Automatica 104 (2019) 126–133 Contents lists available at ScienceDirect Automatica journal homepage: www.elsevier.com/locate/automatica Brief paper Feedforward design for output synchronization of nonlinear heterogeneous systems with output communication ✩ Zhiyong Chen School of Electrical Engineering and Computing, The University of Newcastle, Callaghan, NSW 2308, Australia article info Article history: Received 4 April 2017 Received in revised form 5 November 2018 Accepted 26 January 2019 Available online xxxx Keywords: Synchronization Consensus Nonlinear systems Collaborative control Multi-agent systems Heterogeneous systems abstract Output synchronization of nonlinear heterogeneous networked systems has been well investigated within a two-step framework. A reference model is designed for each agent and they achieve consensus through a proper collaborative control strategy. Then, a local regulation controller is constructed to drive each agent’s output to the desired trajectory generated by its reference model. The local regulation controller was studied mainly based on the internal model principle. As the two steps occur concurrently, a small gain condition must be satisfied between them when the setting is on output communication that allows only agent outputs to be transmitted over network. In this paper, we consider a novel feedforward design that does not rely on internal model but a reference model of a sufficiently high relative degree. With such a design, local regulation can be separately achieved and hence the small gain condition is no longer required, which much simplifies the design when agent dynamics do not contain uncertainties. © 2019 Elsevier Ltd. All rights reserved. 1. Introduction Output synchronization of nonlinear heterogeneous multi- agent systems (MASs) has attracted many researchers. The re- search was motivated by the development of its linear counterpart. The main challenge for heterogeneous MASs is that they lack a well defined ‘‘homogeneous kernel’’, a common dynamics that all agents can reach once synchronization occurs, while such a ‘‘homo- geneous kernel’’ naturally exists for a homogeneous network as all agents always share a common dynamics. The research on linear homogeneous MASs can be found in, e.g., Ma and Zhang (2010), Seo, Shim, and Back (2009) and Tuna (2009). The synchronization problem for heterogeneous agents however is more challenging as agreement occurs only upon proper compensation for the dy- namics to match the homogeneous kernel. Various techniques can be found in Grip, Saberi, and Stoorvogel (2013), Kim, Shim, and Seo (2011), Lunze (2012) and Wieland, Sepulchre, and Allgöwer (2011). Output synchronization of nonlinear MASs has been investi- gated for over ten years. The research has led to many results in various settings, e.g, for systems of passive dynamics in Chopra and Spong (2008), for homogeneous multi-agent systems with a globally Lipschitz-like assumption and a leader–follower network in Su, Chen, Wang, and Lin (2011) and Yu, Chen, and Cao (2011), ✩ The work was substantially supported by the Australian Research Council under Grant No. DP150103745 and the National Natural Science Foundation of China under Grant No. 51729501. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Hideaki Ishii under the direction of Editor Christos G. Cassandras. E-mail address: zhiyong.chen@newcastle.edu.au. and for second order nonlinear dynamics with agreement on a constant in Zhu and Chen (2014). The early accumulation on the research of output synchroniza- tion problem of nonlinear heterogeneous networked systems has led to a fairly developed two-fold framework in recent years. First, a reference model is designed for each agent and they achieve consensus through a proper collaborative control strategy. Then, a local regulation controller is constructed to drive each agent’s output to the desired trajectory generated by its reference model, see, e.g., Chen and Chen (2016), Huang and Su (2015) and Isidori, Marconi, and Casadei (2014). A more complicated and challenging scenario with output communication setup was studied in Zhu, Chen, and Middleton (2016). The novel techniques in Zhu et al. (2016) form so far the most general framework for synchronization of nonlinear heterogeneous MASs using state feedback but output communication. This paper is concerned with a complete output feedback and output communication setting. On one hand, only the agent output is measurable for designing a local (observer based) regulator; on the other hand, only the agent output is allowed to be transmitted in network to achieve synchronization. In other words, neither non-measurable agent state nor local controller state is allowed to be transmitted in network. In the aforementioned works using the two-step framework, consensus of reference models and local internal model based regulation occur concurrently. Therefore, a small gain condition must be satisfied between the two steps when the setting is on output communication. The detailed formulation of the small gain condition was first proposed in Zhu et al. (2016). https://doi.org/10.1016/j.automatica.2019.02.027 0005-1098/© 2019 Elsevier Ltd. All rights reserved.