Design of tracking observers for locally jointly observable systems
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RESEARCH ARTICLE
Design of tracking observers for locally jointly observable systems Dabo Xu1 · Xinghu Wang2 · Yiguang Hong3 Received: 7 August 2020 / Revised: 21 September 2020 / Accepted: 21 September 2020 © South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper considers distributed state estimation of continuous-time linear system monitored by a network of multiple sensors. Each sensor can only access locally partial measurement output of the system and effectively communicates with its neighbors to cooperatively achieve the asymptotic estimation of the target full system state. For a constructive design, we shall incorporate the concept of system immersions and propose a class of distributed tracking observers for the problem under a reasonable condition of the locally joint observability. Moreover, as a direct application of the proposed observer design, we further present an interesting leader-following consensus design for multi-agent system. Keywords Observer · Estimation · Distributed control · Immersion · Invariance · Consensus
1 Introduction In the past few decades, there have witnessed tremendous developments in coordination of multi-agent systems from various aspects; see [1, 2]. Particularly, a major effort has been made to develop various distributed control methodologies of managing the fundamental consensus control goal. For example, to our familiarity, one may refer to [3–9] and the relevant references therein for an overview of the studies on leader-following consensus. Meanwhile, to deal with spatially allocated and networked sensors or large-scale systems, the problem of distributed state estimation has also attracted increasing research interest. Different from centralized state estimation [10–12] and decentralized state estimation [13, 14], the emerging * Dabo Xu [email protected] Xinghu Wang [email protected] Yiguang Hong [email protected] 1
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2
Department of Automation, University of Science and Technology of China, Hefei 230027, Anhui, China
3
Key Laboratory of Systems and Control, Chinese Academy of Sciences, Beijing 100190, China
challenge is to achieve the state estimation of a system by a network of multiple sensors by means of distributed network. For example, the authors of [15] proposed a discretetime state augmented observer design based on casting the distributed estimation problem as a decentralized stabilization one. For the observer-based distributed state estimation of continuous-time linear systems, it has gained a variety of interesting developments. For example, the author of [16] proposed some detectability conditions for a linear plant via a network of state estimators. Whereas the authors of [17] proposed a distributed observer with an arbitrary convergence rate. Later, the authors of [18, 19] developed LMIbased distributed observers for both f
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