Cooperative robust output regulation of a class of heterogeneous linear uncertain multi‐agent systems

The cooperative output regulation of a linear multi‐agent system can be viewed as a generalization of the leader‐following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi‐agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi‐agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi‐agent system. We then solve our problem by combining a simultaneous high‐gain state feedback control technique and a distributed high‐gain observer technique. A special case of our result leads to the solution of the leader‐following robust consensus problem for a class of uncertain multi‐agent systems. Copyright © 2013 John Wiley & Sons, Ltd.     

Cooperative robust output regulation problem for discrete‐time linear time‐delay multi‐agent systems

In this paper, we study the cooperative robust output regulation problem for discrete‐time linear multi‐agent systems with both communication and input delays by a distributed internal model approach. We first introduce the distributed internal model for discrete‐time multi‐agent systems with both communication and input delays. Then, we define the so‐called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi‐agent systems.     

Leader‐Following Output Synchronization for a Class of Uncertain Nonlinear Multi‐Agent Systems Under Uniformly Connected Network

In this paper we study the cooperative global output regulation problem of a class of uncertain nonlinear multi‐agent systems under dynamic network topology. Distributed dynamic observers are introduced to estimate the states of the leader system or the called exosystem. Furthermore, we propose a multi‐channel input version of the changing supply rate theorem, through which the changing supply rate technique can be applied to the subsystem with multiple channels of the control inputs, and therefore control laws can be designed in a fully distributed way. As opposed to the existing results, in the current paper we allow the communication network topology to be uniformly connected. Finally, we apply our result to a group of well‐known Lorenz systems.     

Adaptive iterative learning control for coordination of second‐order multi‐agent systems

In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi‐agent systems with second‐order dynamics and unknown time‐varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi‐agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Semi‐global cooperative output regulation of a class of nonlinear uncertain multi‐agent systems under switching networks

In this paper, we consider the semi‐global cooperative output regulation problem for a class of nonlinear uncertain multi‐agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time‐varying system, which is then used in the design of distributed adaptive internal model‐based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed‐loop multi‐agent system from the viewpoint of singular perturbation. In fact, the singular perturbation‐based method provides an effective tool to handle the multi‐agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 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.     

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.     

Containment control of linear multi‐agent systems with multiple leaders of bounded inputs using distributed continuous controllers

This paper considers the containment control problem for multi‐agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and time varying. Based on the relative states of neighboring agents, a distributed static continuous controller is designed, under which the containment error is uniformly ultimately bounded and the upper bound of the containment error can be made arbitrarily small, if the subgraph associated with the followers is undirected and, for each follower, there exists at least one leader that has a directed path to that follower. It is noted that the design of the static controller requires the knowledge of the eigenvalues of the Laplacian matrix and the upper bounds of the leaders’ control inputs. In order to remove these requirements, a distributed adaptive continuous controller is further proposed, which can be designed and implemented by each follower in a fully distributed fashion. Extensions to the case where only local output information is available and to the case of multi‐agent systems with matching uncertainties are also discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Distributed consensus of delayed multi‐agent systems with nonlinear dynamics via intermittent control

In this paper, a distributed consensus of delayed multi‐agent systems with a leader is investigated, and a nonlinear protocol is proposed based on intermittent control. A notable feature of this protocol is to address second‐order consensus problems for delayed nonlinear multi‐agent systems, where agents can only communicate with each other over some disconnected time intervals. Some sufficient conditions to guarantee the consensus over fixed and switching topologies are derived. It is shown that second‐order consensus for delayed multi‐agent system with intermittent control can be achieved if the time delay is less than a critical value and the communication time duration is larger than a threshold value. In addition, some numerical examples are given to illustrate the effectiveness and feasibility of the theoretical results.     

Quantized tracking control for a multi‐agent system with high‐order leader dynamics

This paper presents a study of a tracking control problem for a multi‐agent system with an active leader and quantized communication constraints. We first design a discrete‐time distributed estimator‐based tracking control for each follower‐agent and analyze the tracking convergence with the help of the Riccati equation and common Lyapunov function when the communication channel is perfect and the interconnection topology is time‐varying. Then a stochastic quantization strategy is applied to model the information communication in the agent coordination and the corresponding solution to the tracking control problem is also given. Finally, a numerical example is given to illustrate the tracking control algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Semi‐global bipartite output consensus of heterogeneous multi‐agent systems subject to input saturation by finite‐time observer

In this paper, the semi‐global bipartite output consensus problem of heterogeneous linear multi‐agent systems is studied. Compared with related works, both cooperative interactions and antagonistic interactions between agents are considered, and the input saturation on each follower is taken into account. First, two distributed finite‐time observers are designed to recover the leader's state. Particularly, the setting time can be independent of any initial states. Due to the antagonistic interactions, estimation values are the same as the leader's state in modulus but may not in sign. Then, the low‐gain feedback technique is used to develop the distributed control law for each follower. Moreover, we summarize a framework for solving the semi‐global bipartite output consensus problem of heterogeneous multi‐agent systems subject to input saturation. Finally, examples are given to illustrate the results.     

High‐precision formation control of nonlinear multi‐agent systems with switching topologies: A learning approach

Arbitrary high precision is considered one of the most desirable control objectives in the relative formation for many networked industrial applications, such as flying spacecrafts and mobile robots. The main purpose of this paper is to present design guidelines of applying the iterative schemes to develop distributed formation algorithms in order to achieve this control objective. If certain conditions are met, then the control input signals can be learned by the developed algorithms to accomplish the desired formations with arbitrary high precision. The systems under consideration are a class of multi‐agent systems under directed networks with switching topologies. The agents have discrete‐time affine nonlinear dynamics, but their state functions do not need to be identical. It is shown that the learning processes resulting from the relative output formation of multi‐agent systems can converge exponentially fast with the increase of the iteration number. In particular, this work induces a distributed algorithm that can simultaneously achieve the desired relative output formation between agents and regulate the movement of multi‐agent formations as desired along the time axis. The illustrative numerical simulations are finally performed to demonstrate the effectiveness and performance of the proposed distributed formation algorithms. Copyright © 2014 John Wiley & Sons, Ltd.     

Cooperative Adaptive Fuzzy Output Feedback Control for Synchronization of Nonlinear Multi‐Agent Systems in the Presence of Input Saturation

This paper considers the leader‐following synchronization problem of nonlinear multi‐agent systems with unmeasurable states in the presence of input saturation. Each follower is governed by a class of strict‐feedback systems with unknown nonlinearities and the information of the leader can be accessed by only a small fraction of followers. An auxiliary system is introduced and its states are used to design the cooperative controllers for counteracting the effect of input saturation. By using fuzzy logic systems to approximate the unknown nonlinearities, local adaptive fuzzy observers are designed to estimate the unmeasurable states. Dynamic surface control (DSC) is employed to design distributed adaptive fuzzy output feedback controllers. The developed controllers guarantee that the outputs of all followers synchronize to that of the leader under directed communication graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are semiglobally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. An example is provided to show the effectiveness of the proposed control approach.     

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.     

Distributed Adaptive Event‐Triggered Control for Leader‐Following Consensus of Multi‐Agent Systems

This paper studies the leader‐following consensus problem for Lipschitz nonlinear multi‐agent systems using novel event‐triggered controllers. A distributed adaptive law is introduced for the event‐based control strategy design such that the proposed controllers are independent of system parameters and only use the relative states of neighboring agents, and hence are fully distributed. Due to the introduction of an event‐triggered control scheme, the controller of the agent is only triggered at it's own event times, and thus reduces the amount of communication between controller and actuator and lowers the frequency of controller updates in practice. Based on a quadratic Lyapunov function, the event condition which uses only neighbor information and local computation at trigger instants is established. Infinite triggers within a finite time are also verified to be impossible. The effectiveness of the theoretical results are illustrated through simulation examples.     

Fixed‐Time Synchronization of a Class of Second‐Order Nonlinear Leader‐Following Multi‐Agent Systems

The fixed‐time synchronization problem for a class of second‐order nonlinear multi‐agent systems with a leader‐follower architecture is investigated in this paper. To achieve the fixed‐time tracking task, the design procedure is divided into two steps. At the first step, a distributed fixed‐time observer is designed for each agent to estimate the leader's state in a fixed time. Then, at the second step, based on the technique of adding a power integrator, a fixed‐time tracking controller for each agent is proposed such that the estimate leader's state can be tracked in a fixed time. Finally, an observer‐based fixed‐time controller is developed such that the leader can be tracked by all the followers in a fixed time, which can be predetermined. Simulations are presented to verify the effectiveness of the proposed approach.     

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     

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.