obtained, which is of vital importance to analyse the stabilization problem of considered system. Secondly, by means of the average dwell time technique, some sufficient conditions in terms of linear matrix inequalities for the existence of desired stabilizing controller are derived. Finally, an illustrative example is given to illustrate the effectiveness of the proposed stabilizing controller and some less conservative results are obtained.     

A delay system approach to networked control systems with limited communication capacity

This paper addresses the problem of quantized feedback control for networked control systems (NCSs). Firstly, with consideration of the effect of network conditions, such as network-induced delays, data packet dropouts and signal quantization, the sampled-data model of closed-loop feedback system based on the updating sequence of the event-driven holder is formulated, from which a continuous system with two additive delay components in the state is developed. Subsequently, by making use of a novel interval delay system approach, the stability analysis and control synthesis for NCSs with two/one static quantizer are solved accordingly. Finally, two illustrative examples are given to show the effectiveness and advantage of the method.     

Stabilization of networked periodic piecewise linear systems under asynchronous switching with packet dropouts

In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples.     

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.     

Estimation fusion for networked systems with multiple asynchronous sensors and stochastic packet dropouts

This paper studies the asynchronous state fusion estimation problem for multi-sensor networked systems subject to stochastic data packet dropouts. A set of Bernoulli sequences are adopted to describe the random packet losses with different arriving probabilities for different sensor communication channels. The asynchronous sensors considered in this paper can have arbitrary sampling rates and arbitrary initial sampling instants, and may even sample the system non-uniformly. Asynchronous measurements collected within the fusion interval are transformed to the fusion time instant as a combined equivalent measurement. An optimal asynchronous estimation fusion algorithm is then derived based on the transformed equivalent measurement using the recursive form of linear minimum mean squared error (LMMSE) estimator. Cross-correlations between involved random variables are carefully calculated with the stochastic data packet dropouts taken into account. A numerical target tracking example is provided to illustrate the feasibility and effectiveness of the proposed algorithm.     

Generalized pseudo-Bayesian estimator for networked control systems over UDP-like channels

This paper focuses on state estimation issues for networked control systems (NCSs) with both control input and observation packet dropouts over user datagram protocol (UDP) communication channels. For such systems, which are usually known as UDP-like systems, the computation cost of the optimal estimator is too high to afford in practice due to exponential growth of complexity. Although quite a few suboptimal estimators could be alternatives for improving the computational efficiency, yet researches on the stability of suboptimal estimators are rarely reported. Based on the generalized pseudo-Bayesian (GPB) algorithm, an efficient suboptimal algorithm is developed for UDP-like systems. More crucially, a sufficient condition is obtained, which guarantees the stability of its mean estimation error covariance. This stability condition explicitly expresses that the rate of observation packet dropout is a critical factor in determining the stability of the proposed GPB estimator, while the rate of control input packet dropout has no influence on it. The results are illustrated by numerical examples.     

Networked predictive control for linear systems with quantizers by an event-driven strategy

In this paper, networked predictive control is investigated for a networked control system with quantizers by an event-driven strategy. An event generator is designed according to a deviation of state estimation between the current time and last trigger time. A predictive strategy is proposed to compensate effect of network-induced delays and packet dropouts. The quantizers are used to deal with signals by converting real-valued signals into effective ones in both feedback and forward channels. Based on a “zoom” strategy, sufficient conditions are given to ensure stabilization of the networked control system by solving linear matrix inequalities. A simulation example is proposed to exhibit advantages and availability of the developed techniques.     

Stochastic synchronization of semi-Markovian jump chaotic Lur’e systems with packet dropouts subject to multiple sampling periods

This paper is concerned with the problem of stochastic synchronization for semi-Markovian jump chaotic Lur’e systems. Firstly, packet dropouts and multiple sampling periods are both considered. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original system is transformed to a stochastic time-delay system. Secondly, by getting the utmost out of the usable information on the actual sampling pattern, the probability distribution values of stochastic delay taking values in m given intervals can be explicitly obtained. Then, a newly augmented Lyapunov-Krasovskii functional is constructed. Based on that, some sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the error system, and thus, the master system stochastically synchronize with the slave system. Finally, the effectiveness and potential of the obtained results is verified by a simulation example.     

Stability analysis of networked control systems with round-robin scheduling and packet dropouts

In this paper, the stability of networked control systems (NCSs) with communication constraints at both channels is investigated. A Conventional Round-Robin Scheduling (CRRS) is applied to deal with the communication constraints issue for its simple structure. Furthermore, a Dynamic Round-Robin Scheduling (DRRS), which can preserve the controllability and the detectability of the systems, is considered. For the unreliable communication channels, two independent homogeneous Markov chains are selected to model the packet dropouts phenomenon in the sensor-to-controller (S/C) channel and the controller-to-actuator (C/A) channel. According to the periodic property of the Round-Robin Scheduling (RRS), an auxiliary system with augmented Markov chain is established by the lifting technique to facilitate the stability analysis of the closed-loop system. A necessary and sufficient condition of the exponential mean-square stability for the NCSs is derived. Two illustrative examples are shown to demonstrate the effectiveness of the proposed stability analysis method.     

Centralized fusion estimation over wireless sensor-actuator networks with unobservable packet dropouts

This paper studies centralized fusion estimation over a wireless sensor-actuator network, where packet dropouts cannot be observed by the fusion estimator. For such a system, we obtain an optimal linear fused estimation of system states, also known as optimal linear estimator. Then, we establish a necessary and sufficient condition for the stability of the optimal linear estimator. Finally, we show that the estimation performance is monotonically decreasing with respect to the observation packet-arrival rate. By analyzing a sequence that converges to the covariance of the optimal linear estimator, an analytical relationship between the estimation performance and the control packet-arrival rate is obtained. Simulation examples are given to illustrate the main results.     

Decentralized control for multi-sensors networked systems with different transmission delays and packet dropouts

In this paper, the linear quadratic (LQ) optimal decentralized control and stabilization problems are investigated for multi-sensors networked control systems (MSNCSs) with multiple controllers of different information structure. Specifically, for a MSNCS, in view of the packet dropouts and the transmission delays, each controller may access different information sets. To begin with, the sufficient and necessary solvability conditions for the LQ decentralized control problems are developed. Consequently, for the purpose of deriving the optimal decentralized control strategy, an innovative orthogonal decomposition method is proposed to decouple the forward and backward stochastic difference equations (FBSDEs) from the maximum principle. In the following, we show that the optimal decentralized controller can be calculated according to a set of Riccati-type equations. Finally, a stabilizing controller is derived for the stabilization problem.     

Security-based resilient event-triggered control of networked control systems under denial of service attacks

This paper is concerned with the security control problem of the networked control system (NCSs) subjected to denial of service (DoS) attacks. In order to guarantee the security performance, this paper treats the influence of packet dropouts due to DoS attacks as a uncertainty of triggering condition. Firstly, a novel resilient triggering strategy by considering the uncertainty of triggering condition caused by DoS attacks is proposed. Secondly, the event-based security controller under the resilient triggering strategy is designed while the DoS-based security performance is preserved. At last, the simulation results show that the proposed resilient triggering strategy is resilient to DoS attacks while guaranteing the security performance.     

Widely linear estimation for multisensor quaternion systems with mixed uncertainties in the observations

The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.     

Strong γc-γcl H∞ stabilization for networked control systems under denial of service attacks

This paper is concerned with the strong γ_c-γ_cl H_∞ stabilization problem for networked control systems (NCSs) subject to denial of service (DoS) attacks, which are common attack behaviors that affect the packet transmission of measurement or control signals. The purpose of the problem under consideration is to design a stable dynamic output feedback (DOF) controller (strong stabilizing controller) with the prescribed H_∞ performance norm bound γ_c to tolerate multiple packet dropouts caused by DoS attacks, such that, the closed-loop system is mean-square stable and captures the H_∞ disturbance attenuation norm bound γ_cl. Based on the Lyapunov functional and the stochastic control approach, some sufficient conditions with the form of matrix inequalities for the existence of the desired stable DOF controller are established. Then, by an orthogonal complement space technique, the controller gain is parameterized. Next, an iterative linear matrix inequality (LMI) algorithm is developed to obtain the controller gain. Finally, the usefulness of the proposed method is indicated by a numerical simulation example.     

Networked feedback control for nonlinear systems with random varying delays

This paper discusses the controller synthesis problem of a nonlinear networked controlled system subject to delays in the measurement and actuation channels. The communication through the network also suffers non-stationary packet dropouts. The bounded nonlinearities in the plant state satisfy Lipschitz conditions. A Lyapunov function is developed for the closed-loop system considering dynamic output feedback and the resulting stabilization conditions are drawn in the form of linear matrix inequalities to ensure that the system is exponentially stable in the mean-square sense. The developed conditions are represented in the form of a convex optimization problem and the results are tested by simulation on a quadruple-tank process.