280 research outputs found
On duality in problems of optimal control described by convex differential inclusions of Goursat–Darboux type
AbstractSufficient conditions of optimality are derived for convex and non-convex problems with state constraints on the basis of the apparatus of locally conjugate mappings. The duality theorem is formulated and the conditions under which the direct and dual problems are connected by the duality relation are searched for
Approximation and optimization of discrete and differential inclusions
[No abstract available]Publisher's Versio
Maximum Principle for Linear-Convex Boundary Control Problems applied to Optimal Investment with Vintage Capital
The paper concerns the study of the Pontryagin Maximum Principle for an
infinite dimensional and infinite horizon boundary control problem for linear
partial differential equations. The optimal control model has already been
studied both in finite and infinite horizon with Dynamic Programming methods in
a series of papers by the same author, or by Faggian and Gozzi. Necessary and
sufficient optimality conditions for open loop controls are established.
Moreover the co-state variable is shown to coincide with the spatial gradient
of the value function evaluated along the trajectory of the system, creating a
parallel between Maximum Principle and Dynamic Programming. The abstract model
applies, as recalled in one of the first sections, to optimal investment with
vintage capital
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 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
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