46,912 research outputs found
State-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions
We consider a control- and state-constrained optimal control problem
governed by a semilinear elliptic equation with nonlocal interface
conditions. These conditions occur during the modeling of diffuse-gray
conductive-radiative heat transfer. The nonlocal radiation interface
condition and the pointwise state-constraints represent the particular
features of this problem. To deal with the state-constraints, continuity of
the state is shown which allows to derive first-order necessary conditions.
Afterwards, we establish second-order sufficient conditions that account for
strongly active sets and ensure local optimality in an -neighborhood
Optimal Control Problems with Switching Points
The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions
First and second order optimality conditions for optimal control problems of state constrained integral equations
This paper deals with optimal control problems of integral equations, with
initial-final and running state constraints. The order of a running state
constraint is defined in the setting of integral dynamics, and we work here
with constraints of arbitrary high orders. First and second-order necessary
conditions of optimality are obtained, as well as second-order sufficient
conditions
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