| Abstract: |
| In this talk, we present a framework for tackling Stochastic Optimal Control Problems of Extended McKean-Vlasov type, which are characterized by scalar interactions with respect to the laws of the state and control variables.
We employ a continuous-time Lagrangian relaxation that transforms the original extended McKean-Vlasov control problem into a saddle-point problem, where the inner minimization represents a standard stochastic optimal control problem in the physical state space.
We derive a Hamilton-Jacobi-Bellman (HJB) equation on the state space by applying the traditional Bellman principle of optimality, which provides optimality conditions for the control variable.
To tackle the resulting relaxed problem and the associated HJB equation, we resort to gradient-based methods along with semi-implicit partial differential equation solvers.
As a specific application, we focus on the energy sector, particularly on the optimal scheduling of the day-ahead dispatch plan for an aggregated consumer that manages its smart grid.
An innovative, Neural Network-based, Markovian projection is proposed to reduce the dimensionality of the state space by condensing the uncontrolled residual consumption into a single stochastic process. Numerical results validate the framework we presented. |
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