Mean-Field Control Approach to Decentralized Stochastic Control with Finite-Dimensional Memories
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Decentralized stochastic control (DSC) considers the optimal control problem of a multi-agent system. However, DSC cannot be solved except in the special cases because the estimation among the agents is generally intractable. In this work, we propose memory-limited DSC (ML-DSC), in which each agent compresses the observation history into the finite-dimensional memory. Because this compression simplifies the estimation among the agents, ML-DSC can be solved in more general cases based on the mean-field control theory. We demonstrate ML-DSC in the general LQG problem. Because estimation and control are not clearly separated in the general LQG problem, the Riccati equation is modified to the decentralized Riccati equation, which improves estimation as well as control. Our numerical experiment shows that the decentralized Riccati equation is superior to the conventional Riccati equation.Keywords:
Algebraic Riccati equation
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The optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated. Both the case in which the terminal state is free and that in which the terminal state is constrained to be zero are treated. The integrand of the performance criterion is allowed to be fully quadratic in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem. Frequency-domain and time-domain conditions for the existence of solutions are derived. The algebraic Riccati equation is then examined, and a complete classification of all its solutions is presented. It is finally shown how the optimal control problems introduced in the beginning of the paper may be solved analytically via the algebraic Riccati equation.
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