Cooperative Systems Under Communication Delay

Abstract

In this paper, dynamic feasibility of a finite set of distributed systems to engage in a formation is investigated. When system design capabilities such as state and input constraints are given, formation options may be limited due to modeling errors, exogenous inputs and initial condition uncertainties. These underlying factors in turn affect the feasibility of interconnections, which are the design variables used to synthesize a formation. In leader-follower framework, it is shown that, in some cases, the communication delay has a favorable effect on the feasibility of interconnections. That is, analogous to the computational time delay used to phase stabilize a dynamical system, the communication delay converts infeasible interconnections into feasible and increases formation options. A mobile robot example is provided for illustration. Aggressive maneuvers in control of distributed systems (DS) are anticipated when DS are instructed to follow higher-level policies and perform a certain cooperative control operation. These instructions are typically static decisions based on factors such as obstacle avoidance, geographical constraints, system capabilities and targetthreat distributions. The dynamic interaction of these same factors may force the DS to perform complex maneuvers to meet mission constraints. In such operations, it is important to consider the system capabilities resulting from design constraints. The subject of dynamic feasibility considers input and state constraints (or any other design constraints) of the DS and develops a methodology to determine whether or not a particular system is maneuverable subject to its uncertain initial conditions.