Resilient distributed MPC for systems under synchronous round-robin scheduling

This paper is concerned with the resilient dynamic output-feedback (DOF) distributed model predictive control (DMPC) problem for discrete-time polytopic uncertain systems under synchronous Round-Robin (RR) scheduling. In order to alleviate the computation burden and improve the system robustness against uncertainties, the global system is decomposed into several subsystems, where each subsystem under synchronous RR scheduling communicates with each other via a network. The RR scheduling is adopted to avoid data collisions, however the updating information at each time instant is unfortunately reduced, and the underlying RR scheduling of subsystems are deeply coupled. The main purpose of this paper is to design a set of resilient DOF-based DMPC controllers for systems under the consideration of polytopic uncertainties and synchronous RR scheduling, such that the desirable performance can be obtained at a low cost of computational time. A novel distributed performance index dependent of the synchronous RR scheduling is constructed, where the last iteration information from the neighbor subsystems is used to deal with various couplings. Then, by resorting to the distributed RR-dependent Lyapunov-like approach and inequality analysis technique, a certain upper bound of the objective is put forward to establish a solvable auxiliary optimization problem (AOP). Moreover, by using the Jacobi iteration algorithm to solve such a problem online, the distributed feedback gains are directly obtained to guarantee the convergence of system states. Finally, two examples including a distillation process example and a numerical example are employed to show the effectiveness of the proposed resilient DMPC strategy.     

An adaptive penalty-like continuous-time algorithm to constrained distributed convex optimization

This paper considers a nonsmooth constrained distributed convex optimization over multi-agent systems. Each agent in the multi-agent system only has access to the information of its objective function and constraint, and cooperatively minimizes the global objective function, which is composed of the sum of local objective functions. A novel continuous-time algorithm is proposed to solve the distributed optimization problem and effectively characterize the appropriate gain of the penalty function. It should be noted that the proposed algorithm is based on an adaptive strategy to avoid introducing the primal-dual variables and estimating the related exact penalty parameters. Additional, it is demonstrated that the state solution of the proposed algorithm achieves consensus and converges to an optimal solution of the optimization problem. Finally, numerical simulations are given and the proposed algorithm is applied to solve the optimal placement problem and energy consumption problem.     

Adaptive resilient containment control for nonlower triangular multiagent systems with time-varying delay and sensor faults

This paper investigates the adaptive resilient containment control for nonlinear multiagent systems (MASs) with time-varying delay, unmodeled dynamics and sensor faults. To solve the coupling problem of unknown state delays and sensor faults in a nonlower triangular structure, we develop an effective method by using a new lemma and the Lyapunov-Krasovskii functional. Then, to reduce the negative impact of unknown sensor faults, a novel adaptive resilient containment control method is designed based on a distributed sliding-mode estimator, which can effectively improve the transient performance of the MASs. Moreover, by using a dynamic signal, the problem of unmodeled dynamics is solved. The proposed control scheme can not only drive all followers suffering from sensor faults to converge to the convex hull formed by the leaders but also relatively reduce the undesired chattering phenomenon. Finally, a comparative simulation example is given to illustrate the effectiveness of the proposed strategy.     

Resilient sampled-data control design for singular networked systems with random missing data

This paper proposes an active resilient control strategy for singular networked control systems with external disturbances and missing data scenario based on sampled-data scheme. To characterize the missing data scenario, a stochastic variable satisfying Bernoulli distributed white sequence is introduced. Based on this scenario, in this paper, two different models are proposed. For both the models, by using Lyapunov–Krasovskii functional approach, which fully uses the available information about the actual sampling pattern, some sufficient conditions in terms of linear matrix inequalities (LMIs) are separately obtained to guarantee that the resulting closed-loop system is admissible and strictly dissipative with a prescribed performance index. In particular, Jensen’s and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results. Then, if the obtained LMIs are feasible, the corresponding parameters of the designed resilient sampled-data controller are determined. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed control design technique.     

Data augmentation of credit default swap transactions based on a sequence GAN

Credit default swap transaction data repositories are frequently applied with credit default swap spread estimation and financial market risk assessment. However, in practical applications, there is poor liquidity, some missing data, and inaccurate definitions. Small samples tend to lead to poor prediction accuracy and poor adaptability of the statistical algorithm. Data generation can effectively increase the sample size and improve the effect of the risk assessment model. In this paper, a credit default swap data generation algorithm based on a sequence generative adversarial network (SeqGAN) is proposed, and the policy gradient algorithm in reinforcement learning is introduced to optimize the traditional generative adversarial network (GAN) algorithm to solve the gradient disappearance and poor data adaptability problems in the traditional algorithm. Gradient disappearance is due to the generator network in GAN being designed to be able to adjust the output continuously, which does not work on discrete data generation. The optimization algorithm proposed in this paper is used to train randomly distributed sequence data and generate credit default swap transactions with diversity and good model applicability. The credit default swap data generated in this paper are verified by the synthetic ranking agreement (SRA) index. The results show that SeqGAN can effectively synthesize various simulation samples, which can provide support for the risk discrimination model.     

Distributed optimization with information-constrained population dynamics

In a multi-agent framework, distributed optimization problems are generally described as the minimization of a global objective function, where each agent can get information only from a neighborhood defined by a network topology. To solve the problem, this work presents an information-constrained strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the so-called distributed replicator equation (DRE) converges to an optimal global outcome by means of the local-information exchange subject to the topological constraints of the graph. To show the application of the proposed strategy, we implement the DRE to solve an economic dispatch problem with distributed generation. We also present some simulation results to illustrate the theoretic optimality and stability of the equilibrium points and the effects of typical network topologies on the convergence rate of the algorithm.     

False data injection attacks on sensors against state estimation in cyber-physical systems

In this paper, the problem about the false data injection attacks on sensors to degrade the state estimation performance in cyber-physical systems(CPSs) is investigated. The attack strategies for unstable systems and stable ones are both designed. For unstable systems, based on the idea of zero dynamics, an unbounded attack strategy is proposed which can drive the state estimation error variations to infinity. The proposed method is more general than existing unbounded attack strategies since it relaxes the requirement for the initial value of the estimation error. For stable systems, it is difficult to bring unbounded impacts on the estimation error variations. Therefore, in this case, an attack strategy with adjustable attack performance which makes the estimation error variations track predesigned target values is proposed. Furthermore, a uniform attack strategy which aims to deteriorate state estimation for both stable systems and unstable ones is derived. Finally, simulations are provided to illustrate the effectiveness of the proposed attack strategies.     

Multi-cluster distributed optimization via random sleep strategy

In this paper, the distributed optimization problem over multi-cluster networks is considered. Different from the existing works, this paper studies the optimization algorithm under uncoordinated step sizes. More specifically, by combining a random sleep strategy and the round-robin communication among clusters, a new hierarchical algorithm is developed to solve the considered problem. In the proposed algorithm, the random sleep strategy enables each agent to independently choose either performing the projected subgradient descent, or keeping the previous estimate by a Bernoulli decision, based on which the step size of each agent is selected as an uncoordinated form that only relates to the independent Bernoulli decision variable. Technically, by introducing a key definition on the algorithm history, it is proven that the estimates of the proposed algorithm can converge to the optimal solution even with the uncoordinated step sizes. In addition, we also study the convergence performance of the proposed algorithm with simpler constant step sizes. In this case, it is proven that the random sleep strategy can efficiently improve the convergence accuracy of the algorithm. Finally, the theoretical findings are verified via simulation examples.     

Distributed reconstruction of time-varying graph signals via a modified Newton’s method

This paper develops a distributed reconstruction algorithm, that can be implemented efficiently, for time-varying graph signals. The reconstruction problem is formulated as an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and the regularization term. The regularizer used is the nonsmoothness measure of the temporal difference signal. The classical Newton’s method can be used to solve the optimization problem. However, computation of the Hessian matrix inverse is required, and this does not scale well with the graph size. Furthermore, a distributed implementation is not possible. An approximation to the inverse Hessian, that exploits the graph topology, is developed here. The resulting iterative algorithm can be implemented in a distributed manner, and scales well with the graph size. Convergence analysis of the algorithm is presented, which shows convergence to the global optimum. Numerical results, using both synthetic and real world datasets, will demonstrate the superiority of the proposed reconstruction algorithm over existing methods.     

Consensus-based distributed fixed-time optimization for a class of resource allocation problems

A class of resource allocation problems with equality constraint are considered in this paper, such as economic dispatch problem in smart grid systems, which is essentially an optimization problem. Inspired by the Lagrange multiplier method, the resource allocation problem is transformed into a multi-agent consensus problem for large-scale networked distributed nodes. A consensus-based distributed fixed-time optimization algorithm is presented, where the information exchange network is depicted by a strongly connected and weight-balanced digraph. This type of communication network can ensure that the equality constraint always holds. Moreover, a new globally fixed-time stability theorem for nonlinear systems is first given in this paper. Based on this theorem and consensus theory, the optimal resource allocation scheme can be given in a fixed time. Finally, the application and comparison of the designed algorithm show that the algorithm can effectively solve the allocation problem of power resources such as economic dispatch.     

Distributed event-triggered target tracking under cyber attacks

Distributed target tracking is an important problem in sensor networks (SNs). In this paper, the problem of distributed target tracking is addressed under cyber-attacks for targets with discrete-time and continuous-time nonlinear dynamics. Two distributed filters are obtained for every node of the SN to estimate the states of a general class of nonlinear targets which can be seen in many practical applications. Compared with the existing results in the literature, the network topology of the SN is assumed to be subjected to the denial-of-service attack such that the communication links among sensor nodes are paralyzed or destroyed by this kind of attack. Moreover, the proposed algorithms are designed based on an event-triggered communication strategy that means the frequency of information transmission and unnecessary resource consumption are significantly reduced. The presented algorithms’ stability is also analyzed in the presence of noise to achieve secure event-triggered target tracking in mean-square. Two simulation examples are utilized to demonstrate the efficiency of the proposed event-triggered algorithms.     

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.     

Resilient event-triggered consensus control for nonlinear muti-agent systems with DoS attacks

The distributed event-triggered secure consensus control is discussed for multi-agent systems (MASs) subject to DoS attacks and controller gain variation. In order to reduce unnecessary network traffic in communication channel, a resilient distributed event-triggered scheme is adopted at each agent to decide whether the sampled signal should be transmitted or not. The event-triggered scheme in this paper can be applicable to MASs under denial-of-service (DoS) attacks. We assume the information of DoS attacks, such as the attack period and the consecutive attack duration, can be detected. Under the introduced communication scheme and the occurrence of DoS attacks, a new sufficient condition is achieved which can guarantee the security consensus performance of the established system model. Moreover, the explicit expressions of the triggering matrices and the controller gain are presented. Finally, simulation results are provided to verify the effectiveness of the obtained theoretical results.     

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.     

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.     

基于求解TSP问题的ACA-GA-PSO算法

为了有效求解TSP问题,提出一种融合蚁群算法、遗传算法、粒子群优化算法思想的混合算法。该算法基于最大-最小蚁群系统框架,在选择下一个城市时采用局部搜索策略避免陷入局部最优,在每次循环结束时用演化交叉策略优化得到的全局最短路径,从而提高求解TSP问题的求解精度及收敛速度。TSPLIB中不同规模的TSP问题的仿真实验结果表明了该算法的有效性与可行性。     

Distributed filtering algorithm based on local outlier factor under data integrity attacks

Network security is becoming a prominent issue for the development of information technology, and intelligent network attacks pose great challenges to system security due to its strong concealment. The existence of these attacks threatens the operation process of the complicated control system. Motivated by such a security problem, we study the secure distributed filtering algorithm under a kind of complex data integrity attack which can attack in two forms. We design a detection mechanism based on local outlier factor to distinguish the rightness of exchanged data, which determines whether to fuse the estimates by comparing the local density (LD) of the estimation of each sensor. Such a detection mechanism does not need the sensor to transmit redundant data information, thus greatly saving calculation cost and improving transmission efficiency. Meanwhile, we optimize the distributed filtering algorithm and obtain a suboptimal estimation gain. Finally, we demonstrate a numerical example to verify the availability of the filtering algorithm, and explore the influence of detector parameters on the performance of the estimation system.     

Connectivity-preserving rendezvous of heterogeneous multi-agent systems under denial-of-Service attacks

This article investigates the rendezvous problem of heterogeneous multi-agent systems against Denial-of-Service attacks with preserving initial connectivity under a dynamic communication topology. The algorithm of resisting Denial-of-Service attack is first introduced to connectivity-preserving rendezvous problem of heterogeneous multi-agent systems. First of all, in order to observe the information of the leader, the distributed observers are designed to estimate the state of the leader with the communication network in the presence of Denial-of-Service attack by adaptive algorithm. Then, a switching system model is constructed by taking into account the influence of Denial-of-Service attacks. By means of the obtained model combined with a artificial potential function technique, the proposed distributed control algorithm allows all agents to accomplish rendezvous assignment with connectivity preservation as well as resisting Denial-of-Service attacks. Finally, detailed simulation validates the effectiveness of the proposed distributed observer and controller algorithm.     

Resilient control co-design for cyber-Physical systems with DoS attacks via a successive convex optimization approach

This paper addresses the issue of resilient control in the presence of denial-of-service (DoS) attacks for a class of cyber-physical systems. The primary objective is to design a static output feedback controller and event-triggered condition simultaneously such that the globally exponential stability of the closed-loop system is ensured. Compared with stepwise techniques, the co-design achieves the trade-off between control performance and communication cost. The control co-design process is formulated as a bilinear matrix inequality (BMI) problem, which involves nonlinear terms. A successive convex optimization approach is proposed to solve the BMI problem. Further, we develop a self-triggered communication scheme to reduce the cost caused by continuous event detection. It is shown that the proposed event/self-triggered strategy is Zeno-free and excludes singular triggering. Finally, a numerical example is presented to demonstrate the validity of the proposed method.     

Switching resilient control scheme for cyber-physical systems against DoS attacks

This paper investigates the problem of resilient control for cyber-physical systems (CPSs) described by T-S fuzzy models. In the presence of denial-of-service (DoS) attacks, information transmission over the communication network is prevented. Under this circumstance, the traditional control schemes which are proposed based on perfect measurements will be infeasible. To overcome this difficulty, with the utilization of an equivalent switching control method, a novel gain-switched observer-based resilient control scheme is proposed. According to whether the DoS attack is activated, two different controller synthesis conditions are given by combining the information of the tolerable DoS attacks. In addition, a quantitative relationship between the resilience against DoS attacks and the obtained disturbance attenuation level is revealed, which is helpful for balancing the tradeoff between the abilities to tolerate DoS attacks and attenuate the influence of external disturbance. Finally, simulation results are provided to verify the effectiveness of the proposed switching control scheme.