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.     

Consensus of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises

This paper studies the consensus problem of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises. Directed switching topologies are considered. Firstly, for a kind of switching topology with each digraph containing a spanning tree, we give a weak consensus result on the basis of the mode‐dependent average dwell time method. Then, if all digraphs in a switching topology are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue, we prove that the mean square and almost sure consensus can always be guaranteed for an arbitrary switching sequence with some constant distributed control gains, and we also give the statistic properties of the final consensus points. Numerical examples are presented to illustrate the effectiveness of our results. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

This paper investigates the problem of distributed reliable H_∞ consensus control for high‐order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi‐agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time‐varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology‐based average dwell time approach is introduced to deal with switching jumps. By applying topology‐based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H_∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.     

Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

Based on proportional‐integral‐derivative (PID)/PD controls, we in the article investigate the tracking problem of a class of second‐order time‐varying switched nonlinear systems. To start with, for tracking a given point under arbitrary switching signals, we propose a sufficient condition about PID controller parameters, which can be implicitly described as semialgebraic sets. Successively, we consider the tracking problem under average dwell time (ADT)‐based switching signals and propose an alternative sufficient condition about PID controller parameters. Especially, for tracking an equilibrium point of the system without controls, we can further simply utilize the proportional‐derivative control and similarly construct corresponding semialgebraic conditions about proportional‐derivative controller parameters under arbitrary switching signals and ADT‐based switching signals. Finally, two examples are given to show the applicability of our theoretical results.     

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.     

Finite‐Time Consensus Problem for Second‐Order Multi‐Agent Systems Under Switching Topologies

This paper investigates the finite‐time consensus problem for multi‐agent systems with second‐order individual dynamics under switching topologies. A distributed continuous‐time protocol is designed to guarantee finite‐time consensus for homogeneous agents without predetermined leaders, i.e., it ensures agents asymptotically converge to an average consensus within finite time, even if the interaction topology among them is time‐varying but stepwise jointly‐connected. In particular, it introduces a distributed continuous‐time protocol to reach consensus in finite time and reduce the chattering together. Finally, the simulation results are also given to validate the proposed approach.     

Observer‐based leaderless and leader‐following consensus for multiagent systems: A modified integral‐type event‐triggered design

This article aims to solve leaderless and leader‐following consensus problems for general linear systems by integral‐type event‐triggered control method. Different from the existing integral‐type event‐triggered controllers for multiagent systems (MASs), a modified distributed integral‐type event‐triggered scheme is designed via defining a measurement error without continuous communication. Then, distributed event‐triggered protocols are proposed for MASs to achieve the leaderless and leader‐following consensus. Moreover, for the case that all the agents' states are not available, distributed observers are given to estimate the full states. Meanwhile, leaderless and leader‐following consensus problems are investigated based on the observer‐based event‐triggered schemes. In addition, no agent will exhibit Zeno behavior. Finally, simulations are given to verify the effectiveness of our results.     

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.     

Time‐varying output formation control for linear multi‐agent systems with switching topologies

Time‐varying output formation control problems for linear multi‐agent systems with switching topologies are studied, where two types of switching topologies are considered: (1) the topology is undirected and jointly connected, and 2) each topology is directed and has a spanning tree. An output formation protocol under switching topologies is constructed using the outputs of neighboring agents via dynamic output feedback. Two algorithms are proposed to design the dynamic protocols under both jointly connected topologies and switching directed topologies. Time‐varying output formation feasibility conditions are given to describe the compatible relationship among the desired time‐varying output formation, the dynamics of each agent, and the switching topologies. The stability of the closed‐loop multi‐agent systems under the proposed two algorithms is investigated based on the common Lyapunov functional theory and the piecewise Lyapunov functional theory, respectively. In the case where the topologies are jointly connected, time‐varying output formation can be achieved for multi‐agent systems using the designed protocol if the given time‐varying output formation satisfies the feasible constraint. For the case where the switching topologies are directed and have a spanning tree, the time‐varying output formation can be realized if the output formation feasibility constraint is satisfied and the dwell time is larger than a positive threshold. Moreover, approaches to determine the output formation references are provided to describe the macroscopic movement of the time‐varying output formation. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Scaled consensus for asynchronous high‐order discrete‐time multiagent systems

This paper investigates the distributed scaled consensus problem of multiple agents with high‐order dynamics under the asynchronous setting, where each agent measures the neighbors' information at certain discrete time instants according to its own clock rather than the whole discrete process and all agents' clocks are independent of each other. Assume that the communication topology can be arbitrarily switched and the information transfer between agents has a time‐varying delay. Under the designed asynchronous distributed control protocol, it is shown that the agents with the same scale will reach a common final state, while the agents with different scales will reach different final states. Moreover, an effective parameters selection strategy is presented for a large number of gain parameters in high‐order multiagent systems based on novel model transformation techniques. Simulation examples are provided to demonstrate the high‐order scaled consensus performances for the agents in the presence of asynchronous setting.     

Stabilization of Discrete‐time Switched Systems with State Constraints Based on Mode‐Dependent Average Dwell Time

This paper considers the stabilization problem for a class of switched systems with state constraints based on mode‐dependent average dwell time (MDADT) in discrete‐time context. An improved average dwell time method is proposed, which is less conservative than the common average dwell time method. The sufficient conditions and stabilizing state feedback controllers for stabilization of discrete‐time switched systems with state constraints under MDADT switching are derived. Finally, the simulation results show that the approach designed by this paper is effective.     

Robust state‐feedback control of stochastic state‐multiplicative discrete‐time linear switched systems with dwell time

Linear discrete‐time switched stochastic systems are considered, where the problems of mean square stability, stochastic l₂‐gain and state‐feedback control design are treated and solved. Solutions are obtained for both nominal and polytopic‐type uncertain systems. In all these problems, the switching obeys a dwell time constraint. In our solution, to each subsystem of the switched system, a Lyapunov function is assigned that is nonincreasing at the switching instants. The latter function is allowed to vary piecewise linearly, starting at the end of the previous switch instant, and it becomes time invariant after the dwell. In order to guarantee asymptotic stability, we require the Lyapunov function to be negative between consecutive switchings. We thus obtain Linear Matrix Inequalities conditions. Based on the solution of the stochastic l₂‐gain problem, we derive a solution to the state‐feedback control design, where we treat a variety of special cases. Being affine in the system matrices, all the aforementioned solutions are extended to the uncertain polytopic case. The proposed theory is demonstrated by a practical example taken from the field of flight control. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed fixed‐time consensus for multiagent systems with unknown control directions

This paper investigates the consensus problem for high‐order multiagent systems with unknown control directions and directed communication constraints. To handle the problem of unknown control directions, a logic switching rule is established in the framework of fixed‐time stability. Then, the consensus is achieved in two steps. A group of distributed fixed‐time observers is designed to estimate the reference signals first. Based on these estimates and the designed logic switching rule, a novel control protocol is proposed for each follower system. Different from the existing results, the consensus is achieved with a fixed‐time convergence rate, and the unknown control directions are allowed to be nonidentical for each agent. Finally, simulation results are given to exhibit the validity of the proposed method.     

A novel consensus algorithm for second‐order multi‐agent systems without velocity measurements

In this paper, a novel consensus protocol for second‐order multi‐agent systems is elegantly designed, and it relaxes the common requirement of the velocity information of the agents. An interesting consensus criterion is explicitly derived in terms of the proposed cooperation law provided that the dynamical equation for each agent is linear. As an extension, the proposed cooperation rule is further extended to a general scenario, where the coupling weights characterizing the relationships among the neighboring agents are time‐varying. Accordingly, two distributed cooperative algorithms (node/edge‐based scheme) are explicitly designed. Moreover, we study the case of network with switching communication setting. It shows that edge‐based law is capable with the time‐varying topology, while the node‐based scheme is not. In addition, the proposed coordination strategies are applied to the tracking problem as well. Finally, these obtained consensus results are well supported in the light of the pendulum models. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed output regulation of leader–follower multi‐agent systems

In this paper, distributed leader–follower control algorithms are presented for linear multi‐agent systems based on output regulation theory and internal model principle. By treating a leader to be followed as an exosystem, the proposed framework can be used to generalize existing multi‐agent coordination solutions to allow the identical agents to track an active leader with different dynamics and unmeasurable variables. Moreover, the obtained results for multi‐agent coordination control are an extension of previous work on centralized and decentralized output regulation to a distributed control context. Necessary and sufficient conditions for the distributed output regulation problem are given. Finally, distributed output regulation of some classes of multi‐agent systems with switching interconnection topologies are discussed via both static and dynamic feedback. Copyright © 2011 John Wiley & Sons, Ltd.     

Event‐triggered output synchronization of heterogeneous multi‐agent systems

This paper proposes a control architecture that employs event‐triggered control techniques to achieve output synchronization of a group of heterogeneous linear time‐invariant agents. We associate with each agent an event‐triggered output regulation controller and an event‐triggered reference generator. The event‐triggered output regulation controller is designed such that the regulated output of the agent approximately tracks a reference signal provided by the reference generator in the presence of unknown disturbances. The event‐triggered reference generator is responsible for synchronizing its internal state across all agents by exchanging information through a communication network linking the agents. We first address the output regulation problem for a single agent where we analyze two event‐triggered scenarios. In the first one, the output and input event detectors operate synchronously, meaning that resets are made at the same time instants, while in the second one, they operate asynchronously and independently of each other. It is shown that the tracking error is globally bounded for all bounded reference trajectories and all bounded disturbances. We then merge the results on event‐triggered output regulation with previous results on event‐triggered communication protocols for synchronization of the reference generators to demonstrate that the regulated output of each agent converges to and remains in a neighborhood of the desired reference trajectory and that the closed‐loop system does not exhibit Zeno solutions. Several examples are provided to illustrate the advantages and issues of every component of the proposed control architecture. Copyright © 2016 John Wiley & Sons, Ltd.     

Formation control for a class of nonlinear multiagent systems using model‐free adaptive iterative learning

In this paper, the problem of formation control is considered for a class of unknown nonaffine nonlinear multiagent systems under a repeatable operation environment. To achieve the formation objective, the unknown nonlinear agent's dynamic is first transformed into a compact form dynamic linearization model along the iteration axis. Then, a distributed model‐free adaptive iterative learning control scheme is designed to ensure that all agents can keep their desired deviations from the reference trajectory over the whole time interval. The main results are given for the multiagent systems with fixed communication topologies and the extension to the switching topologies case is also discussed. The feature of this design is that formation control can be solved only depending on the input/output data of each agent. An example is given to demonstrate the effectiveness of the proposed method.     

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.