A Class of Mean-field LQG Games with Partial Information

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of large-population system when studying its dynamic optimizations. Unlike other large-population literature, this current paper possesses the following distinctive features. First, our setting includes the partial information structure of large-population system which is practical from real application standpoint. Specially, two cases of partial information structure are considered here: the partial filtration case (see Section 2, 3) where the available information to agents is the filtration generated by an observable component of underlying Brownian motion; the noisy observation case (Section 4) where the individual agent can access an additive white-noise observation on its own state. Also, it is new in filtering modeling that our sensor function may depend on the state-average. Second, in both cases, the limiting state-averages become random and the filtering equations to individual state should be formalized to get the decentralized strategies. Moreover, it is also new that the limit average of state filters should be analyzed here. This makes our analysis very different to the full information arguments of large-population system. Third, the consistency conditions are equivalent to the wellposedness of some Riccati equations, and do not involve the fixed-point analysis as in other mean-field games. The $\epsilon$-Nash equilibrium properties are also presented.Comment: 19 page

Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731