Partial Approximate Controllability for Linear Stochastic Control Systems

Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation

“…In Lemma 3.2, we derive the Malliavin differentiability of the solution to BSPDE h (2.14), i.e., the spatial discretization for BSPDE (2.10). Indeed, the Malliavin differentiability of solution to (2.10) can also be verified; see e.g [12,. Proposition 3.2].…”

Switching controls for linear stochastic differential systems

“…As the development of control theory, controllability problems for stochastic systems drew more and more attention in recent years(see [2,5,7,8,9,10,11,12,13,14,17,20,21,22,23] and the rich references therein). Especially, the controllability problem for linear stochastic differential equations are studied in [2,4,8,14,17,21]. In [17], it is proved that (2) is exact controllable only if the rank of D is n. Moreover, a sufficient condition (in the form of rank condition) for exact controllability of (2) is given in [17].…”

“…Particularly, a rank condition for the approximate controllability of (2) is given in [8]. In [4], a negative result for approximate controllability is given when D = 0. Furthermore, a characterization of the reachable set of (2) when when D = 0 is given in [4].…”

“…In [4], a negative result for approximate controllability is given when D = 0. Furthermore, a characterization of the reachable set of (2) when when D = 0 is given in [4].…”

“…However, whether one can find some weaker conditions to get the null/approximate controllability of ( 1) is unknown. In fact, according to some recent results in [4], the null/approximate controllability problem for stochastic differential equations is much more complex than the exact controllability problem.…”