12 research outputs found
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
Optimal control for the stochastic fitzhugh-nagumo model with recovery variable
In the present paper we derive the existence and uniqueness of the solution for the optimal control problem governed by the stochastic FitzHugh-Nagumo equation with recovery variable. Since the drift coefficient is characterized by a cubic non-linearity, standard techniques cannot be applied, instead we exploit the Ekeland\u2019s variational principle
Optimal distributed control of a stochastic Cahn-Hilliard equation
We study an optimal distributed control problem associated to a stochastic
Cahn-Hilliard equation with a classical double-well potential and Wiener
multiplicative noise, where the control is represented by a source-term in the
definition of the chemical potential. By means of probabilistic and analytical
compactness arguments, existence of an optimal control is proved. Then the
linearized system and the corresponding backward adjoint system are analysed
through monotonicity and compactness arguments, and first-order necessary
conditions for optimality are proved.Comment: Key words and phrases: stochastic Cahn-Hilliard equation, phase
separation, optimal control, linearized state system, adjoint state system,
first-order optimality condition
Stochastic maximum principle for SPDEs with delay.
In this paper we develop necessary conditions for optimality, in the form of
the Pontryagin maximum principle, for the optimal control problem of a class of
infinite dimensional evolution equations with delay in the state. In the cost
functional we allow the final cost to depend on the history of the state. To
treat such kind of cost functionals we introduce a new form of anticipated
backward stochastic differential equations which plays the role of dual
equation associated to the control problem
Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation
A Cahn-Hilliard equation with stochastic multiplicative noise and a random
convection term is considered. The model describes isothermal phase-separation
occurring in a moving fluid, and accounts for the randomness appearing at the
microscopic level both in the phase-separation itself and in the flow-inducing
process. The call for a random component in the convection term stems naturally
from applications, as the fluid's stirring procedure is usually caused by
mechanical or magnetic devices. Well-posedness of the state system is addressed
and optimisation of a standard tracking type cost with respect to the velocity
control is then studied. Existence of optimal controls is proved and the
G\^ateaux-Fr\'echet differentiability of the control-to-state map is shown.
Lastly, the corresponding adjoint backward problem is analysed, and first-order
necessary conditions for optimality are derived in terms of a variational
inequality involving the intrinsic adjoint variables.Comment: 38 page
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 infinitedimensional additive noise. In particular, we treat the case in which the nonlinear 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 nonlinear parabolic equations such as reaction-diffusion equations