Darcy-type law associated to an optimal control problem.
Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method
In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter ϵ, is studied. In particular, we prove convergence of solutions of penalized control problem to the...
Div-curl Young measures and optimal design in any dimension.
We explicitly introduce and exploit div-curl Young measures to examine optimal design problems governed by a linear state law in divergence form. The cost is allowed to depend explicitly on the gradient of the state. By means of this family of measures, we can formulate a suitable relaxed version of the problem, and, in a subsequent step, put it in a similar form as the original optimal design problem with an appropriate set of designs and generalized state law. Many of the issues involved has been...
Domain optimization in -axisymmetric elliptic problems by dual finite element method
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
Dual extremum principles for a homogeneous Dirichlet problem for a parabolic equation.
Dynamic coverage control design of multi-agent systems under ellipse sensing regions
This paper studies the dynamic coverage control problem for cooperative region reconnaissance where a group of agents are required to reconnoitre a given region. The main challenge of this problem is that the sensing region of each agent is an ellipse. This modeling results in asymmetric(directed) interactions among agents. First, the region reconnaissance is formulated as a coverage problem, where each point in the given region should be surveyed until a preset level is achieved. Then, a coverage...
Dynamic programming for stochastic target problems and geometric flows
Dynamic programming for the stochastic Navier-Stokes equations
Dynamic Programming for the stochastic Navier-Stokes equations
We solve an optimal cost problem for a stochastic Navier-Stokes equation in space dimension 2 by proving existence and uniqueness of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation.