Inverse optimal stabilization of cooperative control in networked multi-agent systems

For constructing a decentralized optimal control strategy for networked multi-agent systems that can accomplish consensus in a leaderless structure, we employ the inverse optimal control approach which circumvents the task of solving a HJB equation by introducing a cooperative control Lyapunov function. The decentralized controller we obtain is more flexible than the controller u = Lx in fixed network, because it not only has the advantages to handle systems of high relative degree, but it can also improve the performance of networked multi-agent systems by adjusting a positive definite and symmetrical matrix. On the other hand, the decentralized controller is optimal with respect to a meaningful cost functional which is useful to quantify and improve the performance of networked multi-agent systems. Finally, examples are presented to illustrate both the design process and performance of cooperative controls.