Linear Exponential Quadratic Control for Mean Field Stochastic Systems
- Moon, Jun; Kim, Yoonsoo
- Issue Date
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Optimal control; Stochastic processes; Games; Differential equations; Game theory; Standards; Stochastic systems; Linear exponential quadratic (LEQ) control; LEQ zero sum differential game; mean field stochastic systems
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL, v.64, no.12, pp.5094 - 5100
- Journal Title
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL
- Start Page
- End Page
- In this technical note, we consider linear exponential quadratic (LEQ) control for mean field stochastic differential equations (MFSDEs). The MFSDE includes the expectation value of state and control, and the objective functional is exponential of a quadratic functional in state, control, and their expectations. We obtain the explicit optimal solution as well as the optimal cost. The corresponding optimal solution is linear in state and its expectation, which is characterized by the Riccati differential equations (RDEs). The results are obtained by showing that after applying the completion of squares method, the remaining exponentiated stochastic integral and additional RDE terms can be eliminated together by taking expectation since they constitute the associated Radon-Nikodym derivative. As an extension of the problem, the LEQ zero-sum differential game is considered, for which we obtain the explicit optimal solution (saddle-point equilibrium) as well as the optimal cost.
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- 공학계열 > Division of Mechanical and Aerospace Engineering > Journal Articles
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