Decentralised dynamic games for large population stochastic multi‐agent systems

Abstract

In this study, the authors consider the large population dynamic games where each agent evolves according to a dynamic equation containing the input average of all agents. The long time average (LTA) cost that each agent aims to minimise is coupled with other agents' states via a population state average (PSA), which is also known as the mean field term. In order to design decentralised controls, the Nash certainty equivalence is introduced. It is shown that the resulting decentralised mean field control laws lead the system to mean-consensus asymptotically as time goes to infinity. The stability property of the mass behaviour and the almost sure asymptotic Nash equilibrium property of the optimal controls are also guaranteed, and the case with non-linear system dynamics is also discussed. In addition, the influence of inaccurate mean field information on individual agent is analysed. Finally, they investigate the socially cooperative formulation where the objective is to minimise the social cost as the sum of all individual LTA costs containing the PSA. In this case, they show that the decentralised mean field social controls are the same as the mean field Nash controls for infinite population systems.

Nonlinear Sliding Mode Control for Interconnected Systems With Application to Automated Highway Systems

“…From the Definitions 1 and 2 above, it is clear that the decentralized control paradigm for interconnected systems is different from the one adopted for multi-agent systems as the interconnected systems are interconnected through interconnection terms for the case of decentralised control. With a multi-agent system, the systems are interconnected through distributed controls [3], [8].…”

“…A class of complex systems, including multi-machine power systems [1], automated highway systems [2] and multi-agent systems [3], [4], can be modelled as a collection of subsystems with appropriate interconnections [8], [5]. Such classes of systems are called large scale interconnected systems.…”

Finite‐time consensus protocol for stochastic multi‐agent systems

“…Wang et al . [21] proposed an linear matrix inequality (LMI) approach to design a mean square consensus protocol. In [22], a sufficient condition was proposed to ensure the tracking consensus in the mean square sense under both directed and switching topologies.…”

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

“…The main weakness of the mentioned approach is the strong assumption of homogeneity of the agents which leads to the pre-computable behaviour of the mass of the other agents using the Fokker-Planck equation. In [24], a stochastic MFG is applied to a large population of heterogeneous agents, where the PSA is approximated by an iterative method. In [25], a cost coupled mean field LQG game with non-uniform agents is proposed.…”