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

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

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

Cooperative Global Robust Output Regulation for a Class of Nonlinear Multi-Agent Systems by Distributed Event-Triggered Control

This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact sets. Second, the nonlinear functions in our system do not need to satisfy the global Lipchitz condition. Thus our systems are general enough to include some benchmark nonlinear systems that cannot be handled by existing approaches. Finally, our control law is a specific distributed output-based event-triggered control law, which lends itself to a direct digital implementation.Comment: This paper has been submitted to a journal on July 17, 201

On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs

The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittent communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are shown to be computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an important feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. The performance of the considered consensus algorithms is illustrated through simulations, comparing it to existing approaches for dynamic networks with finite-time and fixed-time convergence. It is shown that the settling time of the considered algorithms grows slower when the number of nodes increases than with other consensus algorithms for dynamic networks

Event-Triggered Cooperative Robust Practical Output Regulation for a Class of Linear Multi-Agent Systems

In this paper, we consider the event-triggered cooperative robust practical output regulation problem for a class of linear minimum-phase multi-agent systems. We first convert our problem into the cooperative robust practical stabilization problem of a well defined augmented system Based on the distributed internal model approach. Then, we design a distributed event-triggered output feedback control law together with a distributed output-based event-triggered mechanism to stabilize the augmented system, which leads to the solvability of the cooperative robust practical output regulation problem of the original plant. Our distributed control law can be directly implemented in a digital platform provided that the distributed triggering mechanism can monitor the continuous-time output information from neighboring agents. Finally, we illustrate our design by an example.Comment: This paper has been accepted for publication in Automatica on May 21, 201

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

Multi-Agent Distributed Coordination Control: Developments and Directions

In this paper, the recent developments on distributed coordination control, especially the consensus and formation control, are summarized with the graph theory playing a central role, in order to present a cohesive overview of the multi-agent distributed coordination control, together with brief reviews of some closely related issues including rendezvous/alignment, swarming/flocking and containment control.In terms of the consensus problem, the recent results on consensus for the agents with different dynamics from first-order, second-order to high-order linear and nonlinear dynamics, under different communication conditions, such as cases with/without switching communication topology and varying time-delays, are reviewed, in which the algebraic graph theory is very useful in the protocol designs, stability proofs and converging analysis. In terms of the formation control problem, after reviewing the results of the algebraic graph theory employed in the formation control, we mainly pay attention to the developments of the rigid and persistent graphs. With the notions of rigidity and persistence, the formation transformation, splitting and reconstruction can be completed, and consequently the range-based formation control laws are designed with the least required information in order to maintain a formation rigid/persistent. Afterwards, the recent results on rendezvous/alignment, swarming/flocking and containment control, which are very closely related to consensus and formation control, are briefly introduced, in order to present an integrated view of the graph theory used in the coordination control problem. Finally, towards the practical applications, some directions possibly deserving investigation in coordination control are raised as well.Comment: 28 pages, 8 figure

Designing Distributed Fixed-Time Consensus Protocols for Linear Multi-Agent Systems Over Directed Graphs

This technical note addresses the distributed fixed-time consensus protocol design problem for multi-agent systems with general linear dynamics over directed communication graphs. By using motion planning approaches, a class of distributed fixed-time consensus algorithms are developed, which rely only on the sampling information at some sampling instants. For linear multi-agent systems, the proposed algorithms solve the fixed-time consensus problem for any directed graph containing a directed spanning tree. In particular, the settling time can be off-line pre-assigned according to task requirements. Compared with the existing results for multi-agent systems, to our best knowledge, it is the first-time to solve fixed-time consensus problems for general linear multi-agent systems over directed graphs having a directed spanning tree. Extensions to the fixed-time formation flying are further studied for multiple satellites described by Hill equations

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