Ergodic Boundary/Point Control of Stochastic Semilinear Systems

Ergodic 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 ...

Ergodic 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 ...

Approximation of a Stochastic Ergodic Control Problem

We study a degenerate non linear optimal stochastic control problem of ergodic type. We rst prove that for each feedback control law, there exists a unique invariant measure which is equivalent to Lebesgue measure. This is proved using an accessibility property of the stochastic diierential equation, after the discontinuous part of the drift has been removed via a change of probability measure....

Controllability of semilinear stochastic integrodifferential systems

Approximate Controllability of Delayed Semilinear Control Systems

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations ẏ(t) =Ay(t) +A1y(t−∆) +F(t, y(t), yt) + (Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate cont...