A Parallel Distributed Coordination-by-Constraint Strategy for Multi-agent Networked Systems Francesco Tedesco, Alessandro Casavola, Emanuele Garone Abstract— In this paper a novel parallel distributed super- vision strategy for networked interconnected linear systems is presented. We assume that such systems are locally regulated, possibly dynamically coupled and connected via data links. Pointwise-in-time coordination constraints on the evolutions of relevant system variables are present and need to be en- forced during the overall system evolutions. The paper extends some recent results related to this coordination-by-constraint approach, achieved by resorting to Sequential Distributed Com- mand Governor ideas. This novel parallel distributed strategy is fully described and analyzed and it is compared with earlier sequential strategies in the final example. I. I NTRODUCTION The problem of interest here is the design of distributed supervision strategies based on Feed-forward Command Governor (CG) ideas recently proposed in [1] for large- scale multi-agent systems in situations where the use of a centralized coordination unit might be impracticable. The distributed context is depicted in Figure 1, where the supervisory task is distributed amongst many master agents which are assumed to be able to communicate each other. There, each master station is in charge of supervising and coordinating one specific slave system via a data network. In particular, r i , g i , y i and c i represent respectively: the nominal references, the possibly modified references, the states, the performance-related and the coordination-related outputs of the slave systems. In such a context, the supervision task can be expressed as the requirement of satisfying some tracking performance, viz. y i ≈ r i , whereas the coordination task consists of enforcing some pointwise-in-time constraints c i ∈C i and/or f (c 1 ,c 2 , ....,c N ) ∈C on each slave system and/or on the overall network evolutions. To this end, each i − th supervisor is in charge of modifying the nominal local references r i into the feasible ones g i , when the tracking of the nominal references would produce constraint violations and hence loss of coordination. In this paper, we resort to a recently proposed Feed- Forward CG solution [1] which was shown, at the price of some additional conservativeness, to be able to accomplish the CG task in the absence of an explicit measure or estimate of the state. This is of paramount importance in distributed implementations, because the task of distributing the overall state amongst all master nodes can be difficult or unrealistic in some applications. A. Casavola and F. Tedesco are with the Dipartimento di Elettronica, Informatica e Sistemistica, Universit` a degli Studi della Calabria, Via Pietro Bucci, Cubo 42-c, Rende (CS), 87036, Italy. E. Garone is with Universit´ e Libre de Bruxelles, 50 Av. F.D. Roosvelt, B-1050 Brussels, Belgium {casavola, ftedesco}@deis.unical.it,egarone@ulb.ac.be Fig. 1. Multi-agent architectures In this paper we introduce a new parallel scheme for the distributed reference management of system. The main improvement w.r.t. the sequential one presented in [2] and [3], where only one agent at a time was allowed to update its action while all others were instructed to keep applying the old ones, is that here all agents are allowed to modify their actions simultaneously. As a result, the parallel approach scales better with the system dimension and behaves better in problems with fast changing reference signals than the sequential one, the latter becoming increasingly slower for an increasing number of agents. The main technical expedient behind the derivation of such a scheme is the on-line determination of a suitable Cartesian inner approximation of the global constraint set [4], which allows the agents to optimize independently and simultaneously their reference signals and ensure the fulfilment of the global constraints at the price of a slight loss of optimality. One of the main advantages of such a scheme are the low communication rates required for its implementation, remarkably lower than those pertaining to other distributed approaches -e.g those based on consensus mechanisms. Preliminary results for the development of dis- tributed CG scheme were proposed in [5]. The feasibility and stability properties of the presented approach are analyzed and the coordination of an eight-tank cascaded water system is considered in the final example for assessment. II. SYSTEM DESCRIPTION AND PROBLEM FORMULATION Consider a set of N subsystems A = {1,...,N }, each one being a LTI closed-loop dynamical system regulated by a local controller which ensures stability and good closed- loop properties when the constraints are not active (small- signal regimes when the coordination is effective). Let the 51st IEEE Conference on Decision and Control December 10-13, 2012. Maui, Hawaii, USA 978-1-4673-2064-1/12/$31.00 ©2012 IEEE 284