The purpose of this paper is to utilize adaptive dynamic programming to
solve an optimal consensus problem for double-integrator multi-agent
systems with completely unknown dynamics. In double-integrator
multi-agent systems, flocking algorithms that neglect agents' inertial
effect can cause unstable group behavior. Despite the fact that an
inertias-independent protocol exists, the design of its control law is
decided by dynamics and inertia. However, inertia in reality is
difficult to measure accurately, therefore, the control gain in the
consensus protocol was solved by developing adaptive dynamic programming
to enable the double-integrator systems to ensure the consensus of the
agents in the presence of entirely unknown dynamics. Firstly, we
demonstrate in a typical example how flocking algorithms that ignore the
inertial effect of agents can lead to unstable group behavior. And even
though the protocol is independent of inertia, the control gain depends
quite strongly on the inertia and dynamic of the agent. Then, to address
these shortcomings, an online policy iteration-based adaptive dynamic
programming is designed to tackle the challenge of double-integrator
multi-agent systems without dynamics. Finally, simulation results are
shown to prove how effective the proposed approach is.