H_∞andH₂control of multi-agent systems with transient performance improvement

Abstract

In this paper, the H ∞ consensus control and H 2 robust control synthesised with transient performance problems are investigated for a group of autonomous agents with linear or linearised dynamics. Based on the relative information between neighbouring agents and a subset of absolute information of the agents, distributed controllers are proposed for both H ∞ and H 2 cases. Compared with the existing protocols, the one presented in this article focuses on improving the transient performance of the consensus problem. By using the tools from matrix analysis and robust control theory, conditions for the existence of controllers to those problems under an undirected communication topology are provided. Then, it is shown that the H 2 performance limit of uncertain systems under a distributed controller equals the minimum H ∞ consensus index synthesised with transient performance of a single agent by using a state feedback controller, independent of the communication topology. Finally, a simulation example as an application in Raptor-90 helicopter is proposed to illustrate the effectiveness of the theoretical results.

Non-fragile H<inf>&#x221E;</inf> consensus of linear multi-agent systems with interval-bounded variations

“…This will reduce the conservativeness of the previous results in [4]- [7], [13] which require c to be larger than a threshold value.…”

“…(3) The issue of robustness with respect to system uncertainties and controller coefficient variations simultaneously is considered. Thus the multi-agent systems under consideration are more general than those in [4]- [7], [13]. The rest of this paper is organized as follows.…”

“…The designed controller is insensitive to additive interval-bounded model coefficient variations and multiplicative controller coefficient variations simultaneously. (2) In contrast to artificial selection methods in [4]- [7], [13], the coupling strength among neighboring agents can be determined by solving some LMI conditions. (3) The issue of robustness with respect to system uncertainties and controller coefficient variations simultaneously is considered.…”

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

“…In the early pioneering works ( ( ), ( )), Vicsek et al proposed a simple model of autonomous agents, and Olfati et al established a framework of consensus control for the first-order integrators with different topologies. Since then, many results have been done under different conditions such as finite-time consensus ( ( ), ( ), ( )), quantized Kashyap et al 2007Carli & Bullo 2009Zhu & Martinez 2011Wang & Slotine 2006Lin & Jia 2011Wen et al 2013bYu et al 2013Hu 2011Chen et al 2014Wen et al 2012Yu et al 2010Li et al 2010Li et al 2013Wang et al 2013Diao et al 2014Mei et al 2011Zhao et al 2014Hong et al 2008 Peng & Yang 2009 Hu 2011 …”

Distributed robust control of uncertain linear multi‐agent systems

“…These call for a distributed consensus protocol supplying H 1 control strategy with good transient performance or assuring H 1 control robustness against initial states uncertainty. In this pursuit, the results in [25] for a single linear system were extended to multiple coupled linear systems in [28], and distributed state-feedback protocols were proposed to improve the transient performance of individual agents. It was shown that such controllers not only stabilize the closed-loop system, reach faster consensus using fewer energy and attenuate the disturbance to the output caused by external signals but also effectively reduce big overshoots and eliminate large oscillations in the transient responses of agents.Motivated by the previous observations, this article investigates the distributed robust control problem, synthesized with transient performance, for multi-agent systems with general linear dynamics subject to norm-bounded parameter uncertainties.…”