Leadership Hierarchy-based Formation Control via Adaptive Chaotic Pigeon-inspired Optimization Jianxia Zhao, Haibin Duan*, Lin Chen, Mengzhen Huo Bio-inspired Autonomous Flight Systems Research Group, School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, 100083, PR CHINA (*e-mail: hbduan@ buaa.edu.cn). Peng Cheng Laboratory, Shenzhen, 518000, PR CHINA. Abstract: Formation control of multi-agent systems (MASs) is a significant research subject in the field of cooperative control. In this paper, we propose a novel consensus-based formation control approach with minimal resource cost and excellent adaptability for second-order nonlinear multi-agent systems. Specifically, an improved constrained adaptive chaotic pigeon- inspired optimization algorithm (ACPIO) is proposed for tuning parameters, which promotes the automation of controller design and alleviates the workload of conventional designer. Moreover, a variant of pinning control method integrating with hierarchical leadership model of pigeon flocks is introduced, which achieves excellent adaptability and reduces computational complexity simultaneously. Additionally, sufficient conditions are derived for achieving the desired formation pattern based on Lyapunov stability theory and matrix theory. Numerical simulation results demonstrate the feasibility and effectiveness of the proposed method for formation control of second-order nonlinear MASs. Keywords: multi-agent systems, formation control, leadership hierarchy, pinning control, improved pigeon-inspired optimization 1. INTRODUCTION The multi-agent systems (MASs) (Li et al. (2004); Zhou et al. (2019)) are composed of multiple interacting intelli- gent agents, generally used to conduct complex tasks coop- eratively within various environments, such as surveillance (Nigam et al. (2011)), source seek (Han and Chen (2014)) and military combat (Cil and Mala (2010)). Formation control is one of the most actively studied topics within the realm of MASs, aiming to drive multiple agents to achieve prescribed constraints on their states. However, this is no easy task due to its sensitivity to external interference and system uncertainty. In order to establish and maintain a certain spatial con- figuration for MASs, a variety of formation control meth- ods have been proposed. Common methods of formation control falls into three strategies: leader-follower, virtual structure and behavior-based strategy. It has been in- dicated these approaches have their own disadvantages though they are applied widely in formation problem (Beard et al. (2001)). For instance, the leader-follower strategy lacks robustness because that the failure of the leader may destroy the whole formation. The virtual struc- ture strategy is not fully distributed. To improve the ro- bustness, Ren (2007) unified these control strategies within the framework of consensus protocol. Since many pinning control methods for MASs have been developed, it would be useful to study the consensus prob- lem. However, existing studies on pinning control achieve a limited success with failure to tie hierarchy relationship with nodes. Encouragingly, Qiu and Duan (2017) proposed a hierarchical leadership strategy that could theoretically construct a hierarchical model with satisfactory adapt- ability. Based on the strategy, the MASs may have the following advantages: information transfers more efficient than other types of networks (Zafeiris and Vicsek (2015)), and agents with certain hierarchical structures can im- prove individual navigation accuracy (Flack et al. (2015)). Therefore, it is worth proposing a variant of pinning con- trol that integrates with hierarchical leadership strategy. However, it is time-consuming to manually adjust param- eters(Hai et al. (2019)). Therefore, establishing an effec- tive mechanism of tuning parameters is necessary. Pigeon- inspired optimization (PIO) algorithm (Duan and Qiao (2014); Zhang and Duan (2015); Duan and Wang (2015)) has proven to be feasible and effective for optimization problems. But there are still some shortcomings. In or- der to improve the population diversity and promote the searching ability for global optima, many efforts have been made (Duan et al. (2018); Xu and Deng (2018); Qiu and Duan (2020)). In this paper, the weight adaptive strategy and chaos theory(Luo and Duan (2014)) are applied in PIO algorithm, namely ACPIO algorithm. To address aforementioned issues, formation control prob- lems of second-order nonlinear MASs are investigated in this paper. Specifically, based on hierarchical leadership, the pinning strategy with optimal control parameters is Preprints of the 21st IFAC World Congress (Virtual) Berlin, Germany, July 12-17, 2020 Copyright lies with the authors 9483