Robust Output Synchronization of a Network of Heterogeneous Nonlinear Agents Via Nonlinear Regulation Theory

Abstract

In this paper, we consider the output synchronization problem for a network of heterogeneous diffusively-coupled nonlinear agents. Specifically, we show how the (non-identical) agents can be controlled in such a way that their outputs asymptotically track the output of a prescribed nonlinear exosystem. The problem is solved in two steps. In the first step, the problem of achieving consensus among (identical) nonlinear reference generators is addressed. In this respect, it is shown how the techniques recently developed to solve the consensus problem among linear agents can be extended to agents modeled by nonlinear d-dimensional differential equations, under the assumption that the communication graph is connected. In the second step, the theory of nonlinear output regulation is applied in a decentralized control mode, to force the output of each agent of the network to robustly track the (synchronized) output of a local reference model.

Multipattern Output Consensus in Networks of Heterogeneous Nonlinear Agents With Uncertain Leader: A Nonlinear Regression Approach

“…By following [11]- [12], the local controllers (6) can be designed in two steps. By defining η k in (6) as η k = col(w k , ζ k ), the local controllers can be written aṡ…”

“…This choice may depend in general on the properties of system (5). For instance, under a minimum phase assumption, one may use nonlinear output regulation tools [20], as shown in [12]. Moreover, since in our framework each agent has the information of the tracking reference y ref k…”

“…In [11] it has been proved that a necessary and sufficient condition for output synchronization in heterogeneous networks is the internal model principle. This concept has been adapted and extended to the nonlinear case in [12] and has become the widely accepted technique to face the problem known in literature as cooperative output regulation. The key aspect of this D. Astolfi is with the Université de Lorraine, CRAN, UMR 7039, Nancy, France and the CRNS, CRAN, UMR 7039, Nancy, France, daniele.astolfi@univ-lorraine.fr approach is that the consensus trajectory can be thought as generated by an exosystem, whose model is known to all the agents in the network.…”

Network Games: Condensation of the Graph as a Hierarchical interpretation of the Game

“…In this framework the agents in the network are willing to collaborate and find an agreement between each other in such a way that they coordinate their motion. This approach is represented by the huge literature of consensus/synchronization problems (Isidori et al (2014), Arcak (2007)) and its application to robot-swarm coordination (Sepulchre et al (2008), Olfati-Saber (2006)), power networks (Dhople et al (2014), Xiang and Hill (2014)) and social networks (Mirtabatabaei and Bullo (2012), Blondel et al (2010)). However, not in all the frameworks and not in all the situations, it is possible to consider a cooperative approach.…”

Output Regulation and Active Disturbance Rejection Control: Unified Formulation and Comparison

“…In addition to numerous research papers, some monographs on this topic were published [21][22][23][24]. More recent works on output regulation theory are concerned with nonlinear multi-agent systems [25][26][27][28].…”