Robust decentralised mean field control in leader following multi-agent systems

This study addresses a robust counterpart of the deterministic mean field control in a multi-agent system. A decentralised mean field algorithm is proposed to solve a min–max control problem for a large population of heterogeneous agents. In the proposed leader following scheme, the leader tracks a reference signal which is unknown to the followers and each follower tracks a convex combination of the population state average and the leader's state. The leader plays a robust min–max game against disturbance and the followers play a mean field ${\varepsilon _N}$εN-Nash game against each other and at the same time, each follower plays a robust min–max game against the disturbance. For all the players, finite horizon quadratic cost is considered. In the proposed decentralised algorithm, followers do not need the knowledge about each of leader's and other followers' states and they only use an estimate of the population state average. In this way, propose a policy iteration method which guarantees the convergence to the saddle point mean field ${\varepsilon _N}$εN-Nash solution. The proposed method is applied to a large population of agents and compared with centralised algorithm to demonstrate the results.