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Decentralized strategies for finite population LQG social control: A reinforcement learning approach
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DOI：10.1016/j.automatica.2026.113239.png)
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Abstract
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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.
Keywords:
Decentralized social control
Reinforcement learning
Finite population
Indefinite weighting matrix
Journal
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5.9
Papers:
1.1W
Citations:
5.2W
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