Carlo Orrieri — Page 2

arXiv2015

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.

math.PR↗

arXiv2013

A stochastic maximum principle with dissipativity conditions

In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual Lipschitz assumption on the drift term and substitute it with dissipativity conditions, allowing polynomial growth. The control enter both the drift and the diffusion term and takes values in a general metric space.

math.OC↗