This seminar is about cooperative control of noncooperative double-integrator
multi-agent systems (MASs) with input delay on connected directed graphs in the
context of a differential graphical game (DGG). In the distributed DGG, each
agent seeks a distributed information control policy by optimizing an
individual
local performance index (PI) of distributed information from its graph
neighbors. The local PI, which quadratically penalizes the agent's deviations
from cooperative behavior (e.g., the consensus here), is constructed through
the
use of the graph Laplacian matrix. For DGGs for double-integrator MASs, the
existing body of literature lacks the explicit characterization of Nash
equilibrium actions and their associated state trajectories with distributed
information. To address this issue, we first convert the N-player DGG with m
communication links into m coupled optimal control problems (OCPs), which, in
turn, convert to the two-point boundary-value problem (TPBVP). We derive the
explicit solutions for the TPBV that constitute the explicit distributed
information expressions for Nash equilibrium actions and the state trajectories
associated with them for the DGG. An illustrative example verifies the explicit
solutions of local information to achieve fully distributed consensus.