A liveliness analysis of a distributed constrained coordination strategy for multi-agent linear systems

In this paper we present a complete liveliness analysis for a novel distributed supervision strategy for multi-agent systems connected via data links and subject to coordination constraints. A geometrical Constraints Qualification (CQ) condition on the prescribed constraints is proposed whose fulfilment avoid deadlock situations and ensure viable solutions. Such a coordination paradigm, referred to as coordination-by-constraint, is accomplished by solving on-line in a distributed manner a convex optimization problem involving the modification of the prescribed nominal set-point of each agent. A sequential strategy, where only one agent at the time is allowed to manipulate its own setpoint, is discussed and it is shown that the solvability at each time instant of the underlying optimization problem, unlike the centralized case, can be ensured only if the constraints satisfy such a (CQ) condition, which can be easily checked from the outset via a numerical procedure provided in the paper. An algorithm to compute Constraints Qualified (CD) arbitrarily accurate inner approximations of the original constraint set is also presented and exemplified in final example.