Search

This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponential consensus using a Lyapunov function consisting of a sum of terms of the same functional form. We first investigate necessary conditions, starting by examining the system parameters. It is found that controllability of the linear agents is necessary for achieving consensus. Then, to work out necessary conditions incorporating the network topology, we construct a set of Laplacian matrix-valued functions. The precompactness of this set of functions is shown to be a significant generalization of existing assumptions on network topology. With the aid of such a precompactness assumption and restricting the Lyapunov function to one consisting of a sum of terms of the same functional form, we prove that a joint $(\delta, T)$-connectivity condition on the network topology is necessary for exponential consensus. Finally, we investigate how the above two “necessities” work together to guarantee exponential consensus. To partially address this problem, we define a synchronization index to characterize the interplay between agent parameters and network topology. Based on this notion, it is shown that by designing a proper feedback matrix and under the precompactness assumption, exponential consensus can be reached globally and uniformly if the joint $(\delta,T)$-connectivity and controllability conditions are satisfied, and the synchronization index is not less than one.

This paper investigates the distributed optimization problem with adversarial agents over Markov switching topology. A Push-DIGing type algorithm is applied to find optimizer of the distributed optimization problem. Different from most existing results on distributed optimization problems with adversary agents, we mainly focus on seeking a fixed step size algorithm under Markov switching communication graph. We first divide the agents into three sets, namely the trust agent set, the normal agent set, and the adversarial agent set. All normal agents only use the state of non-attacked agents for iterations. A practical method is presented to distinguish the adversary agents. It is shown that the states of the trust and normal agents will synchronize to the optimizer with a bounded error if (1) the step size does not exceed an upper bound, (2) the union of the communication graph has a spanning tree, and (3) the differential of a local function is decreasing. Furthermore, we also present the upper and lower bounds on distances between the converged state and the optimizer. An example is presented to verify the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

Introduction:Developmental dysplasia of the hip (DDH) is one of the most common diseases in the pediatric orthopedics, with an incidence of 1–5%. Genetic factors are the bases of the pathogenesis of DDH, but the pathogenic variants and pathogenesis of DDH are still unknown. There are no key accurate diagnostic or prognostic molecular markers for DDH. The purpose of our study was to screen for genetic variant associated with DDH and explore its pathogenesis.Materials and Methods:The genetic variation of DDH was tested by variant NGS-based exome analyses, verified by the Sanger sequencing.Results:A four-generation family in which DDH was present in three generations was recruited. A novel heterozygous missense variant c.629C>T (p.(Ala210Val)) in exon 7/8 of the parathyroid hormone 1 receptor (PTH1R) gene was identified through screening of two affected and one unaffected family members. The candidate variant was validated in all available family members with all three affected members being positive for the PTH1Rvariant.Conclusion:Our results are highly supportive of PTH1Ras a novel candidate gene for DDH and demonstrated that the combination of pedigree information and next-generation sequencing is an effective method for identifying pathogenic variants associated with DDH.

This article studies the resilient distributed state estimation over the sensor networks under measurement attacks, which make the measurements of variant subsets of sensors aberrant at different time instants. For this problem, while most of the existing works focus on the static target states that do not change over time, we investigate the estimation for the dynamic ones, which evolve according to general linear time-invariant (LTI) systems. To achieve the resilient distributed state estimation for the general LTI systems under the measurement attacks, we propose a dynamic-target regulative gain estimation (DTRGE) algorithm, in which an attack detector, a regulative gain matrix, and an adaptive gain are designed. The detector helps agents monitor the measurement anomalies, and once the attacks are detected, the adaptive gain can counteract the deviation of the estimates induced by them. The regulative gain matrix restrains the negative effects on the convergence of the estimates caused by the system matrix of the target LTI system, especially the unstable one. We demonstrate that all the sensors can recover the target state by running the DTRGE algorithm, if the topology and the observability of the sensor network satisfy certain conditions. Moreover, we further apply the DTRGE algorithm to the sensor networks with switching topologies, and demonstrate that the estimation task can also be completed by these sensors. Finally, simulation and experiment results are given to illustrate the performance of the DTRGE algorithm.

In this article, we investigate the interval consensus for a network of agents with flocking dynamics, i.e., second-order multiagent systems, where each agent imposes an interval constraint on its preferred consensus values, with the aim of driving the agent into a favorable interval. Specifically, we work on two different frameworks of interval constraints, viz., the first one that the node states are constrained in their own constraint intervals and the second one that the node states are constrained in their neighbors’ constraint intervals. For both of the frameworks, we provide a complete solution to the equilibrium seeking problem by resolving a system of nonlinear equations. It is proved that if the underlying graph is strongly connected and the intersection of constraint intervals is empty, then there exists a unique equilibrium point; and if the intersection is nonempty, then there exist multiple equilibrium points, all of which lead to state consensus. We also establish several conditions for the local stability of the unique equilibrium point (corresponding to the case with empty intersection of constraint intervals) or local constraint consensus (corresponding to the case with nonempty intersection of constraint intervals) by invoking Lyapunov’s indirect method. Characterization of the global behavior of such a second-order multiagent system is technically rather challenging at this stage. As a first step toward this end, we show in two special cases that global convergence to the unique equilibrium point or state consensus can be guaranteed by employing Lyapunov stability theory and robust analysis techniques. Finally, some numerical examples are provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we deal with the consensus problem of multiple partial-state coupled linear systems, which are neutrally stable. These systems communicate over dynamic undirected networks, which change continuously and can be disconnected at any time. We develop an analysis framework from uniform complete observability theory to work out the necessary and sufficient conditions for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly if and only if a jointly $(\delta,T)$ -connected condition and an observability condition relying only on system and input matrices are satisfied. A lower bound of the convergence rate is also provided. We figure out the proof by applying matrix analysis and linear functional analysis. A simulation example is presented to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

• First, a general setup that the output consensu of heterogeneous systems is considered for both without model-switching delay and with model switching delay under Markov switching topologies. • Second, under mild connectivity assumption , the coupled system with or without model-switching delay can achieve output synchronization by using the Lyapunov method. • Third, the criterion in theorem is significant difficulty, we propose some certain techniques to circumvent the difficulty. • Fourth, we also prove that an exponentially stable stochastic system, in mean square, with nonvanishing perturbation can achieve ultimately bounded in a small bound. In this paper, output consensus for a series of heterogeneous systems under semi-markov switching topology is investigated. The scenario under consideration is that none of the graph is assumed to be connected and the mode-switching delay is existed. The main technical challenge is model and controller dismatch because of time delay. Assuming every individual system is stabilizable and detectable and mild connectivity assumption on communication topology, the coupled system without model-switching delay can achieve output synchronization by using the Lyapunov method. For the coupled systems with model-switching delay, a bounded output synchronization conclusion can be given. The existence of controller design is also investigated. By the way, we prove an exponentially stable stochastic system, in mean square, with non-vanishing perturbation can achieve uniform boundedness and ultimate boundedness. Finally, two examples are presented to verify our main theories. [ABSTRACT FROM AUTHOR]

Considering the fact that in the real world, a certain agent may have some sort of advantage to act before others, a novel hierarchical optimal synchronization problem for linear systems, composed of one major agent and multiple minor agents, is formulated and studied in this article from a Stackelberg–Nash game perspective. The major agent herein makes its decision prior to others, and then, all the minor agents determine their actions simultaneously. To seek the optimal controllers, the Hamilton–Jacobi–Bellman (HJB) equations in coupled forms are established, whose solutions are further proven to be stable and constitute the Stackelberg–Nash equilibrium. Due to the introduction of the asymmetric roles for agents, the established HJB equations are more strongly coupled and more difficult to solve than that given in most existing works. Therefore, we propose a new reinforcement learning (RL) algorithm, i.e., a two-level value iteration (VI) algorithm, which does not rely on complete system matrices. Furthermore, the proposed algorithm is shown to be convergent, and the converged values are exactly the optimal ones. To implement this VI algorithm, neural networks (NNs) are employed to approximate the value functions, and the gradient descent method is used to update the weights of NNs. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this article, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel analysis framework from both algebraic and geometric perspectives to justify the attractiveness of the synchronization manifold. Specifically, it is proven that the complementary space of the synchronization manifold can be spanned by certain subspaces constructed from the network structure. This allows to project the states of the dynamical systems onto these subspaces and transform the synchronization problem under consideration equivalently into a convergence one of the projected states in each subspace. Then, assuming the joint connectivity condition on the communication topologies, we are able to work out a unified convergence analysis for both types of dynamical systems. More specifically, for partial-state coupled generic linear systems, it is proven that synchronization can be reached if an extra condition, which is easy to verify in several cases, on the system dynamics is satisfied. For Lipschitz nonlinear systems with positive-definite inner coupling matrix, synchronization is realized if the coupling strength is strong enough to stabilize the evolution of the projected states in each subspace under certain conditions. The above claims generalize the existing results concerning both types of dynamical systems to so far the most general framework. Some illustrative examples are provided to verify our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we aim to investigate the optimal synchronization problem for a group of generic linear systems with input saturation. To seek the optimal controller, Hamilton–Jacobi–Bellman (HJB) equations involving nonquadratic input energy terms in coupled forms are established. The solutions to these coupled HJB equations are further proven to be optimal and the induced controllers constitute interactive Nash equilibrium. Due to the difficulty to analytically solve HJB equations, especially in coupled forms, and the possible lack of model information of the systems, we apply the data-based off-policy reinforcement learning algorithm to learn the optimal control policies. A byproduct of this off-policy algorithm is shown that it is insensitive to probing noise that is exerted to the system to maintain persistence of excitation condition. In order to implement this off-policy algorithm, we employ actor and critic neural networks to approximate the controllers and the cost functions. Furthermore, the estimated control policies obtained by this presented implementation are proven to converge to the optimal ones under certain conditions. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

In this paper, we aim to investigate the output group synchronization problem for a network of heterogeneous linear systems such that the outputs of the nodes, each representing a linear system, synchronize with each other in every cluster. Two different setups in terms of availability of the states of the reference generators are taken into consideration. A unified approach inspired by the internal model principle is proposed. First, the coupled reference generators are constructed so as to produce synchronized reference trajectories. Second, feedback controllers are designed to steer the output of each node to its corresponding reference trajectory. The two setups differ from each other in that the coupling configuration for reference generators and design of feedback controllers are rather different. Specifically, when the states of the reference generators are not available, the small gain theorem is exploited to drive the outputs of the nodes to the synchronized ones of virtual reference generators. Finally, simulations are carried out to validate the theoretical findings. [ABSTRACT FROM PUBLISHER]

The cluster synchronization problem is investigated using intermittent pinning control for the interacting clusters of nonidentical nodes that may represent either general linear systems or nonlinear oscillators. These nodes communicate over general network topology, and the nodes from different clusters are governed by different self-dynamics. A unified convergence analysis is provided to analyze the synchronization via intermittent pinning controllers. It is observed that the nodes in different clusters synchronize to the given patterns if a directed spanning tree exists in the underlying topology of every extended cluster (which consists of the original cluster of nodes as well as their pinning node) and one algebraic condition holds. Structural conditions are then derived to guarantee such an algebraic condition. That is: 1) if the intracluster couplings are with sufficiently strong strength and the pinning controller is with sufficiently long execution time in every period, then the algebraic condition for general linear systems is warranted and 2) if every cluster is with the sufficiently strong intracluster coupling strength, then the pinning controller for nonlinear oscillators can have its execution time to be arbitrarily short. The lower bounds are explicitly derived both for these coupling strengths and the execution time of the pinning controller in every period. In addition, in regard to the above-mentioned structural conditions for nonlinear systems, an adaptive law is further introduced to adapt the intracluster coupling strength, such that the cluster synchronization for nonlinear systems is achieved. [ABSTRACT FROM AUTHOR]

The containment control is studied for the second-order multiagent systems over a heterogeneous network where the position and velocity interactions are different. We consider three cases that multiple leaders are stationary, moving at the same constant speed, and moving at the same time-varying speed, and develop different containment control algorithms for each case. In particular, for the former two cases, we first propose the containment algorithms based on the well-established ones for the homogeneous network, for which the position interaction topology is required to be undirected. Then, we extend the results to the general setting with the directed position and velocity interaction topologies by developing a novel algorithm. For the last case with time-varying velocities, we introduce two algorithms to address the containment control problem under, respectively, the directed and undirected interaction topologies. For most cases, sufficient conditions with regard to the interaction topologies are derived for guaranteeing the containment behavior and, thus, are easy to verify. Finally, six simulation examples are presented to illustrate the validity of the theoretical findings.

In this technical note, we investigate the H\infty group consensus for networks of agents modeled by single-integrator with model uncertainty and external disturbance. By developing tools from algebraic graph theory, matrix analysis as well as Lyapunov stability theory, we are able to derive some sufficient conditions in terms of the structure and strength of the couplings among agents so as to guarantee the group consensus with desired H\infty performance. Such conditions are structural and easy to check. Furthermore, some adaptation laws are proposed to address the coupling strength problem arising from the consideration that the theoretical value is usually much larger than expected in practice. Finally, some simulation examples are presented to demonstrate the efficiency of the theoretical findings. [ABSTRACT FROM PUBLISHER]

In this article, we study a distributed, second-order, event-triggered network flow for solving linear algebraic equations described by the form z = H y in the sense of least squares. An undirected graph is utilized to describe the distributed computation network. In the network, each node broadcasts its dynamic states to its neighbors in an asynchronous fashion, and updates the flow at the isolated event times. We construct a specific trigger function to determine the event times, in which an exponential decay function is introduced as a comparison term. We show that if the linear algebraic equation has a unique least squares solution, all nodes states converge to this unique solution exponentially fast, when the applied network is connected and the decay rate of the comparison term satisfies certain bounds determined jointly by the topology and the linear equations information. We obtain a strictly positive lower bound on the time interval between consecutive events for time t ∈ [ 0 , ∞) , and therefore the event-triggered system does not exhibit Zeno behavior. We provide numerical examples to verify the effectiveness of the proposed event-based network flow. In addition, we illustrate the importance of the strictly positive inter-event time interval, in comparison with the case that the inter-event time interval may converge to zero when time t goes to infinity. [ABSTRACT FROM AUTHOR]

Aviation and aerospace system are typical Phased-Mission Systems (PMSs) featured with varying configuration, phased load condition and cross phase failure correlation. The coupling effect of Functional Dependency (FDEP) and Physical Dependency (PDEP) has a unique influence on the failure behavior of PMS. In this article, the coupling effect is analyzed, and the degradation of components is modeled with the positive drift wiener process, in which the drift coefficient is related to environmental conditions and operation stress. Finally, failure behavior and system reliability are simulated. An avionics controller is studied as a case, with the degradation time distribution model and simulation algorithm, the coupling effect and dynamical system reliability can be achieved. Results show that this modeling method can describe the coupling effects of FDEP and PDEP and their influence on the failure behavior and reliability of the PMS system.

This paper studies the charging/discharging scheduling problem of plug-in electric vehicles (PEVs) in smart grid, considering the users' satisfaction with state of charge (SoC) and the degradation cost of batteries. The objective is to collectively determine the energy usage patterns of all participating PEVs so as to minimize the energy cost of all PEVs while ensuring the charging needs of PEV owners. The challenges herein are mainly in three folds: 1) the randomness of electricity price and PEVs' commuting behavior; 2) the unknown dynamics model of SoC; and 3) a large solution space, which make it challenging to directly develop a model-based optimization algorithm. To this end, we first reformulate the above energy cost minimization problem as a Markov game with unknown transition probabilities. Then a multi-agent deep reinforcement learning (DRL)-based data-driven approach is developed to solve the Markov game. Specifically, the proposed approach consists of two networks: an extreme learning machine (ELM)-based feedforward neural network (NN) for uncertainty prediction of electricity price and PEVs' commuting behavior and a Q network for optimal action-value function approximation. Finally, the comparison results with three benchmark solutions show that our proposed algorithm can not only adaptively decide the optimal charging/discharging policy by on-line learning process, but also yield a lower energy cost within an unknown market environment. [ABSTRACT FROM AUTHOR]