Optimal consensus control for double-integrator multi-agent systems with unknown dynamics using adaptive dynamic programming

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.