Consensus with quantized relative state measurements

Chen

Intl J Robust & Nonlinear

et al. 2017

Summary In this paper, an output‐feedback adaptive consensus tracking control scheme is proposed for a class of high‐order nonlinear multi‐agent systems. The agents are allowed to have unknown parameters, unknown nonlinearities, and input quantization simultaneously. The desired trajectory to be tracked is available for only a subset of agents, and only the relative outputs and the quantized inputs need to be measured or transmitted as signal exchange among neighbors regardless of the system order. By introducing a kind of high‐gain K‐filters and a smooth function, the effect among agents caused by the unknown nonlinearities is successfully counteracted, and all closed‐loop signals are proved to be globally uniformly bounded. Moreover, it is shown that the tracking errors converge to a residual set that can be made arbitrarily small. Simulation results on robot manipulators are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.

Section: Introductionmentioning

confidence: 99%

Output‐feedback adaptive consensus tracking control for a class of high‐order nonlinear multi‐agent systems

Chen

Intl J Robust & Nonlinear

et al. 2017

“…The poor perfomance of the dynamics in terms of approaching consensus explains the scarcity 1 of known results about (2). Instead, papers like [12,22,20,25,29] have considered other possible quantizations of (1): in [12,22] all states are quantized in the right-hand side, while in [20,25] distances between couples of states are seen through the quantizer. In these papers convergence to consensus is proved under appropriate but generally mild assumptions [38].…”

mentioning

confidence: 99%

Consensus and Disagreement: The Role of Quantized Behaviors in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

SIAM J. Control Optim.

Abstract. This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous and thus their solutions must be intended in some generalized sense: in our analysis, we consider both Carathéodory and Krasovskii solutions. We first prove existence and completeness of Carathéodory solutions from every initial condition and we highlight a pathological behavior of Carathéodory solutions, which can converge to points that are not (Carathéodory) equilibria. Notably, such points can be arbitrarily far from consensus and indeed simulations show that convergence to non-consensus configurations is common. In order to cope with these pathological attractors, we study Krasovskii solutions. We give an estimate of the asymptotic distance of all Krasovskii solutions from consensus and we prove its tightness by an example of equilibrium such that this distance is quadratic in the number of agents. This fact implies that quantization can drastically destroy consensus. However, consensus is guaranteed in some special cases, for instance when the communication among the individuals is described by either a complete or a complete bipartite graph.

“…Consensus means that a team of subsystems reaches an agreement on a common value by interacting with their local neighbors. Due to its potential applications in several areas such as spacecraft formation flying, sensor networks, and cooperative surveillance (Ren, Beard, & Atkins, 2007), the consensus control problem has been addressed by many researchers from various perspectives; see Antonelli (2013), Guo and Dimarogonas (2013), Hong, Chen, and Bushnell (2008), Olfati-Saber and Murray (2004), Ren and Beard (2005), Ren et al (2007), Zhang, Lewis, and Qu (2012) and references therein. Existing consensus algorithms can be roughly categorized into two classes, namely, consensus without a leader (i.e., leaderless consensus) and consensus with a leader which is also called leader-follower consensus or distributed tracking.…”

Section: Introductionmentioning

confidence: 99%

Distributed adaptive consensus and output tracking of unknown linear systems on directed graphs

Ding

2015

Automatica

a b s t r a c tThis paper considers both the distributed consensus control and output tracking problems of a group of unknown linear subsystems using the relative output information of neighboring subsystems. Each system is a minimum-phase SISO system with relative degree one and unknown parameters, and the interaction graph among the subsystems is directed. For the case where the directed graph is strongly connected, a distributed adaptive protocol is designed to achieve consensus. For the case where there exists an arbitrary constant reference signal, a distributed adaptive controller together with an internal model are presented to achieve output tracking in the sense that the subsystem outputs asymptotically follow a reference constant. The proposed adaptive protocols are independent of the parameters of the subsystems, only use the relative outputs of neighboring subsystems, and hence are fully distributed.