IFAC PapersOnLine 51-23 (2018) 100–105 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2018.12.018 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 1. INTRODUCTION Recently the consensus approach has been widely applied for solving various practical problems such as cooper- ative control of multivehicle networks Granichin et al. (2012); Ren et al. (2007), distributed control of robotic networks Bullo et al. (2009), flocking problem Yu et al. (2010a); Vir´ agh et al. (2014), optimal control of sensor networks Kar and Moura (2010) and others. A possible way to utilize consensus approach in the task of load balancing in computer, production, transport, logistics, and other service networks is to formulate the problem of load balancing as the consensus achievement among nodes’ loads across the network Amelina et al. (2015a). An inter- esting application is adaptation of airplane’s “feathers” in a turbulence flow Granichin et al. (2017). In works Ren and Beard (2007); Chebotarev and Agaev (2009); Li and Zhang (2009); Yu et al. (2010b); Huang (2012); Proskurnikov (2013); Lewis et al. (2014); Olfati-Saber and Murray (2004) the authors considered the conditions for achieving consensus in multi-agent network systems. Achieveing an optimal performance for the problem of task redistribution in a stochastic network with randomized priorities by choosing an optimal step-size for consensus- type protocol was considered in Amelina et al. (2015b). ⋆ Russian Foundation for Basic Research (projects 16-01-00759 and 18-013-00646\18) The paper proposed a way of choosing step-size for max- imizing convergence precision in the network system with noised information exchange and switching topology. In case of unknown of changing in time parameters it is im- portant to adjust the value of step-size of control protocol to achieve or keep a high level of system performance. In Amelina et al. (2016) the stochastic approximation type algorithm for consensus protocol step-size choice was suggested. In Granichin and Amelina (2015) simultaneous perturbation stochastic approximation (SPSA) is applied for the problem of tracking under influence of disturbances. SPSA type methods allow effective optimization problems solving when it is difficult or impossible to obtain a gradi- ent of the objective function with respect to the parame- ters being optimized Spall (1992); Granichin (1992). In the networks processing tasks with several priority levels to equalize agents’ loads different priority levels should be treated separately. In order to balance the load across the network system via consensus protocol the consensus should be targeted for each class separately since the consensus values of agents’ loads could differ for separate priority levels. This calls for differentiated consensuses problem setting i.e. achieving the consensus for each priority level in the network with tasks of different priorities Amelina et al. (2014a,b). In this paper we give the stochastic approximation type algorithm for local voting protocol step-size choice Keywords: Consensus achievement, Mult-Agent Systems, Stochastic Approximation Abstract: A multi-agent network system of different computing nodes processing tasks of different priority levels is considered. Agents exchange information about their states in presence of noise in communication channels in the system with switching topology. Load balancing problem in the network for each priority level is formulated as differentiated consensuses achievement problem and solved via local voting protocol. The stochastic approximation type algorithm is used to adjust step-size of proposed protocol for each priority level. Simulation example demonstrating step-size adjustment is provided. * Faculty of Mathematics and Mechanics, Saint Petersburg State University 198504, Universitetskii pr. 28, St. Petersburg, Russia, Institute of Problems of Mechanical Engineering, the Russian Academy of Sciences, 199178, Bolshoy pr. 61, V.O., St. Petersburg, Russia (e-mail: natalia amelina@mail.ru, oleg granichin@mail.ru, ivanskiy.yuriy@gmail.com). ** Herzen State Pedagogical University, 191186, Moika Emb. 48, St.Petersburg, Russia) *** Norwegian University of Science and Technology, NO-7491, Trondheim, Norway (e-mail: jiang@item.ntnu.no) Natalia Amelina * Oleg Granichin * Olga Granichina ** Yury Ivanskiy * Yuming Jiang *** Adjustment of Consensus Protocol Step-Size in a Network System with Different Task Priorities via SPSA-like Algorithm under the Cost Constraints ⋆