Connectivity Of Communication Graph Research Articles

Distributed output consensus of heterogeneous linear multi‐agent systems with dynamic quantization

AbstractThe output consensus problem for heterogeneous linear multi‐agent systems (MASs) without strongly connected communication graphs is investigated via quantization communication. In this work, we propose an efficient distributed control law composed of distributed quantized observers and compensators to accomplish this task. Particularly, we first employ a dynamic encoding–decoding scheme to design the distributed quantized observer, which is able to accurately estimate the state of the leader for MASs. Then, an appropriate compensator is constructed to show that asymptotic output consensus can be achieved with 5‐level quantizer, even if neither global knowledge of communication graphs nor the information about initial states of all agents is required. Finally, a numerical example is used to validate the effectiveness of our distributed control law for MASs.

Dissipativity-based consensus for P-one-sided Lipschitz multi-agent systems via ILC

Abstract Based on dissipativity theory, the consensus via iterative learning control (ILC) is investigated for P-one-sided Lipschitz (P-OSL) nonlinear multi-agent systems (MASs). This paper only considers the P-OSL condition without using the quadratically inner-bounded constraint. Firstly, the ILC protocol is designed for such nonlinear MASs. Then, the convergence conditions of the consensus algorithm under a connected communication graph are presented from the viewpoint of dissipativity. It is shown that, on a fixed finite-time interval, the proposed algorithm can achieve perfect consensus tracking. Finally, two examples are constructed to show the effectiveness of the proposed method.

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equilibrium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization of players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized information flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respectively. Through Lyapunov stability analysis, it is shown that players' actions can be steered to a neighborhood of the Nash equilibrium with logarithmic and uniform quantizers, and the quantified convergence error depends on the parameter of the quantizer for both undirected and directed cases. A numerical example is given to verify the theoretical results.

Distributed k-Winners-Take-All Network: An Optimization Perspective.

In this article, we proposed an equivalent formulation of the k-winners-take-all (k-WTA) problem as a constrained optimization problem by including the Laplacian matrix of the undirected connected communication graph to adapt to the distributed computing scenario, where an additional auxiliary variable is introduced. To solve the optimization problem in a distributed fashion, we design projection neural networks by using the convex optimization theory, leading to the emergence of a distributed k-WTA network. Our theoretical analysis shows that the proposed distributed k-WTA network has a globally asymptotically stable equilibrium that is identical to the optimal solution to the optimization problem, that is, the correct k-WTA solution. The effectiveness and advantages, including the extendability to constrained k-WTA problems, of the proposed k-WTA network are demonstrated via simulations.

Wind Field Estimation Using Multiple Quadcopters

We consider a wind field estimation problem with multiple quadcopters. The wind field is assumed to affect the motion of the quadcopters in an additive fashion. Starting with a single quadcopter case, we first design an Extended Kalman filter (EKF) for constant and spatial-varying wind estimation. We next extend the EKF wind estimator for multiple quadcopters with directed connected communication graphs. To fuse the estimates of the wind field, we develop a sequential covariance intersection (SCI) method and a sequential weighted exponential product (SWEP) method for constant and spatially-varying wind fields. The effectiveness of the designed partial state fusion methods is validated and compared in simulations for various communication topologies with constant and Rankine wind models.

Nonnegative Consensus Tracking of Networked Systems With Convergence Rate Optimization.

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies.

Distributed Adaptive Output Feedback Consensus of Parabolic PDE Agents on Undirected Networks.

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader-follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader-follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained.

Distributed Differential Games for Control of Multi-Agent Systems

Motivated by the challenges arising in the field of multi-agent system (MAS) control, we consider linear heterogeneous MAS subject to local communication and investigate the problem of designing distributed controllers for such systems. We provide a game theoretic framework for systematically designing distributed controllers, taking into account individual objectives of the agents and their possibly incomplete knowledge of the MAS. Linear state-feedback control laws are obtained via the introduction of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed differential game</i> , namely, the combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local non-cooperative differential games</i> , which are solved in a decentralized fashion. Conditions for stability of the MAS are provided for the special cases of acyclic and strongly connected communication graph topologies. These results are then exploited to provide stability conditions for general graph topologies. The proposed framework is demonstrated on a tracking synchronization problem associated with the design of a distributed secondary voltage controller for microgrids and on a numerical example.

Convert a Strongly Connected Directed Graph to a Black-and-White 3-SAT Problem by the Balatonboglár Model

In a previous paper we defined the black and white SAT problem which has exactly two solutions, where each variable is either true or false. We showed that black and white 2-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonboglár model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a black and white SAT problem. We prove a powerful theorem, the so called transitions theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as black and white SAT problems. We show that the Balatonboglár model is between the strong and the weak model, and it generates 3-SAT problems, so the Balatonboglár model represents strongly connected communication graphs as black and white 3-SAT problems. Our motivation to study these models is the following: The strong model generates a 2-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonboglár model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonboglár model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: the SAT problem and directed graphs.

Distributed consensus tracking control of second‐order non‐linear multi‐agent systems with unmodelled dynamics

In this study, the consensus tracking control problem is considered for a class of second-order non-linear multi-agent systems with unmodelled dynamics. Radial basis function neural networks are introduced to approximate the unknown non-linearities and a dynamic signal is utilised to deal with the unmodelled dynamics. Meanwhile, appropriate Lyapunov functions are constructed and a new distributed adaptive control protocol is designed to guarantee that all the tracking error signals in the considered multi-agent systems are ultimately bounded, under which the distributed tracking consensus is reached for all undirected connected communication graphs. Finally, two demonstrative examples are given to illustrate the validity of the designed protocols.

Formation tracking of multiple amphibious robots with unknown nonlinear dynamics

Cooperative tracking control problem of multiple water–land amphibious robots is discussed in this article with consideration of unknown nonlinear dynamics. Firstly, the amphibious robot dynamic model is formulated as an uncoupled nonlinear one in horizontal plane through eliminating relatively small sway velocity of the platform. Then cooperative tracking control algorithm is proposed with a two-stage strategy including dynamic control stage and kinematic control stage. In dynamic control stage, adaptive consensus control algorithm is obtained with estimating nonlinear properties of amphibious robots and velocities of the leader by neural network with unreliable communication links which is always the case in underwater applications. After that, kinematic cooperative controller is presented to guarantee formation stability of multiple water–land amphibious robots system in kinematic control stage. As a result, with the implementation of graph theory and Lyapunov theory, the stability of the formation tracking of multiple water–land amphibious robots system is proved with consideration of jointly connected communication graph. At last, simulations are carried out to prove the effectiveness of the proposed approaches.

Robust Bipartite Consensus and Tracking Control of High-Order Multiagent Systems With Matching Uncertainties and Antagonistic Interactions

This paper is concerned with general coopetition networks with signed graphs, based on which both the bipartite consensus and tracking control problems for networked systems subject to nonidentical matching uncertainties are studied. For the case of undirected and connected communication graphs, we propose a distributed discontinuous nonlinear controller which can achieve the bipartite consensus. To cancel the chattering phenomenon of the discontinuous controller, a continuous one is designed by using the boundary layer technique, under which the bipartite consensus error is shown to be uniformly ultimately bounded and can exponentially converge to a small adjustable bounded set. Further, considering the case of a leader having a bounded control action, we present a continuous controller to guarantee the ultimate boundedness of the bipartite tracking error.

Distributed Optimization for Two Types of Heterogeneous Multiagent Systems.

This article studies distributed optimization algorithms for heterogeneous multiagent systems under an undirected and connected communication graph. Two types of heterogeneities are discussed. First, we consider a class of multiagent systems composed of both continuous-time dynamic agents and discrete-time dynamic agents. The agents coordinate with each other to minimize a global objective function that is the sum of their local convex objective functions. A distributed subgradient method is proposed for each agent in the network. It is proved that driven by the proposed updating law, the agents' position states converge to an optimal solution of the optimization problem, provided that the subgradients of the objective functions are bounded, the step size is not summable but square summable, and the sampling period is bounded by some constant. Second, we consider a class of multiagent systems composed of both first-order dynamic agents and second-order dynamic agents. It is proved that the agents' position states converge to the unique optimal solution if the objective functions are strongly convex, continuously differentiable, and the gradients are globally Lipschitz. Numerical examples are given to verify the conclusions.

Global Social Cost Minimization With Possibly Nonconvex Objective Functions: An Extremum Seeking-Based Approach

A social cost minimization problem is addressed in this article. In the considered problem, a network of agents work collaboratively to minimize the social cost function, which is defined as the sum of the agents’ local objective functions. The engaged agents are supposed to be equipped with an undirected and connected communication graph. Different from most of the existing works, the social cost function in the considered problem is allowed to be nonconvex and possibly admits local extrema. To avoid local extrema and achieve the global minimization of the social cost function, an extremum-seeking-based approach is proposed by introducing a dynamic average consensus protocol to the sinusoidal-dither-signal-based extremum seeking scheme. The dynamic average consensus protocol is leveraged in the proposed extremum-seeker for information sharing and the sinusoidal probing signal is utilized for information extraction. For the avoidance of local extrema, the amplitude of the dither signal is designed to be adaptive. Through Lyapunov stability analysis, it is shown that the proposed method enables the decision variable to converge to a neighborhood of the global minimum point if the conditions on the network connectivity, the existence of unique global minimum and achievability of the global minimum are satisfied. The theoretical result is verified via simulating a numerical example.

Leader‐following consensus of fractional‐order multi‐agent systems via adaptive control

SummaryThis article focuses on the consensus problem of leader‐following fractional‐order multi‐agent systems (MASs) with general linear and Lipschitz nonlinear dynamics. First, the distributed adaptive protocols for linear and nonlinear fractional‐order MASs are constructed, respectively. We allow the control coupling gains to be time varying for each agent. Moreover, the adaptive modification schemes for the control gain are designed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence. Second, based on fractional‐order Lyapunov stability theorem and Barbalat's lemma, two novel sufficient conditions in terms of linear matrix inequalities are provided to ensure that the leader‐following consensus can be obtained in the case for any undirected connected communication graph. Furthermore, we show that the proposed algorithm also works for consensus of agents with intrinsic Lipschitz nonlinear dynamics. As a result, the proposed framework requires no global information and thus can be implemented in a fully distributed manner. Finally, the numerical simulations are given to demonstrate the effectiveness of obtained the theoretical results.

Decentralised finite‐time consensus for second‐order multi‐agent system under event‐triggered strategy

In this technical note, the authors address the finite-time consensus problem of a second-order multi-agent system (SOMAS) under an event-triggered control strategy. This problem arises from the case where actuators in a SOMAS fail to follow the ideal controller behaviour exactly, due to either the failure of an embedded processor to maintain the desired update rate or a large time constant in the actuators, while still trying to maintain some performance merits from the finite-time control theory. A decentralised event-triggered non-linear protocol is proposed based on only local information for the undirected and connected communication graph. The rigorous proof is then presented and shows that the consensus can be achieved in finite time even under event-triggered schemes. Owing to the event-triggered strategy, they proposed a technique that bounds the steady errors of agent states into a small region around zero in finite time and reduces the update frequency of actuators while excluding the Zeno behaviour. Finally, simulation results are provided to validate the correctness and effectiveness of the proposed method and demonstrate that it can adjust a composed performance metrics with respect to the convergent rate, consensus accuracy, and update frequency of actuators by tuning the parameters in the control protocol.

Saddle-Flow Dynamics for Distributed Feedback-Based Optimization

This letter develops a distributed saddle-flow algorithm to regulate the output of a networked system—modeled as static linear map—to the solution of a constrained convex optimization problem. The algorithm is “feedback-based”, in the sense that measurements of the network output are leveraged in the saddle-flow updates to avoid a complete (oracle-based) knowledge of the network map. In the distributed architecture, each actuator has access to only a subset of measurements; nevertheless, supported by a connected communication graph, a distributed protocol is implemented to achieve consensus on pertinent dual variables associated with network-level output constraints and, therefore, on the solution of the constrained problem. Using a LaSalle argument, we show that under an easily satisfiable linear matrix inequality condition the proposed algorithm converges to an optimal primal–dual solution. We demonstrate the effectiveness of the proposed method in a voltage regulation problem for power systems with high penetration of renewable generation.

H2 and H∞ almost output synchronization of heterogeneous continuous‐time multi‐agent systems with passive agents and partial‐state coupling via static protocol

SummaryThis paper studies H2 and H∞ almost output synchronization problems for heterogeneous continuous‐time multiagent systems with passive agents and strongly connected communication graph. For non‐introspective passive agents, a linear static protocol can be designed to achieve almost output synchronization with arbitrarily small H2 norm. Moreover, we show that the H∞ almost output synchronization problem via static protocol is not solvable for this class of systems.

Power-efficient and interference-free link scheduling algorithms for connected wireless sensor networks

A fundamental aspect in performance engineering of wireless sensor networks (WSN) is optimizing the set of links that can be concurrently activated to meet a given signal-to-interference-plus-noise ratio (SINR) threshold. The solution of this combinatorial problem is a key element in wireless link scheduling. Another key architectural goal in WSN is connectivity. The connectivity of sensor nodes is critical for WSN, as connected graphs can be used for both data collection and data dissemination. In this paper, we investigate the joint scheduling and connectivity problem in WSN assuming the SINR model. We propose algorithms to build connected communication graphs with power-efficient links to be scheduled simultaneously in one time slot. The algorithms aiming at minimizing the number of time slots needed to successfully schedule all the given links such that the nodes can communicate without interference in the SINR model. While power-efficient and interference-free schedules reduce energy consumption, minimization of the schedule length (shortest link scheduling) has the effect of maximizing network throughput. We propose one greedy randomized constructive heuristic, two local search procedures, and three greedy randomized adaptive search procedures metaheuristics. We report computational experiments comparing the effectiveness of the proposed algorithms. Our simulation also shows the trade-off between power consumption and schedule length and the results indicate that not only the overall performance of our algorithms, but also show that the total power and schedule length value of its solutions are better than the existing work.

A Flexible Synthesis Framework of Structured Controllers for Networked Systems

We propose a framework to synthesize a block-diagonally structured $\mathcal {H}_\infty$ -controller that consists of a parametric and a block-triangular dynamic component. Moreover, we present an application to $\mathcal {H}_\infty$ -design with controller constraints that arise from a delayed chained interconnection of subsystems that are, by themselves, described by delayed strongly connected communication graphs. We introduce a compact notation to describe the delayed graph structures and give a precise classification of all tractable network-induced constraint sets that can be handled within our framework. Furthermore, the flexibility of our approach is demonstrated through the application to a vehicle platoon with different controller communication scenarios.