Distributed Average Tracking for Multiple Signals Generated by Linear Dynamical Systems: An Edge-based Framework

This paper studies the distributed average tracking problem for multiple time-varying signals generated by linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In the edge-based framework, a pair of continuous algorithms with, respectively, static and adaptive coupling strengths are designed. Based on the boundary layer concept, the proposed continuous algorithm with static coupling strengths can asymptotically track the average of multiple reference signals without the chattering phenomenon. Furthermore, for the case of algorithms with adaptive coupling strengths, average tracking errors are uniformly ultimately bounded and exponentially converge to a small adjustable bounded set. Finally, a simulation example is presented to show the validity of theoretical results.Comment: accepted in press, Automatica 2016. arXiv admin note: substantial text overlap with arXiv:1312.744

Consensus tracking in multi agent system with nonlinear and non identical dynamics via event driven sliding modes

In this work, leader follower consensus objective has been addressed with the synthesis of an event based controller utilizing sliding mode robust control. The schema has been partitioned into two parts viz. finite time consensus problem and event triggered control mechanism. A nonlinear multi agent system with non identical dynamics has been put forward to illustrate the robust capabilities of the proposed control. The first part incorporates matching of states of the followers with those of the leader via consensus tracking algorithm. In the subsequent part, an event triggered rule is devised to save computational power and restrict periodic updating of the controller involved while ensuring desired closed loop performance of the system. Switching of the event based controller is achieved via sliding mode control. Advantage of using switched controller like sliding mode is that it retains its inherent robustness as well as event triggering approach aids in saving energy expenditure. Efficacy of the proposed scheme is confirmed via numerical simulations.Comment: preprint, "IEEE Transactions on Automatic Control

Cooperative Control of Linear Multi-Agent Systems via Distributed Output Regulation and Transient Synchronization

A wide range of multi-agent coordination problems including reference tracking and disturbance rejection requirements can be formulated as a cooperative output regulation problem. The general framework captures typical problems such as output synchronization, leader-follower synchronization, and many more. In the present paper, we propose a novel distributed regulator for groups of identical and non-identical linear agents. We consider global external signals affecting all agents and local external signals affecting only individual agents in the group. Both signal types may contain references and disturbances. Our main contribution is a novel coupling among the agents based on their transient state components or estimates thereof in the output feedback case. This coupling achieves transient synchronization in order to improve the cooperative behavior of the group in transient phases and guarantee a desired decay rate of the synchronization error. This leads to a cooperative reaction of the group on local disturbances acting on individual agents. The effectiveness of the proposed distributed regulator is illustrated by a vehicle platooning example and a coordination example for a group of four non-identical 3-DoF helicopter models

Cooperative output regulation of multi-agent network systems with dynamic edges

This paper investigates a new class of linear multi-agent network systems, in which nodes are coupled by dynamic edges in the sense that each edge has a dynamic system attached as well. The outputs of the edge dynamic systems form the external inputs of the node dynamic systems, which are termed "neighboring inputs" representing the coupling actions between nodes. The outputs of the node dynamic systems are the inputs of the edge dynamic systems. Several cooperative output regulation problems are posed, including output synchronization, output cooperation and master-slave output cooperation. Output cooperation is specified as making the neighboring input, a weighted sum of edge outputs, track a predefined trajectory by cooperation of node outputs. Distributed cooperative output regulation controllers depending on local state and neighboring inputs are presented, which are designed by combining feedback passivity theories and the internal model principle. A simulation example on the cooperative current control of an electrical network illustrates the potential applications of the analytical results.Comment: 17 pages, 5 figure

Containment Control of Second-order Multi-agent Systems Under Directed Graphs and Communication Constraints

The distributed coordination problem of multi-agent systems is addressed in this paper under the assumption of intermittent communication between agents in the presence of time-varying communication delays. Specifically, we consider the containment control problem of second-order multi-agent systems with multiple dynamic leaders under a directed interconnection graph topology. Also, communication between agents is performed only at some discrete instants of time in the presence of irregular communication delays and packet dropout. First, we present distributed control algorithms for double integrator dynamics in the full and partial state feedback cases. Then, we propose a method to extend our results to second-order systems with locally Lipschitz nonlinear dynamics. In both cases, we show that the proposed approach leads to our control objectives under sufficient conditions relating the characteristics of the communication process and the control gains. We also show that our approach can be applied to solve various similar coordination problems in multi-agent systems under the same communication constraints. The effectiveness of the proposed control schemes is illustrated through some examples and numerical simulations.Comment: Modified version. Paper submitted for publicatio

On the Synchronization of Second-Order Nonlinear Systems with Communication Constraints

This paper studies the synchronization problem of second-order nonlinear multi-agent systems with intermittent communication in the presence of irregular communication delays and possible information loss. The control objective is to steer all systems' positions to a common position with a prescribed desired velocity available to only some leaders. Based on the small-gain framework, we propose a synchronization scheme relying on an intermittent information exchange protocol in the presence of time delays and possible packet dropout. We show that our control objectives are achieved with a simple selection of the control gains provided that the directed graph, describing the interconnection between all systems (or agents), contains a spanning tree. The example of Euler-Lagrange systems is considered to illustrate the application and effectiveness of the proposed approach.Comment: 21 pages, 8 figures. Submitted for journal publicatio

Distributed Average Tracking for Lipschitz-Type Nonlinear Dynamical Systems

In this paper, a distributed average tracking problem is studied for Lipschitz-type nonlinear dynamical systems. The objective is to design distributed average tracking algorithms for locally interactive agents to track the average of multiple reference signals. Here, in both the agents' and the reference signals' dynamics, there is a nonlinear term satisfying the Lipschitz-type condition. Three types of distributed average tracking algorithms are designed. First, based on state-dependent-gain designing approaches, a robust distributed average tracking algorithm is developed to solve distributed average tracking problems without requiring the same initial condition. Second, by using a gain adaption scheme, an adaptive distributed average tracking algorithm is proposed in this paper to remove the requirement that the Lipschitz constant is known for agents. Third, to reduce chattering and make the algorithms easier to implement, a continuous distributed average tracking algorithm based on a time-varying boundary layer is further designed as a continuous approximation of the previous discontinuous distributed average tracking algorithms

Distributed Adaptive Consensus Control of High Order Unknown Nonlinear Networked Systems with Guaranteed Performance

Adaptive cooperative tracking control with prescribed performance function (PPF) is proposed for high-order nonlinear multi-agent systems. The tracking error originally within a known large set is confined to a smaller predefined set using this approach. Using output error transformation, the constrained system is relaxed and mapped to an unconstrained one. The controller is conceived under the assumption that the agents' nonlinear dynamics are unknown and the perceived network is structured and strongly connected. Under the proposed controller, all agents track the trajectory of the leader node with guaranteed uniform ultimately bounded transformed error and bounded adaptive estimate of unknown parameters and dynamics. In addition, the proposed controllers with PPF are distributed such that each follower agent requires information between its own state relative to connected neighbors. Proposed controller is validated for robustness and smoothness using highly nonlinear heterogeneous networked system with uncertain time-varying parameters and external disturbances. Index Terms: Prescribed performance, neuro-adaptive, high order, Transformed error, Multi-agents, Distributed control, Consensus, Synchronization, Transient, Steady-state error, MIMO, SISO

Coordinated Output Regulation of Heterogeneous Linear Systems under Switching Topologies

This paper constructs a framework to describe and study the coordinated output regulation problem for multiple heterogeneous linear systems. Each agent is modeled as a general linear multiple-input multiple-output system with an autonomous exosystem which represents the individual offset from the group reference for the agent. The multi-agent system as a whole has a group exogenous state which represents the tracking reference for the whole group. Under the constraints that the group exogenous output is only locally available to each agent and that the agents have only access to their neighbors' information, we propose observer-based feedback controllers to solve the coordinated output regulation problem using output feedback information. A high-gain approach is used and the information interactions are allowed to be switched over a finite set of fixed networks containing both graphs that have a directed spanning tree and graphs that do not. The fundamental relationship between the information interactions, the dwell time, the non-identical dynamics of different agents, and the high-gain parameters is given. Simulations are shown to validate the theoretical results

Fixed-time consensus of multiple double-integrator systems under directed topologies: A motion-planning approach

This paper investigates the fixed-time consensus problem under directed topologies. By using a motion-planning approach, a class of distributed fixed-time algorithms are developed for a multi-agent system with double-integrator dynamics. In the context of the fixed-time consensus, we focus on both directed fixed and switching topologies. Under the directed fixed topology, a novel class of distributed algorithms are designed, which guarantee the consensus of the multi-agent system with a fixed settling time if the topology has a directed spanning tree. Under the directed periodically switching topologies, the fixedtime consensus is solved via the proposed algorithms if the topologies jointly have a directed spanning tree. In particular, the fixed settling time can be off-line pre-assigned according to task requirements. Compared with the existing results, to our best knowledge, it is the first time to solve the fixed-time consensus problem for double-integrator systems under directed topologies. Finally, a numerical example is given to illustrate the effectiveness of the analytical results