Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach

Abstract

This paper presents a novel model-free algorithm for the finite-population linear quadratic Gaussian (LQG) decentralized social control problem with multiplicative noise. The state and control weights in the cost functional are not limited to be positive semidefinite. For both finite-horizon and infinite-horizon cases, the goal is to obtain a social optimum by solving two algebraic Riccati equations (AREs), without requiring prior knowledge of the system matrices. Then, we complete the design of a model-free algorithm for solving the decentralized social control problem. Especially, in the infinite-horizon case, the algorithm's convergence is based on analyzing the spectral property of the Lyapunov-type operator. The differences of reinforcement learning (RL) solutions between the finite-horizon and infinite-horizon cases are compared. Finally, the effectiveness of the proposed algorithm is demonstrated by a numerical example.