Time-invariant Topology Research Articles

Output-Feedback-Based Consensus Control Without Continuous Interagent Communication

A decentralized event-triggered approach is developed for leader–follower systems with time-invariant and time-varying network topologies in the absence of full-state feedback. Continuous interagent communication is eliminated by communicating information only during events. At the event times, an observer communicates with the neighboring agents to obtain update information. During the interevent intervals, an open-loop estimate is used as a substitute for local feedback. The advantages of our novel approach are that: 1) the amount of communication required can be reduced and determining the event times requires no interagent communication, with the event-triggered condition designed using stability analysis so that bounded consensus is guaranteed; 2) bounded state consensus can be achieved without receiving full-state information from the followers; and 3) the switching sequence of the time-varying network topologies can be arbitrary, since a switching controller is developed based on the common-Lyapunov-function approach to ensure state consensus. Intermittent feedback is present and the dynamics of the time-varying network topologies are discrete, which together prove that Zeno behavior never occurs. The stability of the closed loop is analyzed to guarantee bounded convergence for the designed control methodologies. The results of simulations are presented that demonstrate the efficacy of our novel controllers.

An Alternate Method for Prediction and Analysis of Notch Characteristics in Indoor Power Lines Under Varied Channel Conditions

One of the challenges faced by indoor power line communication systems is the frequency-selective channels that are time varying and dependent on a large number of variabilities. A probable solution is to extract as much determinism as possible through prediction and statistical analysis of the frequency-selective notches. However, such deterministic tools are available only for simple open- and short-circuit branches and not for complex loads and topologies. This paper proposes an alternate method to predict and analyze notches using a minimum of four parameters without evaluating the transfer function. Termed as the load frequency mapping, the method is applicable for any frequency-dependent time-invariant loads and topologies and also capable of performing statistical analysis of random channels. A high decrease in prediction error (99.46–93.63%) is found for all the channels analyzed. Statistical analysis of 26 power line cables using random loads shows that some cables and loads offer more variations in frequency selectivity than others. For capacitive loads, the variation is more for the low-frequency notches and for those modeled as parallel resonant circuits at the frequencies near the resonance. Maximum variation is found for cables with high characteristic impedance with loads having high resonant frequencies and low quality factor and least for inductive loads. The power line therefore has considerable amount of determinism, and this can be incorporated to complement for fading channels or analysis of variability optimized for dual purpose of power delivery and data transfer.

Approximate kernel reconstruction for time-varying networks

BackgroundMost existing algorithms for modeling and analyzing molecular networks assume a static or time-invariant network topology. Such view, however, does not render the temporal evolution of the underlying biological process as molecular networks are typically “re-wired” over time in response to cellular development and environmental changes. In our previous work, we formulated the inference of time-varying or dynamic networks as a tracking problem, where the target state is the ensemble of edges in the network. We used the Kalman filter to track the network topology over time. Unfortunately, the output of the Kalman filter does not reflect known properties of molecular networks, such as sparsity.ResultsTo address the problem of inferring sparse time-varying networks from a set of under-sampled measurements, we propose the Approximate Kernel RecONstruction (AKRON) Kalman filter. AKRON supersedes the Lasso regularization by starting from the Lasso-Kalman inferred network and judiciously searching the space for a sparser solution. We derive theoretical bounds for the optimality of AKRON. We evaluate our approach against the Lasso-Kalman filter on synthetic data. The results show that not only does AKRON-Kalman provide better reconstruction errors, but it is also better at identifying if edges exist within a network. Furthermore, we perform a real-world benchmark on the lifecycle (embryonic, larval, pupal, and adult stages) of the Drosophila Melanogaster.ConclusionsWe show that the networks inferred by the AKRON-Kalman filter are sparse and can detect more known gene-to-gene interactions for the Drosophila melanogaster than the Lasso-Kalman filter. Finally, all of the code reported in this contribution will be publicly available.

Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems

ABSTRACTThis paper is concerned with the design of a distributed cooperative synchronisation controller for a class of higher-order nonlinear multi-agent systems. The objective is to achieve synchronisation and satisfy a predefined time-based performance. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using neural networks. The proposed robust neuro-adaptive controller drives different states of nodes systematically to synchronise with the state of the leader node within the constraints of the prescribed performance. The nodes are connected through a weighted directed graph with a time-invariant topology. Only few nodes have access to the leader. Lyapunov-based stability proofs demonstrate that the multi-agent system is uniformly ultimately bounded stable. Highly nonlinear heterogeneous networked systems with uncertain parameters and external disturbances were used to validate the robustness and performance of the new novel approach. Simulation results considered two different examples: single-input single-output and multi-input multi-output, which demonstrate the effectiveness of the proposed controller.

Distributed Source Seeking Without Global Position Information

We present a distributed control law to steer a group of autonomous communicating sensors toward the source of a diffusion process. The graph describing the communication links between sensors has a time-invariant topology, and each sensor is able to measure (in addition to the quantity of interest) only the relative bearing angle with respect to its neighbor, but has no absolute position information and does not know any relative distance. Using multiple sensors is useful in wide environments (e.g., under the sea), or when the function describing the diffusion process is slowly changing in space, so that a single sensor may have to travel long distances before having a good gradient estimation. Our approach is based on a two-fold control law, which is able to bring and keep the set of sensors on a circular equispaced formation, and to steer the circular formation toward the source via a gradient-ascent technique. The effectiveness of the proposed algorithm is theoretically proven and supported by simulation results.

Distributed adaptive output consensus tracking of higher-order systems with unknown control directions

This paper investigates the distributed adaptive output consensus tracking problem of higher-order subsystems with unknown control directions and unknown dynamic parameters. Only a subset of the subsystems is given access to the desired trajectory information directly, and the subsystems are connected through an undirected and connected graph with a time-invariant topology. A distributed adaptive controller is deduced using the backstepping technique and a Nussbaum-type function to drive all the subsystems to track the desired trajectory asymptotically. Moreover, these controllers are distributed in the sense that the controller design for each subsystem only requires relative state information between itself and its neighbors. It is proven that the output tracking error converges to zero asymptotically and that all the closed-loop system signals are bounded. A simulation is carried out to demonstrate the effectiveness of the proposed control scheme.

Input Delay Compensation in Multi-Agent Systems via Piecewise Constant Control

We consider a multi-agent system with time-invariant topology containing several agents governed by similar linear time-invariant ODEs with constant delay in actuation. Piecewise constant (PWC) control with sampling time larger than the delay value is applied. Assuming the delay-free version of the system can be brought to consensus by the PWC feedback, we design a predictive PWC feedback achieving consensus in the system with delayed input. During prediction, PWC structure is employed to determine future input to the system from its past output. This input is then used to predict the future state and compensate for the delay.

Discrete-Time Analysis of Multi-Agent Networks with Multiple Consensus Equilibria**This work was sponsored by BAP Project 9141 and Scientific and Technical Research Council of Turkey (TUBITAK) under Grant 114E613.

Abstract: In this paper, we investigate the multiple equilibrium consensus problem of first-order multi-agent networks. The problem is handled in a discrete time setting for networks with time invariant and time-varying topologies having undirected information flow. By using matrix theory and algebraic graph theory necessary and sufficient conditions are presented. The results are also illustrated with numerical examples.

Coordinated Motion Control of Distributed Spacecraft with Relative State Estimation

AbstractThis paper addresses the coordination problem of distributed spacecraft systems with time-invariant communication topologies. In order to estimate the neighbor spacecraft’ relative states which are not able to be measured directly, estimating processes are established on each spacecraft by utilizing an unscented Kalman filtering approach with measuring principles of both the pseudorange and the carrier phase. Based on such estimations, a distributed consensus protocol is proposed to address the coordinated motion problem of distributed spacecraft. The effectiveness of the proposed approach is demonstrated through numerical simulations, with a low-Earth-orbit satellites flying scenario.

On Identification of Networked Systems with Time-invariant Topology

This paper studies the problem of identification for networked systems. We consider both heterogeneous and homogeneous networks. It is assumed that the interconnection topology is time-invariant and known. We demonstrate how the parameter matrices of each individual subsystem can be identified from the input-output information obtained from the whole network. To this end, the well-known technique of Maximum-likelihood (ML) is exploited for obtaining estimations of system matrices.

The Metabolism and Growth of Web Forums

We view web forums as virtual living organisms feeding on user's clicks and investigate how they grow at the expense of clickstreams. We find that (the number of page views in a given time period) and (the number of unique visitors in the time period) of the studied forums satisfy the law of the allometric growth, i.e., . We construct clickstream networks and explain the observed temporal dynamics of networks by the interactions between nodes. We describe the transportation of clickstreams using the function , in which is the total amount of clickstreams passing through node and is the amount of the clickstreams dissipated from to the environment. It turns out that , an indicator for the efficiency of network dissipation, not only negatively correlates with , but also sets the bounds for . In particular, when and when . Our findings have practical consequences. For example, can be used as a measure of the “stickiness” of forums, which quantifies the stable ability of forums to remain users “lock-in” on the forum. Meanwhile, the correlation between and provides a method to predict the long-term “stickiness” of forums from the clickstream data in a short time period. Finally, we discuss a random walk model that replicates both of the allometric growth and the dissipation function .

Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems

In this paper we propose a practical design method for distributed cooperative tracking control of a class of higher-order nonlinear multi-agent systems. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using Neural Networks. Linearization-based robust neuro-adaptive controller driving the follower nodes to track the trajectory of the leader node is proposed. The nodes are connected through a weighted directed graph with a time-invariant topology. In addition to the fact that only few nodes have access to the leader, communication among the follower nodes is limited with some nodes having access to the information of their neighbor nodes only. Command generated by the leader node is ultimately followed by the followers with bounded synchronization error. The proposed controller is well-defined in the sense that control effort is restrained to practical limits. The closed-loop system dynamics are proved to be stable and simulation results demonstrate the effectiveness of the proposed control scheme.

An integrated diversity and fusion framework for binary consensus over fading channels

In this paper, we consider a cooperative network that is trying to reach consensus on the occurrence of an event by communicating over not fully connected and time-invariant network topologies with fading channels. We first discuss the fusion and diversity decision-making strategies over time-invariant network topologies and shed light on the underlying trade-offs. We then propose an integrated diversity and fusion framework. Our approach properly takes advantage of both fusion to enable information flow and diversity to increase robustness to link errors. We mathematically analyze the proposed framework and show how the network achieves accurate consensus asymptotically. To show an example, we then utilize the proposed framework over regular ring lattice networks. Our theoretical and simulation results indicate that the proposed technique improves the consensus performance considerably.

Continuous-time quantized consensus: Convergence of Krasovskii solutions

This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE systems are intended in the sense of Krasovskii. A limit connectivity graph is defined, which encodes persistent interactions between nodes: if such graph has a globally reachable node, Krasovskii solutions reach consensus (up to the quantizer precision) after a finite time. Under the additional assumption of a time-invariant topology, the convergence time is upper bounded by a quantity which depends on the network size and the quantizer precision. It is observed that the convergence time can be very large for solutions which stay on a discontinuity surface.

Energy Optimized Topologies for Distributed Averaging in Wireless Sensor Networks

We study the energy efficient implementation of averaging/consensus algorithms in wireless sensor networks. For static, time-invariant topologies we start from the recent result that a bidirectional spanning tree is preferable in terms of convergence time. We formulate the combinatorial optimization problem of selecting such a minimal energy tree as a mixed integer linear programming problem. Since the problem is NP-complete we devise a semi-definite relaxation and establish bounds on the optimal cost. We also develop a series of graph-based algorithms that yield energy efficient bidirectional spanning trees and establish associated bounds on the optimal cost. For dynamic, time-varying topologies we consider a recently proposed load-balancing algorithm which has preferable convergence time properties. We formulate the problem of selecting a minimal energy interconnected network over which we can run the algorithm as a sequential decision problem and cast it into a dynamic programming framework. We first consider the scenario of a large enough time horizon and show that the problem is equivalent to constructing a Minimum Spanning Tree. We then consider the scenario of a limited time horizon and employ a "rollout" heuristic that leverages the spanning tree solution and yields efficient solutions for the original problem. Some of our algorithms can be run in a distributed manner and numerical results establish that they produce near-optimal solutions.

Inferring the time-invariant topology of a nonlinear sparse gene regulatory network using fully Bayesian spline autoregression

We propose a semiparametric Bayesian model, based on penalized splines, for the recovery of the time-invariant topology of a causal interaction network from longitudinal data. Our motivation is inference of gene regulatory networks from low-resolution microarray time series, where existence of nonlinear interactions is well known. Parenthood relations are mapped by augmenting the model with kinship indicators and providing these with either an overall or gene-wise hierarchical structure. Appropriate specification of the prior is crucial to control the flexibility of the splines, especially under circumstances of scarce data; thus, we provide an informative, proper prior. Substantive improvement in network inference over a linear model is demonstrated using synthetic data drawn from ordinary differential equation models and gene expression from an experimental data set of the Arabidopsis thaliana circadian rhythm.

Distributed function calculation and consensus using linear iterative strategies

Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We show that this approach can be viewed as a linear dynamical system, with dynamics that are given by the weight matrix of the linear iteration, and with outputs for each node that are captured by the set of values that are available to that node at each time-step. In connected networks with time-invariant topologies, we use observability theory to show that after running the linear iteration for a finite number of time-steps with almost any choice of weight matrix, each node obtains enough information to calculate any arbitrary function of the initial node values. The problem of distributed consensus via linear iterations, where all nodes in the network calculate the same function, is treated as a special case of our approach. In particular, our scheme allows nodes in connected networks with time-invariant topologies to reach consensus on any arbitrary function of the initial node values in a finite number of steps for almost any choice of weight matrix.