Distributed Energy-Based Estimation Over Harvesting-Constrained Sensor Networks.

This article investigates the distributed joint state and fault estimation issue for a class of nonlinear time-varying systems over sensor networks constrained by energy harvesting. It is assumed that data transmission between sensors requires energy consumption, and each sensor can harvest energy from the external environment. A Poisson process models the energy harvested by each sensor, and the sensor's transmission decision depends on its current energy level. One can obtain the sensor transmission probability through a recursive calculation of the probability distribution of the energy level. Under such energy harvesting constraints, the proposed estimator only uses local and neighbor data to simultaneously estimate the system state and the fault, thereby establishing a distributed estimation framework. Moreover, the estimation error covariance is determined to possess an upper bound, which is minimized by devising energy-based filtering parameters. The convergence performance of the proposed estimator is analyzed. Finally, a practical example is presented to verify the usefulness of the main results.

Dynamic Coding-Based Control Scheme Under Lossy Digital Network: An Optimized Time-Varying Packet Length Approach.

This work proposes a design scheme of the desired controller under the lossy digital network by introducing a dynamic coding and packet-length optimization strategy. First, the weighted try once-discard (WTOD) protocol is introduced to schedule the transmission of sensor nodes. The state-dependent dynamic quantizer and the encoding function with time-varying coding length are designed to improve coding accuracy significantly. Then, a feasible state-feedback controller is designed to attain that the controlled system subject to possible packet dropout is exponentially ultimately bounded in the mean-square sense. Moreover, it is shown that the coding error directly affects the convergent upper bound, which is further minimized by optimizing the coding lengths. Finally, the simulation results are provided via the double-sided linear switched reluctance machine systems.

Synchronization of multiple rigid body systems: A survey.

The multi-agent system has been a hot topic in the past few decades owing to its lower cost, higher robustness, and higher flexibility. As a particular multi-agent system, the multiple rigid body system received a growing interest for its wide applications in transportation, aerospace, and ocean exploration. Due to the non-Euclidean configuration space of attitudes and the inherent nonlinearity of the dynamics of rigid body systems, synchronization of multiple rigid body systems is quite challenging. This paper aims to present an overview of the recent progress in synchronization of multiple rigid body systems from the view of two fundamental problems. The first problem focuses on attitude synchronization, while the second one focuses on cooperative motion control in that rotation and translation dynamics are coupled. Finally, a summary and future directions are given in the conclusion.

Security Analysis of Distributed Consensus Filtering Under Replay Attacks.

This work studies the security of consensus-based distributed filtering under the replay attack, which can freely select a part of sensors and modify their measurements into previously recorded ones. We analyze the performance degradation of distributed estimation caused by the replay attack, and utilize the Kullback-Leibler (K-L) divergence to quantify the attack stealthiness. Specifically, for a stable system, we prove that under any replay attack, the estimation error is not only bounded, but also can re-enter the steady state. In that case, we prove that the replay attack is ϵ -stealthy, where ϵ can be calculated based on two Lyapunov equations. On the other hand, for an unstable system, we prove that the trace of estimation error covariance is lower bounded by an exponential function, which indicates that the estimation error may diverge due to the attack. In view of this, we provide a sufficient condition to ensure that any replay attack is detectable. Furthermore, we analyze the case that the adversary starts to attack only if the current measurement is close to a previously recorded one. Finally, we verify the theoretical results via several numerical simulations.

Distributed Stochastic Constrained Composite Optimization Over Time-Varying Network With a Class of Communication Noise.

This article is concerned with the distributed stochastic multiagent-constrained optimization problem over a time-varying network with a class of communication noise. This article considers the problem in composite optimization setting, which is more general in the literature of noisy network optimization. It is noteworthy that the mainstream existing methods for noisy network optimization are Euclidean projection based. Based on the Bregman projection-based mirror descent scheme, we present a non-Euclidean method and investigate their convergence behavior. This method is the distributed stochastic composite mirror descent type method (DSCMD-N), which provides a more general algorithm framework. Some new error bounds for DSCMD-N are obtained. To the best of our knowledge, this is the first work to analyze and derive convergence rates of optimization algorithm in noisy network optimization. We also show that an optimal rate of O(1/√T) in nonsmooth convex optimization can be obtained for the proposed method under appropriate communication noise condition. Moveover, novel convergence results are comprehensively derived in expectation convergence, high probability convergence, and almost surely sense.

Event-Triggered Distributed Stochastic Mirror Descent for Convex Optimization.

This article is concerned with the distributed convex constrained optimization over a time-varying multiagent network in the non-Euclidean sense, where the bandwidth limitation of the network is considered. To save the network resources so as to reduce the communication costs, we apply an event-triggered strategy (ETS) in the information interaction of all the agents over the network. Then, an event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm, which utilizes the Bregman divergence as the distance-measuring function, is presented to investigate the multiagent optimization problem subject to a convex constraint set. Moreover, we also analyze the convergence of the developed ET-DSMD algorithm. An upper bound for the convergence result of each agent is established, which is dependent on the trigger threshold. It shows that a sublinear upper bound can be guaranteed if the trigger threshold converges to zero as time goes to infinity. Finally, a distributed logistic regression example is provided to prove the feasibility of the developed ET-DSMD algorithm.

Quantized Synchronization Control of Networked Nonlinear Systems: Dynamic Quantizer Design With Event-Triggered Mechanism.

This article investigates the quantized control issue for synchronizing a networked nonlinear system. Due to limited energy and channel resources, the event-triggered control (ETC) method and input quantization are simultaneously taken into account in this article. First, a dynamic quantizer, which discretely adjusts its parameters online and possesses a finite quantization range, is introduced to achieve exact synchronization, rather than quasisynchronization. Next, a new distributed Zeno-free ETC strategy is proposed based on the dynamic quantizer. Then, two different situations, that is, the quantizer is designed with/without the network topology information, are, respectively, discussed. Synchronization criteria are, respectively, derived under such two circumstances by using the Lyapunov method. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

Resilient Output Synchronization of Heterogeneous Multiagent Systems With DoS Attacks Under Distributed Event-/Self-Triggered Control.

This article investigates the resilient output synchronization problem of a class of linear heterogeneous multiagent systems subjected to denial-of-service (DoS) attacks. Two types of control mechanisms, namely, event- and self-triggered control mechanisms, are presented so as to cut down unnecessary information transmission. Both of these two mechanisms are distributed, and thus, only local information of each agent and its neighboring agents is adopted for the event condition design. The DoS attacks are considered to be aperiodic, and the quantitative relationship between the attributes of the DoS attacks and the synchronization is also revealed. It is shown that the output synchronization can be achieved exponentially in the presence of DoS attacks under the proposed control mechanisms. The validness of the provided mechanisms is certified by a simulation example.

Distributed Constrained Optimization With Delayed Subgradient Information Over Time-Varying Network Under Adaptive Quantization.

In this article, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication channel has a limited data rate. We propose an adaptive quantization method to address this problem. A mirror descent algorithm with delayed subgradient information is established based on the theory of Bregman divergence. With a non-Euclidean Bregman projection-based scheme, the proposed method essentially generalizes many previous classical Euclidean projection-based distributed algorithms. Through the proposed adaptive quantization method, the optimal value without any quantization error can be obtained. Furthermore, comprehensive analysis on the convergence of the algorithm is carried out and our results show that the optimal convergence rate can be obtained under appropriate conditions. Finally, numerical examples are presented to demonstrate the effectiveness of our results.

Model-Based Event-Triggered Sliding-Mode Control for Multi-Input Systems: Performance Analysis and Optimization.

This article is concerned with the model-based event-triggered sliding-mode control (SMC) issue for multi-input systems, which is motivated by some existing results in a single-input case. A model-based event-triggered SMC scheme is first designed. In particular, a triggered condition is co-designed with SMC to achieve the reachability condition of a specified sliding surface. Thus, it can effectively mitigate the burden of data communication, and also eliminate the effect of the matched external disturbance and the model uncertainties in both system and input. For ensuring the stability of the model dynamics and the resulting sliding-mode dynamics simultaneously, an auxiliary disturbance input is introduced to the nominal model by compensating the switching term of the designed SMC law. Furthermore, the positive lower bound for the minimum interevent time is analyzed to ensure the feasibility of the proposed approach. To illustrate the proposed model-based event-triggered SMC approach from a practical viewpoint, two design problems to maximize the system robustness and performance are proposed, respectively. The nontrivial optimization problems are then solved by a genetic algorithm (GA). Finally, jet transport aircraft is utilized to demonstrate the effectiveness of the proposed results and algorithm.

Distributed Kalman Filtering for Interconnected Dynamic Systems.

This article is concerned with the distributed Kalman filtering problem for interconnected dynamic systems, where the local estimator of each subsystem is designed only by its own information and neighboring information. A decoupling strategy is developed to minimize the impact of interconnected terms on the estimation performance, and then the recursive and distributed Kalman filter is derived in the minimum mean-squared error sense. Moreover, by using Lyapunov criterion for linear time-varying systems, stability conditions are presented such that the designed estimator is bounded. Finally, a heavy duty vehicle platoon system is employed to show the effectiveness and advantages of the proposed methods.

Distributed LMMSE Estimation for Large-Scale Systems Based on Local Information.

This article studies the distributed linear minimum mean square error (LMMSE) estimation problem for large-scale systems with local information (LSLI). Large-scale systems are composed of numerous subsystems. Each subsystem only transmits information to its neighbors. Thus, only the local information is available to each subsystem. This implies that the information available to different subsystems is different. Using local information to design an LMMSE estimator, the gains of the estimator must satisfy the sparse structure constraint, which makes the estimator design challenging and complicates the boundedness analysis of the estimation error covariance (EEC). In this article, a framework of the distributed LMMSE estimation for LSLI is established. The gains of the LMMSE estimator are effectively constructed by solving linear matrix equations. A gradient descent algorithm is exploited to design the gains of the LMMSE estimator numerically. Sufficient conditions are derived to ensure the boundedness of the EEC. Also, a gradient-based search algorithm is developed to verify whether the sufficient conditions hold or not. Finally, an example is used to illustrate the effectiveness of the proposed results.

Multiplayer Stackelberg-Nash Game for Nonlinear System via Value Iteration-Based Integral Reinforcement Learning.

In this article, we study a multiplayer Stackelberg-Nash game (SNG) pertaining to a nonlinear dynamical system, including one leader and multiple followers. At the higher level, the leader makes its decision preferentially with consideration of the reaction functions of all followers, while, at the lower level, each of the followers reacts optimally to the leader's strategy simultaneously by playing a Nash game. First, the optimal strategies for the leader and the followers are derived from down to the top, and these strategies are further shown to constitute the Stackelberg-Nash equilibrium points. Subsequently, to overcome the difficulty in calculating the equilibrium points analytically, we develop a novel two-level value iteration-based integral reinforcement learning (VI-IRL) algorithm that relies only upon partial information of system dynamics. We establish that the proposed method converges asymptotically to the equilibrium strategies under the weak coupling conditions. Moreover, we introduce effective termination criteria to guarantee the admissibility of the policy (strategy) profile obtained from a finite number of iterations of the proposed algorithm. In the implementation of our scheme, we employ neural networks (NNs) to approximate the value functions and invoke the least-squares methods to update the involved weights. Finally, the effectiveness of the developed algorithm is verified by two simulation examples.

Delay-Dependent Distributed Kalman Fusion Estimation With Dimensionality Reduction in Cyber-Physical Systems.

This article studies the distributed dimensionality reduction fusion estimation problem with communication delays for a class of cyber-physical systems (CPSs). The raw measurements are preprocessed in each sink node to obtain the local optimal estimate (LOE) of a CPS, and the compressed LOE under dimensionality reduction encounters with communication delays during the transmission. Under this case, a mathematical model with compensation strategy is proposed to characterize the dimensionality reduction and communication delays. This model also has the property of reducing the information loss caused by the dimensionality reduction and delays. Based on this model, a recursive distributed Kalman fusion estimator (DKFE) is derived by optimal weighted fusion criterion in the linear minimum variance sense. A stability condition for the DKFE, which can be easily verified by the exiting software, is derived. In addition, this condition can guarantee that the estimation error covariance matrix of the DKFE converges to the unique steady-state matrix for any initial values and, thus, the steady-state DKFE (SDKFE) is given. Note that the computational complexity of the SDKFE is much lower than that of the DKFE. Moreover, a probability selection criterion for determining the dimensionality reduction strategy is also presented to guarantee the stability of the DKFE. Two illustrative examples are given to show the advantage and effectiveness of the proposed methods.

Stochastic Strongly Convex Optimization via Distributed Epoch Stochastic Gradient Algorithm.

This article considers the problem of stochastic strongly convex optimization over a network of multiple interacting nodes. The optimization is under a global inequality constraint and the restriction that nodes have only access to the stochastic gradients of their objective functions. We propose an efficient distributed non-primal-dual algorithm, by incorporating the inequality constraint into the objective via a smoothing technique. We show that the proposed algorithm achieves an optimal O((1)/(T)) ( T is the total number of iterations) convergence rate in the mean square distance from the optimal solution. In particular, we establish a high probability bound for the proposed algorithm, by showing that with a probability at least 1-δ , the proposed algorithm converges at a rate of O(ln(ln(T)/δ)/ T) . Finally, we provide numerical experiments to demonstrate the efficacy of the proposed algorithm.

Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications.

Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

Distributed Secure Cooperative Control Under Denial-of-Service Attacks From Multiple Adversaries.

This paper develops a fully distributed framework to investigate the cooperative behavior of multiagent systems in the presence of distributed denial-of-service (DoS) attacks launched by multiple adversaries. In such an insecure network environment, two kinds of communication schemes, that is, sample-data and event-triggered communication schemes, are discussed. Then, a fully distributed control protocol with strong robustness and high scalability is well designed. This protocol guarantees asymptotic consensus against distributed DoS attacks. In this paper, "fully" emphasizes that the eigenvalue information of the Laplacian matrix is not required in the design of both the control protocol and event conditions. For the event-triggered case, two effective dynamical event-triggered schemes are proposed, which are independent of any global information. Such event-triggered schemes do not exhibit Zeno behavior even in the insecure environment. Finally, a simulation example is provided to verify the effectiveness of theoretical analysis.

Quasi-Consensus of Heterogeneous-Switched Nonlinear Multiagent Systems.

In this paper, the quasi-consensus problem is investigated for a class of heterogeneous-switched nonlinear multiagent systems, in which both cooperation and competition interactions are considered simultaneously. By means of the Lyapunov function method, we show that quasi-consensus can be ensured for switched multiagent systems under the assumption that the activation time of cooperation interactions is sufficiently large. Moreover, a new Lyapunov function is considered to provide the lower and upper bounds of switching intervals explicitly. Thus, these bounds can be used to obtain less conservative stability results of switched systems. Furthermore, the established results are specialized to both the traditional consensus case and the stability of linear-switched systems. Finally, simulations are given to illustrate the theoretical results derived in this paper.

Multilayered Sampled-Data Iterative Learning Tracking for Discrete Systems With Cooperative-Antagonistic Interactions.

The tracking for discrete systems is discussed by designing two kinds of multilayered iterative learning schemes with cooperative-antagonistic interactions in this paper. The definition of the signed graph is presented and iterative learning schemes are then designed to be multilayered and have cooperative-antagonistic interactions. Moreover, considering the limited bandwidth of information storage, the state information of these controllers is updated in light of previous learning iterations but not just dependent on the last iteration. Two simple criteria are addressed to discuss the tracking of discrete systems with multilayered and cooperative-antagonistic iterative schemes. The simulation results are shown to demonstrate the validity of the given criteria.

Robust Partial-Nodes-Based State Estimation for Complex Networks Under Deception Attacks.

In this paper, the partial-nodes-based state estimators (PNBSEs) are designed for a class of uncertain complex networks subject to finite-distributed delays, stochastic disturbances, as well as randomly occurring deception attacks (RODAs). In consideration of the likely unavailability of the output signals in harsh environments from certain network nodes, only partial measurements are utilized to accomplish the state estimation task for the addressed complex network with norm-bounded uncertainties in both the network parameters and the inner couplings. The RODAs are taken into account to reflect the compromised data transmissions in cyber security. We aim to derive the gain parameters of the estimators such that the overall estimation error dynamics satisfies the specified security constraint in the simultaneous presence of stochastic disturbances and deception signals. Through intensive stochastic analysis, sufficient conditions are obtained to guarantee the desired security performance for the PNBSEs, based on which the estimator gains are acquired by solving certain matrix inequalities with nonlinear constraints. A simulation study is carried out to testify the security performance of the presented state estimation method.