Distributed Control with Low-Rank Coordination

Abstract

Abstract-A common approach to distributed control design is to impose sparsity constraints on the controller structure. Such constraints, however, may greatly complicate the control design procedure. This paper puts forward an alternative structure, which is not sparse yet might nevertheless be well suited for distributed control purposes. The structure appears as the optimal solution to a class of coordination problems arising in multi-agent applications. The controller comprises a diagonal (decentralized) part, complemented by a rank-one coordination term. Although this term relies on information about all subsystems, its implementation only requires a simple averaging operation.

Optimal coordination of homogeneous agents subject to delayed information exchange

“…In this section we review the main results of [10], which studies a coordination problem among uncoupled homogeneous systems (agents)…”

“…Yet this approach is not readily scalable if the number of agents grows. Instead, [10] applied a coordinate transformation 1 , which splits problem (2) into a set of uncoupled problems. Using this approach, it was shown that the optimal control law has the following form:…”

“…The problem setup considered in this paper is slightly altered with respect to that studied in [10] (see Section II).…”

“…Recently, we showed that this type of control structure also appears naturally (i.e., without being imposed) as the optimal solution to a class of large-scale linear-quadratic coordination problems [10]. Specifically, we studied a homogeneous group of autonomous agents that are coupled through a constraint on their average behavior.…”

“…A potential limitation of the solution derived in [10], as well as of the earlier examples, is that it assumes immediate information exchange between the agents. This might not be feasible in some applications due to communication constraints.…”