Semi‐global output consensus of a group of linear systems in the presence of external disturbances and actuator saturation: An output regulation approach

This paper studies the problem of semi‐global leader‐following output consensus of a multi‐agent system. The output of each follower agent in the system, described by a same general linear system subject to external disturbances and actuator saturation, is to track the output of the leader, described by a linear system, which also generates disturbances as the exosystem does in the classical output regulation problem. Conditions on the agent dynamics are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the output consensus is achieved when the communication topology among the agents is a digraph containing no loop, and the leader is reachable from any follower agent. We also extend the results to the non‐identical disturbance case. In this case, conditions based on both the agent dynamics and the communication topology are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the leader‐following output consensus is achieved when the communication topology among the follower agents is a strongly connected and detailed balanced digraph, and the leader is a neighbor of at least one follower. In addition, under some further conditions on the agent dynamics, the control algorithm is adapted so as to achieve semi‐global leader‐following output consensus for a jointly connected undirected graph and the leader reachable from at least one follower. Copyright © 2015 John Wiley & Sons, Ltd.     

Subspace controllability of Boolean networks

Many Boolean control networks contain independent uncontrollable subnetworks, which may affect other nodes; and the rest of the system is called subspace of sub‐controllable states. This paper investigates the problem of subspace controllability under free input sequences, while the presumption that the initial states of those independent subnetworks are designable is canceled. An algorithm based on the common asymptotic periodic properties of the states is developed to find the reachable sets. Accordingly, the existing controllability criteria for subspaces when initial states of subnetworks are designable is improved, and a necessary and sufficient condition of subspace controllability via subnetworks and free inputs is derived. A design technique involving a kind of newly defined addition is presented to construct desired controls.     

Consensus analysis for leader‐following multi‐agent systems with second‐order individual dynamics and arbitrary sampling

This paper performs a consensus analysis of leader‐following multi‐agent systems with multiple double integrators in the framework of sampled‐data control. Both single‐leader and multiple‐leader scenarios are considered under the assumption of networks with detectable position‐like state information. The coordination tasks are accomplished by a given protocol with the robustness against the change of sampling periods. The sampling periods can be chosen to be of an arbitrary fixed length or large time‐varying length. Under the proposed protocol, we achieve two objectives: (i) in the single leader‐subgroup case, all followers reach an agreement with leaders on states asymptotically and (ii) in the multiple leader‐subgroup case, each follower converges to some convex combination of the final states of all leaders. It is shown that the final state configuration of the convex combination is uniquely determined by the underlying interaction topology, which can be any weakly connected graph. Compared with the existing results on leader‐following networks, the consensus problem and the containment problem are solved in a unified framework with large sampling periods. Some numerical experiments are conducted to illustrate the dynamic behavior of all agents with this protocol. Copyright © 2017 John Wiley & Sons, Ltd.     

LQR‐based optimal topology of leader‐following consensus

In this paper, we consider the optimal topology for leader‐following consensus problem of continuous‐time and discrete‐time multi‐agent systems based on linear quadratic regulator theory. For the first‐order multi‐agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second‐order multi‐agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second‐order leader‐following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

SOLVING ABSTRACT COOPERATIVE PATH‐FINDING IN DENSELY POPULATED ENVIRONMENTS

The problem of cooperative path‐finding is addressed in this work. A set of agents moving in a certain environment is given. Each agent needs to reach a given goal location. The task is to find spatial temporal paths for agents such that they eventually reach their goals by following these paths without colliding with each other. An abstraction where the environment is modeled as an undirected graph is adopted—vertices represent locations and edges represent passable regions. Agents are modeled as elements placed in the vertices while at most one agent can be located in a vertex at a time. At least one vertex remains unoccupied to allow agents to move. An agent can move into unoccupied neighboring vertex or into a vertex being currently vacated if a certain additional condition is satisfied. Two novel scalable algorithms for solving cooperative path‐finding in bi‐connected graphs are presented. Both algorithms target environments that are densely populated by agents. A theoretical and experimental evaluation shows that the suggested algorithms represent a viable alternative to search based techniques as well as to techniques employing permutation groups on the studied class of the problem.     

Q‐learning for continuous‐time graphical games on large networks with completely unknown linear system dynamics

In this paper, we consider the problem of leader synchronization in systems with interacting agents in large networks while simultaneously satisfying energy‐related user‐defined distributed optimization criteria. But modeling in large networks is very difficult, and for that reason, we derive a model‐free formulation that is based on a separate distributed Q‐learning function for every agent. Every Q‐function is a parametrization of each agent's control, of the neighborhood controls, and of the neighborhood tracking error. It is also evident that none of the agents has any information on where the leader is connected to and from where she spreads the desired information. The proposed algorithm uses an integral reinforcement learning approach with a separate distributed actor/critic network for each agent: a critic approximator to approximate each value function and an actor approximator to approximate each optimal control law. The derived tuning laws for each actor and critic approximators are designed appropriately by using gradient descent laws. We provide rigorous stability and convergence proofs to show that the closed‐loop system has an asymptotically stable equilibrium point and that the control policies form a graphical Nash equilibrium. We demonstrate the effectiveness of the proposed method on a network consisting of 10 agents. Copyright © 2016 John Wiley & Sons, Ltd.     

Controllability of switching networks of multi‐agent systems

This paper addresses the controllability of a switching network of multi‐agent systems with a leader obeying nearest‐neighbor communication rules. The leader is a particular agent acting as an external input to control other member agents. Some computationally efficient sufficient conditions for such multi‐agent systems to be controllable are derived. The results show that a multi‐agent system can be controllable even if each of its subsystem is not controllable, by appropriately selecting one of the agents as the leader and suitably designing the neighbor‐interaction rules via a switching topology. The fixed topology case is analyzed and new controllability conditions and formula of inputs for the desired formation of the network are presented. The controllability of a switching network of multi‐agent systems in the presence of communication delay is also investigated. Examples with numerical simulations are given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete‐time global leader‐following consensus of a group of general linear systems using bounded controls

This paper deals with the problem of global leader‐following consensus of a group of discrete‐time general linear systems with bounded controls. For each follower agent in the group, we construct both a bounded state feedback control law and a bounded output feedback control law. The feedback laws for each input of an agent use a multi‐hop relay protocol, in which the agent obtains the information of other agents through multi‐hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of real eigenvalues on the unit circle and the number of pairs of complex eigenvalues on the unit circle of the subsystem corresponding to the input, and the feedback gains are constructed from the adjacency matrix of the communication network. We show that these control laws achieve global leader‐following consensus when the communication topology among follower agents forms a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower agent. Copyright © 2017 John Wiley & Sons, Ltd.     

Further results on finite‐time consensus of second‐order multi‐agent systems without velocity measurements

This paper investigates the problem of finite‐time consensus (FTC) for second‐order nonlinear multi‐agent systems when the velocity information is unavailable. Based on the global finite‐time stability theory and homogeneity with dilation, a class of novel finite‐time consensus protocols are proposed for the multi‐agent systems. The protocol design is divided into two parts. First, when all the state information of the agents are measurable, a new continuous state feedback is designed to achieve FTC. Then, when the velocity information is unmeasurable, two finite‐time convergent discontinuous observers are presented to estimate the velocities of the followers and the leader, respectively, which further ensure the final FTC for the multi‐agent systems. Finally, one example is given to demonstrate the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

A neural network learning for adaptively extracting cross-correlation features between two high-dimensional data streams

This paper proposes a novel cross-correlation neural network (CNN) model for finding the principal singular subspace of a cross-correlation matrix between two high-dimensional data streams. We introduce a novel nonquadratic criterion (NQC) for searching the optimum weights of two linear neural networks (LNN). The NQC exhibits a single global minimum attained if and only if the weight matrices of the left and right neural networks span the left and right principal singular subspace of a cross-correlation matrix, respectively. The other stationary points of the NQC are (unstable) saddle points. We develop an adaptive algorithm based on the NQC for tracking the principal singular subspace of a cross-correlation matrix between two high-dimensional vector sequences. The NQC algorithm provides a fast online learning of the optimum weights for two LNN. The global asymptotic stability of the NQC algorithm is analyzed. The NQC algorithm has several key advantages such as faster convergence, which is illustrated through simulations.     

A unified framework for off-line permutation routing in parallel networks

In this paper we present a general strategy for finding efficient permutation routes in parallel networks. Among the popular parallel networks to which the strategy applies are mesh networks, hypercube networks, hypercube-derivative networks, ring networks, and star networks. The routes produced are generally congestion-free and take a number of routing steps that is within a small constant factor of the diameter of the network. Our basic strategy is derived from an algorithm that finds (in polynomial time) efficient permutation routes for aproduct network, G×H, given efficient permutation routes forG andH. We investigate the use of this algorithm for routingmultiple permutations and extend its applicability to a wide class of graphs, including several families ofCayley graphs. Finally, we show that our approach can be used to find efficient permutation routes among the remaining live nodes infaulty networks.This research was supported in part by a grant from the NSF, Grant No. CCR-88-12567.     

Flocking coordination using active leader and local information

In this paper coordination of a group of agents by a coordinator agent, called the leader‐agent (LA), is discussed. Agents have identical finite sensing radii and access only the local information. Inter‐agent interactions bring them together as a multi‐agent network system. In a recently proposed flocking algorithm using a virtual leader, it is proved that if a fraction of agents are informed then the center of mass of the multi‐agent system tracks the virtual leader. The minimum number of the fraction is always greater than one. In this paper the only informed agent is the LA. Interaction functions are defined to make the model of the multi‐agent system suitable for the design of the coordination control algorithm. The leader‐agent accesses its local data and actively plans its motions through a nonlinear control method. It is proven in this paper that the multi‐agent system tracks the virtual leader and a locally defined point near the LA converges to the position of the virtual leader. It is also shown that in this case, center of mass of the multi‐agent system follows the virtual leader but with a finite distance. We have also discussed positive effects of the LA on network connectivity. Finally illustrative examples are added as well. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Synchronization of leader‐follower networks with coupling delays via variable structure control

This paper investigates synchronization in leader‐follower networks with varying time‐delay interconnections. In such a network, the leader has its own dynamics and is followed by all the other nodes. Specifically, a variable structure control strategy is developed for the synchronization of the leader‐follower networks based on the Lyapunov stability theory. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Semi‐global leader‐following consensus of discrete‐time linear multi‐agent systems subject to actuator position and rate saturation

This paper deals with the leader‐following consensus of discrete‐time multi‐agent systems subject to both position and rate saturation. Each agent is described by a discrete‐time general linear dynamic with actuator subject to position and rate saturation. A modified algebraic Riccati equation and low‐gain feedback design technique are used to construct both state feedback and output feedback control protocols. It is established that a semi‐global leader‐following consensus can be achieved when the system is asymptotically null controllable with bounded controls and a leader agent has a directed path to every follower agent. Finally, several simulations are carried out to illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Resource finding in store-and-forward networks

We present a model of searching for a resource in a distributed system whose nodes are connected through a store-and-forward network. Based on this model, we show a lower bound on the number of messages needed to find a resource when nothing is known about the nodes that have the current location of the resource. The model also helps us to establish results about the time complexity of determining a message optimal resource finding algorithm when the probability distribution for the location of the resource in the network is known. We show that the optimization problem is NP-hard for general networks. Finally we show that optimal resource finding algorithms can be determined in polynomial time for a class of tree networks and bidirectional rings. The polynomial algorithms can be used as a basis of heuristic algorithms for general networks.This work was supported in part by NSF grants CCR-8806358 and NCR-8604850     

Formation Maneuvering and Target Interception for Multi‐Agent Systems via Rigid Graphs

In this paper, we introduce control laws for multi‐agent formation maneuvering and target interception problems. In the target interception problem, we consider that the target velocity is unknown. Using a single‐integrator agent model, the proposed controls consist of a formation acquisition term, dependent on the graph rigidity matrix, and a formation maneuvering or target interception term. The control laws are only a function of the relative position of agents in an infinitesimally and minimally rigid graph, and either the desired maneuvering velocity of the formation or the target's relative position to the leader. The target interception control includes a continuous dynamic estimation term to identify the unknown target velocity. A Lyapunov‐like stability analysis is used to prove that the control objectives are met.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

Distributed adaptive fault‐tolerant leader‐following formation control of nonlinear uncertain second‐order multi‐agent systems

This paper presents a distributed integrated fault diagnosis and accommodation scheme for leader‐following formation control of a class of nonlinear uncertain second‐order multi‐agent systems. The fault model under consideration includes both process and actuator faults, which may evolve abruptly or incipiently. The time‐varying leader communicates with a small subset of follower agents, and each follower agent communicates to its directly connected neighbors through a bidirectional network with possibly asymmetric weights. A local fault diagnosis and accommodation component are designed for each agent in the distributed system, which consists of a fault detection and isolation module and a reconfigurable controller module comprised of a baseline controller and two adaptive fault‐tolerant controllers, activated after fault detection and after fault isolation, respectively. By using appropriately the designed Lyapunov functions, the closed‐loop stability and asymptotic convergence properties of the leader‐follower formation are rigorously established under different modes of the fault‐tolerant control system.     

Leader‐Following Consensus of Multi‐Agent System with Diffusion

This paper is concerned with the leader‐following consensus problem for multi‐agent systems consisting of one stationary leader and multiple cooperative followers, where the controlling effect of each follower depends on its own state. It is noted that the influence of diffusion among followers is taken into account and the system is modeled by reaction‐diffusion equations. With the assumption of the followers' initial states, a linear control protocol is designed. Based on algebraic graph theory, the method of energy estimates, and Sobolev embedding theorem, the sufficient conditions guaranteeing the leader‐following consensus under the proposed control protocol are provided. Numerical examples illustrate the effectiveness of the theoretical results.     

Evolving modular networks with genetic algorithms: application to nonlinear time series

Abstract: A key problem of modular neural networks is finding the optimal aggregation of the different subtasks (or modules) of the problem at hand. Functional networks provide a partial solution to this problem, since the inter‐module topology is obtained from domain knowledge (functional relationships and symmetries). However, the learning process may be too restrictive in some situations, since the resulting modules (functional units) are assumed to be linear combinations of selected families of functions. In this paper, we present a non‐parametric learning approach for functional networks using feedforward neural networks for approximating the functional modules of the resulting architecture; we also introduce a genetic algorithm for finding the optimal intra‐module topology (the appropriate balance of neurons for the different modules according to the complexity of their respective tasks). Some benchmark examples from nonlinear time‐series prediction are used to illustrate the performance of the algorithm for finding optimal modular network architectures for specific problems.