We investigate team optimal decentralized control of a system with one major and multiple minor agents. The major agent affects the state evolution of the minor agent but not vice-versa. We assume that the major agent perfectly observes its state; the minor agents perfectly observe the state of the major player but observe their local state corrupted by non-Gaussian noise. As far as we are aware, decentralized control of linear quadratic systems with non-Gaussian noise has not been considered in the literature.
Our main result is to show that the optimal strategy has certainty equivalence structure. In particular, the optimal control action at the major player is a linear function of its own state and its estimate of the states of the minor players. The optimal control action at the minor agent is a linear function of the major agent's estimate of the state of all minor agents and the "innovation" of the estimate of its own state based on locally observed data. The corresponding gains are obtained by solving n+1 decoupled Riccati equations. It is worth highlighting that the "innovation" is obtained via non-linear filtering. So the control action is a non-linear function of the observations.
Joint work with Aditya Mahajan
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