Ergodic Boundary/point Control of Stochastic Semilinear Systems
نویسنده
چکیده
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 of an analytic semigroup. The noise for the stochastic differential equation can be distributed, boundary and point. Some ergodic properties of the controlled Markov process are shown to be uniform in the control and the parameter. The existence of an optimal control is verified to solve the ergodic control problem. The optimal cost is shown to depend continuously on the system parameter.
منابع مشابه
Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کاملErgodic Control of Semilinear Stochastic Equations and Hamilton-jacobi Equations
In this paper we consider optimal control of stochastic semilinear equations with linearly increasing drift and cylindrical noise. We show existence and uniqueness (up to an additive constant) of solutions to the stationary Hamilton-Jacobi equation associated with the cost functional given by the asymptotic average per unit time cost. As a consequence we nd the optimizing controls given in the ...
متن کاملApproximate controllability of abstract semilinear stochastic control systems with nonlocal conditions
Abstract: This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approxi...
متن کاملComplete Controllability of Semilinear Stochastic Systems with Delay in Both State and Control
This paper deals with the complete controllability of semilinear stochastic systems with delay in both state and control under the assumption that the corresponding linear system is completely controllable. The control function for this system is suitably constructed by using the controllability operator. With this control function, the sufficient conditions for the complete controllability of ...
متن کاملThe Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations∗
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2. In Part 1, we prove...
متن کامل