OPTIMAL CONTROL OF STOCHASTIC SYSTEMS ON HILBERT SPACE N.U.Ahmed
نویسنده
چکیده
This paper is concerned with optimal control of semilinear stochastic evolution equations on Hilbert space driven by stochastic vector measure. Both continuous and discontinuous (measurable) vector fields are admitted. Due to nonexistence of regular solutions, existence and uniqueness of generalized (or measure valued) solutions are proved. Using these results, existence of optimal feedback controls from the class of bounded Borel measurable maps are proved for several interesting optimization problems. Copyright c ©2005 IFAC
منابع مشابه
Hamilton-Jacobi Equation for Optimal Control of Nonlinear Stochastic Distributed Parameter Systems Applied to Air Pollution Process
This paper derives Hamilton-Jacobi equation (HJE) in Hilbert space for optimal control of stochastic distributed parameter systems (SDPSs) governed by partial differential equations (SPDEs) subject to both state-dependent and additive stochastic disturbances. First, nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equ...
متن کاملA class of stochastic optimal control problems in Hilbert spaces: BSDEs and optimal control laws, state constraints, conditioned processes
We consider a nonlinear controlled stochastic evolution equation in a Hilbert space, with a Wiener process affecting the control, assuming Lipschitz conditions on the coefficients. We take a cost functional quadratic in the control term, but otherwise with general coefficients that may even take infinite values. Under a mild finiteness condition, and after appropriate formulation, we prove exis...
متن کاملOptimal Relaxed Controls for Infinite-dimensional Stochastic Systems of Zakai Type∗
In this paper, we present some new results on partially observed control problems for infinitedimensional stochastic systems in Hilbert space using a fundamental result of Da Prato and Zabczyk on an infinitedimensional Kolmogorov operator. We prove the existence of optimal relaxed controls for an infinite-dimensional Zakai equation following a semigroup approach and the theory of measurable sel...
متن کاملOptimal Control of ∞-dimensional Stochastic Systems via Generalized Solutions of Hjb Equations
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude ...
متن کاملErgodic Boundary/point Control of Stochastic Semilinear Systems
A controlled Markov process in a Hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter-dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain. The linear term of the semilinear differential equation is the infinitesimal generator ...
متن کامل