Discrete-time Dynamical Networks Research Articles

Invariance Principles for Nonlinear Discrete-Time Switched Systems and Its Application to Output Synchronization of Dynamical Networks.

In this article, we develop two invariance principles for nonlinear discrete-time switched systems based on multiple Lyapunov functions and multiple weak Lyapunov functions, respectively, which allow the first differences of multiple weak Lyapunov functions to be positive on certain sets. It is shown that the solution of the system is attracted to the largest weakly invariant set in a certain specific region. Then, based on the invariance principle developed and geometrical dissipativity, we obtain the generalized output synchronization for discrete-time dynamical networks with nonidentical nodes by an appropriate switching among several communication topologies. Finally, two examples are provided to demonstrate the effectiveness of the main results.

Outer synchronization for two discrete-time complex dynamic networks via the synthesized coupling connections

Outer synchronization for two discrete-time complex dynamic networks via the synthesized coupling connections

Discrete-Time Fractional-Order Dynamical Networks Minimum-Energy State Estimation

Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies among the spatial and temporal components of a wide variety of dynamical networks. Notable examples include networked control systems or neurophysiological networks which are created using electroencephalographic (EEG) or blood-oxygen-level-dependent data. As a result, the estimation of the states of fractional-order dynamical networks poses an important problem. To this effect, this article addresses the problem of minimum-energy state estimation for discrete-time fractional-order dynamical networks, where the state and output equations are affected by an additive noise that is considered to be deterministic, bounded, and unknown. Specifically, we derive the corresponding estimator and show that the resulting estimation error is exponentially input-to-state stable with respect to the disturbances and to a signal that is decreasing with the increase of the accuracy of the adopted approximation model. An illustrative example shows the effectiveness of the proposed method on real-world neurophysiological networks. Our results may significantly contribute to the development of novel neurotechnologies, particularly in the development of state estimation paradigms for neural signals such as EEG, which are often noisy signals known to be affected by artifacts not having any particular stochastic characterization.

Dynamic Availability Assessment Using Dynamic Evidential Network: Water Deluge System Case Study

Probabilistic modeling is widespread in engineering practices, mainly to evaluate the safety, risk analysis, and reliability of complex systems. However, insufficient data makes it difficult to estimate the state probability of components or the global system in dynamic complex systems. Furthermore, conventional methods for dependability analysis typically have little capacity to cope with dependence, failure behavior, epistemic uncertainty, and common cause failure simultaneously. This paper presents the application of an extended discrete-time dynamic evidential network (DEN) model to assess the availability of complex systems. The model application combines Dempster-Shafer's theory to treat epistemic uncertainty over a new state-space reconstruction of components and the dynamic Bayesian network to present multi-state system dependability. This model is demonstrated in a real case study of a water deluge system installed as a safety barrier from Algeria's oil and gas plant. The results show the significant influence of these factors on the system's availability. The goal of this modeling is to assure the high availability of a safety barrier in a volatile setting by providing a decision-making tool to prioritize maintenance tasks, preventing the failure of complicated redundant systems, and recommending alterations to the design.

Resilient Filtering of Nonlinear Complex Dynamical Networks Under Randomly Occurring Faults and Hybrid Cyber-Attacks

This paper investigates the problem of recursive resilient filtering for discrete-time nonlinear dynamical networks with randomly switching topologies under randomly occurring faults and hybrid cyber-attacks. The attacks considered are composed of DoS attacks describing by binary random sequences and deception attacks, the amplitude of which obeys the Gaussian mixing distribution. A recursive resilient filter dependent on DoS attack sequences is designed to simultaneously estimate system states and occurred faults, where the desired gain is parameterized via the matrix iterative formula of filtering error covariance. Furthermore, the maximum posterior probability estimation is calculated to identify DoS attack sequences with the help of the classical Bayesian rule. In particular, a modified recursive filtering algorithm is established by replacing the corresponding parameters in the previously derived formulas about filter gains and covariance matrices. Finally, the effectiveness of the proposed recursive filtering algorithm is demonstrated by a simulation example.

Finite-time dissipative synchronization of discrete-time semi-Markovian jump complex dynamical networks with actuator faults

This paper is concerned with the problem of finite-time synchronization for a class of discrete-time semi-Markovian jumping complex dynamical networks (CDNs) with actuator faults based on reliable control. The main aim of this paper is to design a state feedback controller such that the resulting closed-loop system is finite-time synchronized under a prescribed dissipativity performance level even in the presence of actuator failures. Moreover, a stochastic nature followed by Bernoulli distribution is described in the considered networks due to the occurrence of probabilistic nature in time-varying delays. By composing a suitable Lyapunov–Krasovskii functional containing triple summation terms with the aid of Kronecker product properties, Lyapunov stability theory and free weighting matrix approach, sufficient criteria are established in terms of linear matrix inequalities that assure finite-time synchronization and meet the dissipativity performance to the addressed CDNs. The usefulness of the presented design scheme is finally verified by numerical examples.

Discrete-time dynamic graph echo state networks

Relations between entities evolving through discrete time-steps can be represented by discrete-time dynamic graphs. Examples include hourly interactions between social network users or daily infection spreading. In this paper, we present Dynamic Graph Echo State Network (DynGESN), a reservoir computing model for the efficient processing of discrete-time dynamic temporal graphs. We prove a sufficient condition for the echo state property, which ensures that graph embeddings are independent of initial conditions, and we briefly analyze reservoir dynamics. DynGESN is compared against temporal graph kernels (TGKs) on twelve graph classification tasks, and against ten different end-to-end trained temporal graph convolutional networks (TGNs) on four vertex regression tasks, since TGKs are limited to graph-level tasks. Compared to TGKs that need to hold the entire history of vertex interactions, our model provides a vector encoding for the dynamic graph that is updated at each time-step without requiring training. Experiments show that our model achieves accuracy in line with TGKs that have comparable computational complexity, while still offering space and time requirements better suited to scale to large-size data. Moreover, DynGESN overall achieves superior or on par accuracy with respect to TGNs, while improving efficiency by up ten times on inference and training time.

Poisson degree corrected dynamic stochastic block model

Stochastic Block Model (SBM) provides a statistical tool for modeling and clustering network data. In this paper, we propose an extension of this model for discrete-time dynamic networks that takes into account the variability in node degrees, allowing us to model a broader class of networks. We develop a probabilistic model that generates temporal graphs with a dynamic cluster structure and time-dependent degree corrections for each node. Thanks to these degree corrections, the nodes can have variable in- and out-degrees, allowing us to model complex cluster structures as well as interactions that decrease or increase over time. We compare the proposed model to a model without degree correction and highlight its advantages in the case of inhomogenous degree distributions in the clusters and in the recovery of unstable cluster dynamics. We propose an inference procedure based on Variational Expectation-Maximization (VEM) that also provides the means to estimate the time-dependent degree corrections. Extensive experiments on simulated and real datasets confirm the benefits of our approach and show the effectiveness of the proposed algorithm.

Energy Resilience Impact of Supply Chain Network Disruption to Military Microgrids

The ability to provide uninterrupted power to military installations is paramount in executing a country’s national defense strategy. Microgrid architectures increase installation energy resilience through redundant local generation sources and the capability for grid independence. However, deliberate attacks from near-peer competitors can disrupt the associated supply chain network, thereby affecting mission critical loads. Utilizing an integrated discrete-time Markov chain and dynamic Bayesian network approach, we investigate disruption propagation throughout a supply chain network and quantify its mission impact on an islanded microgrid. We propose a novel methodology and an associated metric we term “energy resilience impact” to identify and address supply chain disruption risks to energy security. The proposed methodology addresses a gap in the literature and practice where it is assumed supply chains will not be disrupted during incidents involving microgrids. A case study of a fictional military installation is presented to demonstrate how installation energy managers can adopt this methodology for the design and improvement of military microgrids. The fictional case study shows how supply chain disruptions can impact the ability of a microgrid to successfully supply electricity to critical loads throughout an islanding event.

Dynamic Structural Role Node Embedding for User Modeling in Evolving Networks

Complex user behavior, especially in settings such as social media, can be organized as time-evolving networks. Through network embedding, we can extract general-purpose vector representations of these dynamic networks which allow us to analyze them without extensive feature engineering. Prior work has shown how to generate network embeddings while preserving the structural role proximity of nodes. These methods, however, cannot capture the temporal evolution of the structural identity of the nodes in dynamic networks. Other works, on the other hand, have focused on learning microscopic dynamic embeddings. Though these methods can learn node representations over dynamic networks, these representations capture the local context of nodes and do not learn the structural roles of nodes. In this article, we propose a novel method for learning structural node embeddings in discrete-time dynamic networks. Our method, called HR2vec , tracks historical topology information in dynamic networks to learn dynamic structural role embeddings. Through experiments on synthetic and real-world temporal datasets, we show that our method outperforms other well-known methods in tasks where structural equivalence and historical information both play important roles. HR2vec can be used to model dynamic user behavior in any networked setting where users can be represented as nodes. Additionally, we propose a novel method (called network fingerprinting) that uses HR2vec embeddings for modeling whole (or partial) time-evolving networks. We showcase our network fingerprinting method on synthetic and real-world networks. Specifically, we demonstrate how our method can be used for detecting foreign-backed information operations on Twitter.

Quickest Flow Algorithms with Time-Varying Attributes

In many real-world situations, there are numerous network optimization problems where the network attributes depend on time. In this paper, we consider single-source single-sink discrete-time dynamic network flow problems. We review some algorithms for the quickest flow problems in two environments (to the network attributes): time-invariant and time-variant. This paper mainly focuses on the existing algorithms for a later one. In literature, most of the authors have made their objectives to determine the earliest arrival time paths along which a given amount of flow can be sent in the minimum time. Evacuation is the most recent research area of network optimization, where quickest flow models allow the estimation of the minimum time required to bring a given number of evacuees to safety.

Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations.

This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the l2 - l∞ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the l2 - l∞ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

Detecting interactions in discrete-time dynamics by random variable resetting.

Detecting the interactions in networks helps us to understand the collective behaviors of complex systems. However, doing so is challenging due to systemic noise, nonlinearity, and a lack of information. Very few researchers have attempted to reconstruct discrete-time dynamic networks. Recently, Shi et al. proposed resetting a random state variable to infer the interactions in a continuous-time dynamic network. In this paper, we introduce a random resetting method for discrete-time dynamic networks. The statistical characteristics of the method are investigated and verified with numerical simulations. In addition, this reconstruction method was evaluated for limited data and weak coupling and within multiple-attractor systems.

A Comparison of Extended Dijkstra and ACO Algorithm for Shortest Path Problem in Dynamic Networks with Delay Times

Shortest path problem is a typical routing optimization problem that is generally involved with a multi-criteria decision-making process. Therefore, the main objective of this paper is to find the shortest path in discrete-time dynamic networks based on bi-criteria of time and reliability by considering the effect of delay times that varies according to different departure time scenarios. Firstly, the well-known single-criterion Dijkstra’s algorithm is extended to fit the conditions of a bi-criteria problem. The solutions obtained from the extended Dijkstra was then compared with a proposed ant colony optimization (ACO) algorithm via a set of multi-objective performance metrics including CPU time, error ratio, spacing and diversity metrics. The analysis was made based on three network scales ranged from small (20-100 nodes), to medium (500-1900 nodes) and large (2000-10000 nodes). The computational results obtained from the analysis suggested that the extended Dijkstra’s algorithm has a higher efficiency in medium and large scaled networks. Furthermore, the comparison of the proposed ACO versus Dijkstra’s algorithm proved the preference of ACO for networks with larger-scaled (nodes over 5000), while, for smaller and medium-scaled networks (nodes 20-2000), the extended Dijkstra’s algorithm has a dominantly better performance in CPU time as compared to proposed ACO.

Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

Moving-Horizon Estimation for Linear Dynamic Networks With Binary Encoding Schemes

This article is concerned with moving-horizon state estimation problems for a class of discrete-time linear dynamic networks. The signals are transmitted via noisy network channels and distortions can be caused by channel noises. As such, the binary encoding schemes, which take advantages of the robustness of the binary data, are exploited during the signal transmission. More specifically, under such schemes, the original signals are encoded into a bit string, transmitted via memoryless binary symmetric channels with certain crossover probabilities, and eventually restored by a decoder at the receiver. Novel centralized and decentralized moving-horizon estimators in the presence of the binary encoding schemes are constructed by solving the respective global and local least-square optimization problems. Sufficient conditions are obtained through intensive stochastic analysis to guarantee the stochastically ultimate boundedness of the estimation errors. A simulation example is presented to verify the effectiveness of the proposed moving-horizon estimators.

Optimal agency contract for incentive and control under moral hazard in dynamic electric power networks

The authors propose an optimal contract mechanism under moral hazard in discrete-time dynamic electric power networks. As the utility (system operator) cannot adjust the control input of the agents (end-users) directly in real time out of respect for individual decision–making, the agents’ control input maximising their own profit does not always maximise social welfare. To avoid the issue, the authors introduce an aggregator as intermediary between the utility and the agents. The aggregator pays compensation for defective ancillary services, which are caused by random disturbance and the agents’ voluntary control. To reduce the compensation risk, the authors first present an optimal incentive/control contract problem for the aggregator's compensation. The problem is usually regarded as a principal-agent problem under moral hazard in contract theory. However, it is generally difficult to solve a contract problem with dynamics expressed as discrete-time simultaneous Bellman equations and a hierarchical control structure as a Stackelberg game. The authors next show that the problem can be solved by regarding it as a linear-exponential-quadratic-Gaussian dynamic game and employing a numerical optimisation technique. Due to the ex-ante appropriate payment contract, the agents select control inputs preferable for the aggregator. The effectiveness of the proposed contract mechanism is finally demonstrated through simulation.

Synchronous stability of the fractional-order discrete-time dynamical network system model with impulsive couplings

In this paper, the synchronization of a class of fractional-order discrete-time dynamical networks is concerned. The new model of fractional-order discrete-time dynamical network system with impulsive couplings among nodes is constructed. Based on the multiple Lyapunov function method, the global synchronous stability and the local synchronous stability of the system are studied and several synchronous criteria are obtained. In the end, an example with numerical simulations is presented to verify the effectiveness of our obtained findings.

Simultaneous evacuation and entrance planning in complex building based on dynamic network flows

• This paper presents mathematical models that address the simultaneous evacuation of victims and entrance of responders. • Solutions provide the optimal routes for evacuees and responders within a critical timeframe. • Four types of models are developed according to the three different degrees of the golden time. • A heuristic algorithm is developed by extending the capacity constrained route planner. This paper presents mathematical models and a heuristic algorithm that address a simultaneous evacuation and entrance planning. For the simultaneous evacuation and entrance planning, four types of mathematical models based on the discrete time dynamic network flow model are developed to provide the optimal routes for evacuees and responders within a critical timeframe. The optimal routes obtained by the mathematical models can minimize the densification of evacuees and responders into specific areas. However, the mathematical model has a weakness in terms of long computation time for the large-size problem. To overcome the limitation, we developed a heuristic algorithm. We also analyzed the characteristics of each model and the heuristic algorithm by conducting case studies. This study pioneers area related to evacuation planning by developing and analyzing four types of mathematical models and a heuristic algorithm which take into account simultaneous evacuation and entrance planning.

Influence of Conformist and Manipulative Behaviors on Public Opinion

A discrete-time dynamical opinion network is considered in which individuals express their opinions, modeled by scalars, about a certain subject. The reputation (rating) of the subject, herein also referred to as the public opinion, is defined as the arithmetic mean of the expressed opinions. It is assumed that the expressed opinion of an individual may differ from her actual belief due to two main opposing social behaviors, namely, conformity and manipulation . For the purposes of this paper, conformity refers to the tendency of an individual to express an opinion that matches the public opinion, whereas manipulation refers to the tendency of an individual to express an opinion in order to manipulate the public opinion toward her actual belief. The general goal is to investigate how public opinion evolves in the presence of these behaviors via a game-theoretic approach. Several single- and multistage games are introduced to address different relevant scenarios. In all games, the actual beliefs are modeled by scalars in the interval $[0,1]$ . However, the games are organized into two classes, according to the nature of the expressed opinions that represent the players’ actions: 1) binary, that is, the action set of each player is the set $\lbrace 0,1\rbrace$ , in which case the opinion network resembles a tracking opinion poll, and 2) continuous, that is, the action sets are the interval $[0,1]$ , which better captures realistic opinion dynamics in social networks. For each game, the evolution of the subject's reputation as time grows is investigated.