Control of Some Linear Equations in a Hilbert Space with Fractional Brownian Motions
نویسنده
چکیده
A linear-quadratic control problem for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is solved. The feedback form of the optimal control and the optimal cost are given. The optimal control is the sum of the well known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction of an optimal system response to the future noise. The covariance of the noise as well as the control operator may in general be unbounded, so the results can also be applied where the noise or the control are on the boundary of the domain or at discrete points in the domain. Some examples of controlled stochastic partial differential equations are given.
منابع مشابه
Semilinear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion
The solutions of a family of semilinear stochastic equations in a Hilbert space with a fractional Brownian motion are investigated. The nonlinear term in these equations has primarily only a growth condition assumption. An arbitrary member of the family of fractional Brownian motions can be used in these equations. Existence and uniqueness for both weak and mild solutions are obtained for some ...
متن کاملLinear-quadratic Control for Stochastic Equations in a Hilbert Space with Fractional Brownian Motions
متن کامل
On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کاملSolving Fuzzy Impulsive Fractional Differential Equations by Reproducing Kernel Hilbert Space Method
The aim of this paper is to use the Reproducing kernel Hilbert Space Method (RKHSM) to solve the linear and nonlinear fuzzy impulsive fractional differential equations. Finding the numerical solutionsof this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provi...
متن کاملSolving multi-order fractional differential equations by reproducing kernel Hilbert space method
In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...
متن کامل