In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze via value function. Due to non-smoothness $L^0$ cost functional, in general, function is not differentiable domain. Then, characterize as viscosity solution associated Hamilton-Jacobi-Bellman (HJB) equation. Based on result, derive necessary suffici...

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic filtering and statistics demonstrate the practical relevance of our result.

The purpose of this paper is twofold: i) to introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistics, or information state, in the optimal control of stochastic systems and ii) to apply certain Lie algebraic methods and gauge transformations, widely used in nonlinear control theory and quantum physics, to derive new results concerning finite-dime...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...

Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give th...

In this talk, I will first motivate and describe the master equation introduced in large population stochastic control, which is a PDE written on the Wasserstein space. In particular, I will recall the probabilistic representation of its solution in term of a (fully coupled) FBSDE with McKean-Vlasov interaction. I will then introduce a scheme for this class of BSDEs and demonstrate its converge...

We consider the problem of communication over a discrete memoryless multiple access channel (DM-MAC) with noiseless feedback. A single-letter characterization of the capacity of this channel is not currently known. Several inner and outer bounds exist in the literature that provide expressions involving a number of auxiliary variables. In this paper we formulate the MAC with feedback capacity p...