26 research outputs found
Stochastic maximum principle for optimal control of SPDEs
In this note, we give the stochastic maximum principle for optimal control of
stochastic PDEs in the general case (when the control domain need not be convex
and the diffusion coefficient can contain a control variable)
A Maximum Principle for Optimal Control of Stochastic Evolution Equations
A general maximum principle is proved for optimal controls of abstract
semilinear stochastic evolution equations. The control variable, as well as
linear unbounded operators, acts in both drift and diffusion terms, and the
control set need not be convex.Comment: 20 page
Well Posedness of Operator Valued Backward Stochastic Riccati Equations in Infinite Dimensional Spaces
We prove existence and uniqueness of the mild solution of an infinite
dimensional, operator valued, backward stochastic Riccati equation. We exploit
the regularizing properties of the semigroup generated by the unbounded
operator involved in the equation. Then the results will be applied to
characterize the value function and optimal feedback law for a infinite
dimensional, linear quadratic control problem with stochastic coefficients
Stochastic maximum principle for optimal control of a class of nonlinear SPDEs with dissipative drift
We prove a version of the stochastic maximum principle, in the sense of
Pontryagin, for the finite horizon optimal control of a stochastic partial
differential equation driven by an infinite dimensional additive noise. In
particular we treat the case in which the non-linear term is of Nemytskii type,
dissipative and with polynomial growth. The performance functional to be
optimized is fairly general and may depend on point evaluation of the
controlled equation. The results can be applied to a large class of non-linear
parabolic equations such as reaction-diffusion equations
Stochastic maximum principle for SPDEs with delay.
In this paper we develop necessary conditions for optimality, in the form of
the Pontryagin maximum principle, for the optimal control problem of a class of
infinite dimensional evolution equations with delay in the state. In the cost
functional we allow the final cost to depend on the history of the state. To
treat such kind of cost functionals we introduce a new form of anticipated
backward stochastic differential equations which plays the role of dual
equation associated to the control problem
Stochastic Maximum Principle for Optimal Control ofPartial Differential Equations Driven by White Noise
We prove a stochastic maximum principle ofPontryagin's type for the optimal
control of a stochastic partial differential equationdriven by white noise in
the case when the set of control actions is convex. Particular attention is
paid to well-posedness of the adjoint backward stochastic differential equation
and the regularity properties of its solution with values in
infinite-dimensional spaces