arXiv subjects

Roland Malhamé

Publications and source records attributed to Roland Malhamé.

2 recordsLinked to original sources

arXiv2026

Price-Coordinated Mean Field Games with State Augmentation for Decentralized Battery Charging

This paper addresses the decentralized coordinated charging problem for a large population of battery storage agents (e.g. residential batteries, electrical vehicles, charging station batteries) using Mean Field Game (MFG). Agents are assumed to have affine dynamics and are coupled through a price that is continuous and monotonically increasing with respect to the difference between the average charging power and the grid's desired average charging power. An important modeling feature of the proposed framework is the state augmentation, that is, the charging power is treated as a state variable and its rate of change (i.e. the ramp rate) as the control input. The resulting MFG equilibrium is characterized by two nonlinearly coupled forward-backward differential equations. The existence and uniqueness of the MFG equilibrium is established for any continuous and monotonically increasing nonlinear price function without additional restrictions on the time horizon. Moreover, in the special case where the price is affine in the average charging power, we further simplify the characterization of the MFG equilibrium strategy via two separate Riccati equations, both of which admit unique positive semi-definite solutions without additional assumptions.

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arXiv2025

Social Optimum of a Linear Quadratic Collective Choice Model under Congestion

This paper investigates the social optimum for a dynamic linear quadratic collective choice problem where a group of agents choose among multiple alternatives or destinations. The agents' common objective is to minimize the average cost of the entire population. A naive approach to finding a social optimum for this problem involves solving a number of linear quadratic regulator (LQR) problems that increases exponentially with the population size. By exploiting the problem's symmetries, we first show that one can equivalently solve a number of LQR problems equal to the number of destinations, followed by an optimal transport problem parameterized by the fraction of agents choosing each destination. Then, we further reduce the complexity of the solution search by defining an appropriate system of limiting equations, whose solution is used to obtain a strategy shown to be asymptotically optimal as the number of agents becomes large. The model includes a congestion effect captured by a negative quadratic term in the social cost function, which may cause agents to escape to infinity in finite time. Hence, we identify sufficient conditions, independent of the population size, for the existence of the social optimum. Lastly, we investigate the behavior of the model through numerical simulations in different scenarios.

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